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2016 | Buch

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Model Predictive Control

Classical, Robust and Stochastic

verfasst von: Basil Kouvaritakis, Mark Cannon

Verlag: Springer International Publishing

Buchreihe : Advanced Textbooks in Control and Signal Processing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques.

Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplicative and stochastic model uncertainty. The book provides:

extensive use of illustrative examples; sample problems; and discussion of novel control applications such as resource allocation for sustainable development and turbine-blade control for maximized power capture with simultaneously reduced risk of turbulence-induced damage.

Graduate students pursuing courses in model predictive control or more generally in advanced or process control and senior undergraduates in need of a specialized treatment will find Model Predictive Control an invaluable guide to the state of the art in this important subject. For the instructor it provides an authoritative resource for the construction of courses.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The benefits of feedback control have been known to mankind for more than 2,000 years and examples of its use can be found in ancient Greece, notably the float regulator of the water clock invented by Ktesibios in about 270 BC, Vitruvius, The Ten Books on Architecture, 1914, [1]. The formal development of the field as a mathematical tool for the analysis of the behaviour of dynamical systems is much more recent, beginning around 150 years ago when Maxwell published his work on governors Maxwell, Proc. R. Soc. Lond. 16:270–283, 1868, [2]. Since then the field has seen spectacular developments, promoted by the work of mathematicians, engineers and physicists. Laplace, Lyapunov, Kolmogorov, Wiener, Nyquist, Bode, Bellman are just a few of the major contributors to the edifice of what is known today as control theory.

Basil Kouvaritakis, Mark Cannon

Classical MPC

Frontmatter

Chapter 2. MPC with No Model Uncertainty

Abstract

This section provides a review of some of the key concepts and techniques in classical MPC. Here the term “classical MPC” refers to a class of control problems involving linear time invariant (LTI) systems whose dynamics are described by a discrete time model that is not subject to any uncertainty, either in the form of unknown additive disturbances or imprecise knowledge of the system parameters.In the first instance the assumption will be made that the system dynamics can be described in terms of the LTI state-space model \(x_{k+1} = Ax_k + B u_k\) \(y_k = Cx_k\) where \(x_k\in \mathbb {R}^{n_x}\), \(u_k\in \mathbb {R}^{n_u}\), \(y_k\in \mathbb {R}^{n_y}\) are, respectively, the system state, the control input and the system output, and k is the discrete time index. If the system to be controlled is described by a model with continuous time dynamics (such as an ordinary differential equation), then the implicit assumption is made here that the controller can be implemented as a sampled data system and that (2.1a) defines the discrete time dynamics relating the samples of the system state to those of its control inputs.

Basil Kouvaritakis, Mark Cannon

Robust MPC

Frontmatter

Chapter 3. Open-Loop Optimization Strategies for Additive Uncertainty

Abstract

The essential components of the classical predictive control algorithms considered in Chap. 2 also underpin the design of algorithms for robust MPC. Guarantees of closed-loop properties such as stability and convergence rely on appropriately defined terminal control laws, terminal sets and cost functions. Likewise, to ensure that constraints can be met in the future, the initial plant state must belong to a suitable controllable set. However the design of these constituents and the analysis of their effects on the performance of MPC algorithms become more complex in the case where the system dynamics are subject to uncertainty. The main difficulty is that properties such as invariance, controlled invariance (including recursive feasibility) and monotonicity of the predicted cost must be guaranteed for all possible uncertainty realizations. In many cases this leads to computation which grows rapidly with the problem size and the prediction horizon.

Basil Kouvaritakis, Mark Cannon

Chapter 4. Closed-Loop Optimization Strategies for Additive Uncertainty

Abstract

The performance and constraint handling capabilities of a robust predictive control law are limited by the amount of information on future model uncertainty that is made available to the controller. However, the manner in which the controller uses this information is equally important. Although the realization of future model uncertainty is by definition unknown when a predicted future control trajectory is optimized, this information may be available to the controller at the future instant of time when the control law is implemented.

Basil Kouvaritakis, Mark Cannon

Chapter 5. Robust MPC for Multiplicative and Mixed Uncertainty

Abstract

In this chapter, we consider constrained linear systems with imprecisely known parameters, namely systems that are subject to multiplicative uncertainty.

Basil Kouvaritakis, Mark Cannon

Stochastic MPC

Frontmatter

Chapter 6. Introduction to Stochastic MPC

Abstract

Uncertainty forms an integral part of most control problems and earlier chapters discussed how MPC algorithms can be constructed in order to treat model uncertainty in a robust sense. One of the key features of robust MPC is that it requires constraints to be satisfied for all possible realizations of uncertainty. Thus each element of the set of values that can be assumed by an uncertain model parameter or disturbance input is treated with equal importance, and robust MPC does not discriminate between alternative realizations on the basis of their respective likelihood.

Basil Kouvaritakis, Mark Cannon

Chapter 7. Feasibility, Stability, Convergence and Markov Chains

Abstract

This chapter considers the closed-loop properties of stochastic MPC strategies based on the predicted costs and probabilistic constraints formulated in Chap. 6. To make the analysis of closed-loop stability and performance possible, it must first be ensured that the MPC law is well-defined at all times and the most natural way to approach this is to ensure that the associated receding horizon optimization problem remains feasible whenever it is initially feasible . We therefore begin by discussing the conditions for recursive feasibility.

Basil Kouvaritakis, Mark Cannon

Chapter 8. Explicit Use of Probability Distributions in SMPC

Abstract

The previous chapter introduced the use of tubes with ellipsoidal or polytopic cross sections in stochastic MPC. However the probabilistic constraints on predicted states and control inputs were handled using confidence regions for stochastic model parameters, namely sets determined offline that contain the uncertain parameters of the model with a specified probability.

Basil Kouvaritakis, Mark Cannon

Chapter 9. Conclusions

Abstract

The aim of this final chapter is to give a short discursive summary of some of the key results presented in this book. We also speculate on extensions that could, in our opinion, be pursued in future.

Basil Kouvaritakis, Mark Cannon

Backmatter

Titel: Model Predictive Control
verfasst von: Basil Kouvaritakis
Mark Cannon
Copyright-Jahr: 2016
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-24853-0
Print ISBN: 978-3-319-24851-6
DOI: https://doi.org/10.1007/978-3-319-24853-0