Assessment and Future Directions of Nonlinear Model Predictive Control

Model Predictive Control (MPC) originated in the late seventies and has developed considerably since then. The term Model Predictive Control does not designate a specific control strategy but rather an ample range of control methods which make explicit use of a model of the process to obtain the control signal by minimizing an objective function. The ideas, appearing in greater or lesser degree in the predictive control family, are basically the explicit use of a model to predict the process output at future time instants (horizon), the calculation of a control sequence minimizing an objective function and the use of a receding strategy, so that at each instant the horizon is displaced towards the future, which involves the application of the first control signal of the sequence calculated at each step.

The robustness of asymptotic stability with respect to measurement noise for discrete-time feedback control systems is discussed. It is observed that, when attempting to achieve obstacle avoidance or regulation to a disconnected set of points for a continuous-time system using sample and hold state feedback, the noise robustness margin necessarily vanishes with the sampling period. With this in mind, we propose two modifications to standard model predictive control (MPC) to enhance robustness to measurement noise. The modifications involve the addition of dynamical states that make large jumps. Thus, they have a hybrid flavor. The proposed algorithms are well suited for the situation where one wants to use a control algorithm that responds quickly to large changes in operating conditions and is not easily confused by moderately large measurement noise and similar disturbances.

This paper is devoted to the stabilization problem of nonlinear continuous- time systems with piecewise constant control functions. The controller is to be computed by the receding horizon control method based on discrete-time approximate models. Multi-rate — multistep control is considered and both measurement and computational delays are allowed. It is shown that the same family of controllers that stabilizes the approximate discrete-time model also practically stabilizes the exact discrete-time model of the plant. The conditions are formulated in terms of the original continuoustime models and the design parameters so that they should be veri.able in advance.

We present an overview of our results on stabilizing scheduled output feedback Model Predictive Control (MPC) algorithm for constrained nonlinear systems based on our previous publications [

19

,

20

]. Scheduled MPC provides an important alternative to conventional nonlinear MPC formulations and this paper addresses the issues involved in its implementation and analysis, within the context of the NMPC05 workshop. The basic formulation involves the design of a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which on-line switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. This algorithm provides a general framework for scheduled output feedback MPC design.

This paper first introduces several interpolation schemes, which have been derived for the linear time invariant case, but with an underlying objective of trading off performance for online computational simplicity. It is then shown how these can be extended to linear parameter varying systems, with a relatively small increase in the online computational requirements. Some illustrations are followed with a brief discussion on areas of potential development.

This paper presents a review of recent contributions that unite predictive control approaches with Lyapunov-based control approaches at the implementation level (Hybrid predictive control) and at the design level (Lyapunov-based predictive control) in a way that allows for an explicit characterization of the set of initial conditions starting from where closed-loop stability is guaranteed in the presence of constraints.

This paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with model predictive controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and input-to-state stability (ISS), while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear. For a particular class of discontinuous piecewise affine systems, a new MPC set-up based on infinity norms is proposed, which is proven to be ISS to bounded additive disturbances. This ISS result does not require continuity of the system dynamics nor of the MPC value function.

The topic of this paper is a new model predictive control (MPC) approach for the sampled-data implementation of continuous-time stabilizing feedback laws. The given continuous-time feedback controller is used to generate a reference trajectory which we track numerically using a sampled-data controller via an MPC strategy. Here our goal is to minimize the mismatch between the reference solution and the trajectory under control. We summarize the necessary theoretical results, discuss several aspects of the numerical implemenation and illustrate the algorithm by an example.

We describe here a sampled-data Model Predictive Control framework that uses continuous-time models but the sampling of the actual state of the plant as well as the computation of the control laws, are carried out at discrete instants of time. This framework can address a very large class of systems, nonlinear, time-varying, and nonholonomic.

As in many others sampled-data Model Predictive Control schemes, Barbalat’s lemma has an important role in the proof of nominal stability results. It is argued that the generalization of Barbalat’s lemma, described here, can have also a similar role in the proof of robust stability results, allowing also to address a very general class of nonlinear, time-varying, nonholonomic systems, subject to disturbances. The possibility of the framework to accommodate discontinuous feedbacks is essential to achieve both nominal stability and robust stability for such general classes of systems.

In this paper, an alternative approach to the computation of control invariant sets for piecewise affine systems is presented. Based on two approximation operators, two algorithms that provide outer and inner approximations of the maximal robust control invariant set are presented. These algorithms can be used to obtain a robust control invariant set for the system. An illustrative example is presented.

In many practical situations in process industry, the measurements of process quality variables, such as product concentrations, are available at different sampling rates and than other measured variables and also at irregular sampling intervals. Thus, from the process control viewpoint, multi-rate systems in which measurements are available at slow and/or differing rates and in which the manipulations are updated at relatively fast rate are of particular interest.

This paper presents a novel approach for nonlinear model predictive control based on the concept of passivity. The proposed nonlinear model predictive control scheme is inspired by the relationship between optimal control and passivity as well as by the relationship between optimal control and model predictive control. In particular, a passivity-based state constraint is used to obtain a nonlinear model predictive control scheme with guaranteed closed loop stability. Since passivity and stability are closely related, the proposed approach can be seen as an alternative to control Lyapunov function based approaches. To demonstrate its applicability, the passivity-based nonlinear model predictive control scheme is applied to control a quadruple tank system.

The paper reports on recent progress in the real-time computation of constrained closed-loop optimal control, in particular the special case of nonlinear model predictive control, of large di.erential algebraic equations (DAE) systems arising e.g. from a MoL discretization of instationary PDE. Through a combination of a direct multiple shooting approach and an initial value embedding, a so-called “real-time iteration” approach has been developed in the last few years. One of the basic features is that in each iteration of the optimization process, new process data are being used. Through precomputation – as far as possible – of Hessian, gradients and QP factorizations the response time to perturbations of states and system parameters is minimized. We present and discuss new real-time algorithms for fast feasibility and optimality improvement that do not need to evaluate Jacobians online.

It has recently been shown that the feedback solution to linear and quadratic constrained Model Predictive Control (MPC) problems has an explicit representation as a piecewise linear (PWL) state feedback. For nonlinear MPC the prospects of explicit solutions are even higher than for linear MPC, since the benefits of computational efficiency and verifiability are even more important. Preliminary studies on approximate explicit PWL solutions of convex nonlinear MPC problems, based on multi-parametric Nonlinear Programming (mp-NLP) ideas show that sub-optimal PWL controllers of practical complexity can indeed be computed off-line. However, for non-convex problems there is a need to investigate practical computational methods that not necessarily lead to guaranteed properties, but when combined with verification and analysis methods will give a practical tool for development and implementation of explicit NMPC. The present paper focuses on the development of such methods. As a case study, the application of the developed approaches to compressor surge control is considered.

The benefits of parametric programming for the design of optimal controllers for constrained systems are widely acknowledged, especially for the case of linear systems. In this work we attempt to exploit these benefits and further extend the theoretical contributions to multi-parametric Model Predictive Control (mp-MPC) for non-linear systems with state and input constraints. The aim is to provide an insight and understanding of multi-parametric control and its benefits for non-linear systems and outline key issues for ongoing research work.

In this contribution we present two interior-point path-following algorithms that solve the convex optimisation problem that arises in recentred barrier function model predictive control (MPC), which includes standard MPC as a limiting case. However the optimisation problem that arises in nonlinear MPC may not be convex. In this case we propose sequential convex programming (SCP) as an alternative to sequential quadratic programming. The algorithms are appropriate for the convex program that arises at each iteration of such an SCP.

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm that uses hard variable constraints to allow for control objective prioritization. Traditional prioritized objective approaches can require the solution of a complex mixed-integer program. The formulation presented in this work relies on the feasibility and solution of a relatively small logical sequence of purely continuous nonlinear programs (NLP). The proposed solution method for accomodation of discrete control objectives is equivalent to solution of the overall mixed-integer nonlinear programming problem. The performance of the algorithm is demonstrated on a simulated multivariable network of air pressure tanks.

Model predictive control (MPC) has been a field with considerable research efforts and significant improvements in the algorithms. This has led to a fairly large number of successful industrial applications. However, many small and medium enterprises have not embraced MPC, even though their processes may potentially benefit from this control technology. We tackle one aspect of this issue with the development of a nonlinear model predictive control package NEWCON that will be released as free software. The work details the conceptual design, the control problem formulation and the implementation aspects of the code. A possible application is illustrated with an example of the level and reactor temperature control of a simulated CSTR. Finally, the article outlines future development directions of the NEWCON package.

In view of the widespread success of Model Predictive Control

(MPC)

, in recent years attention has been paid to its robustness characteristics, either by examining the robustness properties inherent to stabilizing

MPC

algorithms, or by developing new

MPC

methods with enhanced robustness properties.

Stochastic uncertainty is present in many control engineering problems, and is also present in a wider class of applications, such as finance and sustainable development. We propose a receding horizon strategy for systems with multiplicative stochastic uncertainty in the dynamic map between plant inputs and outputs. The cost and constraints are defined using probabilistic bounds. Terminal constraints are defined in a probabilistic framework, and guarantees of closed-loop convergence and recursive feasibility of the online optimization problem are obtained. The proposed strategy is compared with alternative problem formulations in simulation examples.

Markov chain Monte Carlo methods can be used to make optimal decisions in very complex situations in which stochastic effects are prominent. We argue that these methods can be viewed as providing a class of nonlinear MPC methods. We discuss decision taking by maximising expected utility, and give an extension which allows constraints to be respected. We give a brief account of an application to air traffic control, and point out some other problem areas which appear to be very amenable to solution by the same approach.

This paper addresses the disturbance attenuation problem in nonlinear moving horizon control. Conceptually a minimax formulation with a general dissipation constraint is suggested and theoretical results on closed-loop dissipation, L

2

disturbance attenuation and stability are discussed. The implementation issue is attacked with respect to tracking a reference trajectory in the presence of external disturbances and control constraints, and a computationally tractable algorithm is given in the framework of LMI optimization. Simulation and comparisons of setpoint tracking control of a CSTR are presented.

A novel robust controller, chance constrained nonlinear MPC, is presented. Time-dependent uncertain variables are considered and described with piecewise stochastic variables over the prediction horizon. Restrictions are satisfied with a user-defined probability level. To compute the probability and its derivatives of satisfying process restrictions, the inverse mapping approach is extended to dynamic chance constrained optimization cases. A step of probability maximization is used to address the feasibility problem. A mixing process with both an uncertain inflow rate and an uncertain feed concentration is investigated to demonstrate the effectiveness of the proposed control strategy.

In this work, two methods based on a nonlinear MPC scheme are proposed to solve close-loop stochastic dynamic optimization problems assuring both robustness and feasibility with respect to output constraints. The main concept lies in the consideration of unknown and unexpected disturbances in advance. The first one is a novel

deterministic

approach based on the

wait-and-see

strategy. The key idea is here to anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a new

stochastic

approach to solving nonlinear chance-constrained dynamic optimization problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation

(here-and-now

strategy). The approach considers a

nonlinear

relation between the uncertain input and the constrained output variables.

This paper shows how interval arithmetic can be used to design stabilizing robust MPC controllers. Interval arithmetic provides a suitable framework to obtain a tractable procedure to calculate an outer bound of the range of a given nonlinear function. This can be used to calculate a guaranteed outer bound on the predicted sequence of reachable sets. This allows us to consider the effect of the uncertainties in the prediction and to formulate robust dual-mode MPC controllers with ensured admissibility and convergence. Interval arithmetic can also be used to estimate the state when only outputs are measurable. This method provides a guaranteed outer bound on the set of states consistent with the output measurements. Generalizing the controllers based on reachable sets, a novel robust output feedback MPC controller is also proposed.

A problem of synthesis of optimal measurement feedbacks for dynamical systems under uncertainty is under consideration. An online control scheme providing a guaranteed result under the worst-case conditions is described.

In dynamical processes states are only partly accessible by measurements. Most quantities must be determined via model based state estimation. Since in general only noisy data are given, this yields an ill-posed inverse problem. Observability guarantees a unique least squares solution. Well-posedness and observability are qualitative behaviours. The quantitative behaviour can be described using the concept of condition numbers, which we use to introduce an observability measure. For the linear case we show the connection to the well known observability Gramian. For state estimation regularization techniques concerning the initial data are commonly applied in addition. However, we show that the least squares formulation is well-posed, avoids otherwise possibly occuring bias and that the introduced observability measure gives a lower bound on the conditioning of this problem formulation.

State estimation is addressed for a class of discrete-time systems that may switch among different modes taken from a finite set. The system and measurement equations of each mode are assumed to be linear and perfectly known, but the current mode of the system is unknown and is regarded as a discrete state to be estimated at each time instant together with the continuous state vector. A new computationally efficient method for the estimation of the system mode according to a minimum-distance criterion is proposed. The estimate of the continuous state is obtained according to a receding-horizon approach by minimizing a quadratic least-squares cost function. In the presence of bounded noises and under suitable observability conditions, an explicit exponentially converging sequence provides an upper bound on the estimation error. Simulation results confirm the effectiveness of the proposed approach.

We introduce stochastic differential algebraic equations for physical modelling of equilibrium based process systems and present a continuous-discrete paradigm for filtering and prediction in such systems. This paradigm is ideally suited for state estimation in nonlinear predictive control as it allows systematic decomposition of the model into predictable and non-predictable dynamics. Rigorous filtering and prediction of the continuous-discrete stochastic differential algebraic system requires solution of Kolmogorov’s forward equation. For non-trivial models, this is mathematically intractable. Instead, a suboptimal approximation for the filtering and prediction problem is presented. This approximation is a modified extended Kaiman filter for continuous-discrete systems. The modified extended Kaiman filter for continuous-discrete differential algebraic systems is implemented numerically efficient by application of an ESDIRK algorithm for simultaneous integration of the mean-covariance pair in the extended Kaiman filter [

1

,

2

]. The proposed method requires approximately two orders of magnitude less floating point operations than implementations using standard software. Numerical robustness maintaining symmetry and positive semi-definiteness of the involved covariance matrices is assured by propagation of the matrix square root of these covariances rather than the covariance matrices themselves.

Nonlinear model predictive controllers (NLMPC) using fundamental dynamic models and online nonlinear optimization have been in service in ExxonMobil Chemical since 1994. The NLMPC algorithm used in this work employs a state space formulation, a finite prediction horizon, a performance specification in terms of desired closed loop response characteristics for the outputs, and costs on incremental manipulated variable action. The controller can utilize fundamental or empirical models. The simulation and optimization problems are solved simultaneously using sequential quadratic programming (SQP). In the paper, we present results illustrating regulatory and grade transition (servo) control by NLMPC on several industrial polymerization processes. The paper outlines the NLMPC technology employed, describes the current status in industry for extending linear model predictive control to nonlinear processes or applying NLMPC directly, and identifies several needs for improvements to components of NLMPC.

This paper discusses the implementation of nonlinear model predictive control on continuous industrial polymer manufacturing processes. Two examples of such processes serve to highlight many of the practical issues faced and the technological solutions that have been adopted. An outline is given of the various phases of deploying such a solution, and this serves as a framework for describing the relevant modeling choices, controller structures, controller tuning, and other practical issues

Advanced model based control is a promising technology that can improve the productivity of industrial processes. In order to find its way into regular applications, advanced control must be integrated with the industrial control systems. Modern control systems, on the other hand, need to extend the reach of traditional automation systems—beyond control of the process—to also cover the increasing amount of information technology (IT) required to successfully operate industrial processes in today’s business markets. The Industrial IT System 800xA from ABB provides a scalable solution that spans and integrates loop, unit, area, plant, and interplant controls.

We will in this paper highlight our experience with NMPC. In our context NMPC shall mean the use of a nonlinear mechanistic model, state estimation, and the solution of an online constrained nonlinear optimisation problem. Our reference base is a number of applications of NMPC in a variety of processes.

This paper summarizes recent developments and applications of dynamic real-time optimization (D-RTO). A decomposition strategy is presented to separate economical and control objectives by formulating two subproblems in closed-loop. Two approaches (model-based and model-free at the implementation level) are developed to provide tight integration of economical optimization and control, and to handle uncertainty. Simulated industrial applications involving different dynamic operational scenarios demonstrate significant economical benefits.

A number of plants of technological interest include transport phenomena in which mass, or energy, or both, flow along one space dimension, with or without reactions taking place, but with neglected dispersion. This type of processes are described by hyperbolic partial differential equations [

4

] and is receiving an increasing attention in what concerns the application of Predictive Control [

6

]. Two examples considered are distributed collector solar fields [

3

,

10

] and tubular bioreactors [

5

]. In both cases the manipulated variable is assumed to be the flow. For lack of space, only the first example is considered hereafter.

A minimum-time optimal recharging control strategy for high pressure gas storage tank systems is described in this work. The goal of the nonlinear model-based controller is to refill the tank in minimum time with a two-component gas mixture of specified composition subject to hard constraints on the component flow rates, tank temperature, and tank pressure. The nonlinearity in this system arises from the non-ideal behavior of the gas at high pressure. The singular minimum-time optimal control law can not be reliably implemented in the target application due to a lack of sensors. Minimum-time optimal control is therefore approximated by a nonlinear model-based constraint controller. In order to account for the uncertainty in the unmeasured state of the storage tank, the state sensitivities to the control and process measurements are propagated along with the state to obtain a state variance estimate. When the variance of the state exceeds a maximum threshold, the constraint control algorithm automatically degrades into a fail-safe operation.

A nonlinear model predictive control (NMPC) formulation is used to prevent an exothermic fed-batch chemical reactor from thermal runaways even in the case of total cooling failure. Detailed modeling of the reaction kinetics and insight into the process dynamics led to the formulation of a suitable optimization problem with safety constraints which is then successively solved within the NMPC scheme. Although NMPC control-loops can exhibit a certain degree of inherent robustness, an explicit consideration of process uncertainties is preferable not only for safety reasons. This is approached by reformulating the open-loop optimization problem as a min-max problem. This corresponds to a worst-case approach and leads to even more cautious control moves of the NMPC in the presence of uncertain process parameters. All results are demonstrated in simulations for the esterification process of 2-butyl.

The application of nonlinear model predictive control (NMPC) for the temperature control of an industrial batch polymerization reactor is illustrated. A real-time formulation of the NMPC that takes computational delay into account and uses an efficient multiple shooting algorithm for on-line optimization problem is described. The control relevant model used in the NMPC is derived from the complex first-principles model and is fitted to the experimental data using maximum likelihood estimation. A parameter adaptive extended Kaiman filter (PAEKF) is used for state estimation and on-line model adaptation. The performance of the NMPC implementation is assessed via simulation and experimental studies.

In recent years, continuous Chromatographic processes have been established as an efficient separation technology in industry, especially when temperature sensitive components or species with similar thermodynamic properties are involved. In SMB processes, a counter-current movement of the liquid and the solid phases is achieved by periodically switching the inlet and the outlet ports in a closed loop of Chromatographic columns. The integration of reaction and separation in one single plant is a promising approach to overcome chemical or thermodynamic equilibria and to increase process efficiency. Reactive Chromatographie SMB processes in which the columns are packed with catalyst and adsorbent have been proposed and demonstrated successfully. However, a full integration often is not efficient because in the columns in the separating zones, the catalyst is not used or even counterproductive. By placing reactors between the separation columns at specific positions around the feed port, a more efficient process, the Hashimoto SMB process, is established. In this contribution, a non-linear predictive control concept for the Hashimoto SMB process is presented. The controller computes optimal control variables (flow rates and the switching time) to optimize an economic objective over a moving horizon. The purity requirements of the product streams are implemented as constraints and not as controlled variables. The optimization-based controller is combined with a scheme to estimate selected model parameters in order to reduce the influence of the inevitable model errors. Simulative results are presented for the example of the racemization of Tröger’s base.

This paper focuses on the design of a nonlinear model predictive control (NMPC) scheme for a cement grinding circuit, i.e., a ball mill in closed loop with an air classifier. The multivariable controller uses two mass fractions as controlled variables, and the input flow rate and the classifier selectivity as manipulated variables. As the particle size distribution inside the mill is not directly measurable, a receding-horizon observer is designed, using measurements at the mill exit only. The performance of the control scheme in the face of measurement errors and plant-model mismatches is investigated in simulation.

Plant-wide control is attracting considerable interest, both as a challenging research field and because of its practical importance. It is a topic [

1

] characterized by complexity in terms of the number and type of equipments involved, diversity of aims, and lack of adequate models and control policies. In this paper, the MPC control of the final part of a beet sugar factory, the so-called sugar house or sugar end, where sugar crystals are made, is presented. Perhaps the most characteristic aspect of its operation is that batch and continuous units operate jointly, which introduce the need for combining on-line scheduling with continuous control. As such, it is a hybrid process that requires non-conventional control techniques. The paper presents a methodology and a predictive controller that takes into account both, the continuous objectives and manipulated variables, as well as the ones related to the discrete operation and logic of the batch units, and, at the end, simulation results of the controller operation are provided.

Increased requirements of flexible production have led to the development of

single-wafer

processing equipment for integrated circuit fabrication. For commercially feasible throughput, it is substantial to minimize the process cycle time by heating only the wafer surface, in an extremely short time period. This is only possible using radiation heating, leading to RTP systems – Rapid Thermal Processing. Under such circumstances the system is no longer isothermal and

temperature uniformity

control becomes an issue of considerable concern and technical difficulty. Commercial RTCVD reactors (Rapid Thermal Chemical Vapor Deposition) have been in use for more than a decade, but the technology still suffers from some limitations [

6

]. One of these is the inability to achieve with commercial control equipment an adequate temperature uniformity across the wafer surface during the rapid heating phases (e.g. from room temperature up to 1100°C in the order of 1 minute). Deposition of silicon should be performed in a manner which minimizes crystalline growth defects, such as lattice slip. Such defects are induced by thermal gradients in the wafer during high temperature processing. For example, while gradients of about 100°C across a wafer may be tolerable at a process temperature of 800°C, respective gradients of only 2—3°C are allowable at process temperatures of 1100°C. Due to the radiant type of heating, these semiconductor reactors represent a highly nonlinear interactive multi-input multi-output system.

The abundance of batch processes and continuous processes with wide operating ranges has motivated the development of nonlinear MPC (NMPC) techniques, which employ nonlinear models for prediction. The prediction model is typically developed once in the beginning of implementation of an NMPC scheme. However, as time progresses, slow drifts in unmeasured disturbances and changes in process parameters can lead to significant mismatch in plant and model behavior. Also, NMPC schemes are typically developed under the assumption that sensors and actuators are free from faults. However,

soft faults

, such as biases in sensors or actuators, are frequently encountered in the process industry. In addition to this, some actuator(s) may fail during operation, which results in loss of degrees of freedom for control. Occurrences of such faults and failures can lead to a significant degradation in the closed loop performance of the NMPC.

In this paper, a new contractive receding horizon scheme is proposed for the stabilization of constrained nonlinear systems. The proposed formulation uses a free finite prediction horizon without explicit use of a contraction stability constraint. Another appealing feature is the fact that the resulting receding horizon control is in pure feedback form unlike existing contractive schemes where open-loop phases or a memorized threshold are used to ensure the contraction property in closed loop. The control scheme is validating on the swing-up and stabilization problem of a simple and a double inverted pendulums.

A formulation of continuous-time nonlinear MPC is proposed in which input trajectories are described by general time-varying parameterizations. The approach entails a limiting case of suboptimal single-shooting, in which the dynamics of the associated NLP are allowed to evolve within the same timescale as the process dynamics, resulting in a unique type of continuous-time dynamic state feedback which is proven to preserve stability and feasibility.

Model predictive control (MPC) is a very effective approach to control nonlinear systems, especially when the systems are high dimensional and/or constrained. MPC formulates the problem of input trajectory generation as an optimization problem. However, due to model mismatch and disturbances, frequent re-calculation of the trajectories is typically called for. This paper proposes a two-time-scale control scheme that uses less frequent repeated trajectory generation in a slow loop and time-varying linear feedback in a faster loop. Since the fast loop reduces considerably the effect of uncertainty, trajectory generation can be done much less frequently. The problem of trajectory generation can be treated using either optimization-based MPC or flatness-based system inversion. As proposed, the method cannot handle hard constraints. Both MPC and the two-time-scale control scheme are tested via the simulation of a flying robotic structure. It is seen that the MPC scheme is too slow to be considered for real-time implementation on a fast system. In contrast, the two-time-scale control scheme is fast, effective and robust.

This paper presents a Receding Horizon Control (RHC) algorithm to the problem of on-line flight path optimization for aircraft in a dynamic Free-Flight (FF) environment. The motivation to introduce the concept of RHC is to improve the robust performance of solutions in a dynamic and uncertain environment, and also to satisfy the restrictive time limit in the real-time optimization of this complicated air traffic control problem. Compared with existing algorithms, the new algorithm proves more efficient and promising for practical applications.

This paper investigates vision based robot control based on a receding horizon control strategy. The stability of the receding horizon control scheme is guaranteed by using the terminal cost derived from an energy function of the visual feedback system. By applying the proposed control scheme to a two-link direct drive manipulator with a CCD camera, it is shown that the stabilizing receding horizon control nicely works for a planar visual feedback system. Furthermore, actual nonlinear experimental results are assessed with respect to the stability and the performance.

In this paper we present a nonlinear predictive control strategy for the supervision of networked control systems subject to coordination constraints. Such a system paradigm, referred hereafter to as constrained dynamic network, is characterized by a set of spatially distributed dynamic systems, connected via communication channels, with possible dynamical coupling and constraints amongst them which need to be controlled and coordinated in order to accomplish their overall objective. The significance of the method is that it is capable of ensuring no constraints violation and loss of stability regardless of any, possibly unbounded, time-delay occurrence. An application to the coordination of two autonomous vehicles under input-saturation and formation accuracy constraints is presented.

Completely centralized control of large, networked systems is impractical. Completely decentralized control of such systems, on the other hand, frequently results in unacceptable control performance. In this article, a distributed MPC framework with guaranteed feasibility and nominal stability properties is described. All iterates generated by the proposed distributed MPC algorithm are feasible and the distributed controller, defined by terminating the algorithm at any intermediate iterate, stabilizes the closed-loop system. The above two features allow the practitioner to terminate the distributed MPC algorithm at the end of the sampling interval, even if convergence is not attained. Further, the distributed MPC framework achieves optimal systemwide performance (centralized control) at convergence. Feasibility, stability and optimality properties for the described distributed MPC framework are established. Several examples are presented to demonstrate the efficacy of the proposed approach.

The purpose of this paper is to demonstrate the application of a recently developed theory for distributed nonlinear model predictive control (NMPC) to a promising domain for NMPC: dynamic management of supply chain networks. Recent work by the first author provides a distributed implementation of NMPC for application in large scale systems comprised of cooperative dynamic subsystems. By the implementation, each subsystem optimizes locally for its own policy, and communicates the most recent policy to those subsystems to which it is coupled. Stabilization and feasibility are guaranteed for arbitrary interconnection topologies, provided each subsystem not deviate too far from the previous policy, consistent with traditional MPC move suppression penalties. In this paper, we demonstrate the scalability and performance of the distributed implementation in a supply chain simulation example, where stages in the chain update in parallel and in the presence of cycles in the interconnection network topology. Using anticipative action, the implementation shows improved performance when compared to a nominal management policy that is derived in the supply chain literature and verified by real supply chain data.

The importance of the obstacle avoidance problem is stressed in [

4

]. Computation of reachability sets for the obstacle avoidance problem is addressed, for continuous-time systems in [

4

,

5

] and for discrete-time systems in [

12

]; further results appear in, for instance [

2

,

17

,

18

]. The obstacle avoidance problem is inherently non-convex. Most existing results are developed for the deterministic case when external disturbances are not present. The main purpose of this paper is to demonstrate that the obstacle avoidance problem in the discrete time setup has considerable structure even when disturbances are present. We extend the robust model predictive schemes using tubes (

sequences of sets of states

) [

9

,

11

,

14

] to address the robust obstacle avoidance problem and provide a mixed integer programming algorithm for robust control of constrained linear systems that are required to avoid specified obstacles. The resultant robust optimal control problem that is solved on-line has marginally increased complexity compared with that required for model predictive control for obstacle avoidance in the deterministic case.

A multi-stage nonlinear model predictive controller is derived for the real-time coordination of multiple aircraft. In order to couple the versatility of hybrid systems theory with the power of NMPC, a finite state machine is coupled to a real time optimal control formulation. This methodology aims to integrate real-time optimal control with higher level logic rules, in order to assist mission design for flight operations like collision avoidance, conflict resolution, and reacting to changes in the environment. Specifically, the controller is able to consider new information as it becomes available. Stability properties for nonlinear model predictive control are described briefly along the lines of a dual-mode controller. Finally, a small case study is presented that considers the coordination of two aircraft, where the aircraft are able to avoid obstacles and each other, reach their targets and minimize a cost function over time.