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Functional Adaptive Control

An Intelligent Systems Approach

verfasst von: Simon G. Fabri, PhD, Visakan Kadirkamanathan, PhD

Verlag: Springer London

Buchreihe : Communications and Control Engineering

Enthalten in: Professional Book Archive

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The field of intelligent control has recently emerged as a response to the challenge of controlling highly complex and uncertain nonlinear systems. It attempts to endow the controller with the key properties of adaptation, learn ing and autonomy. The field is still immature and there exists a wide scope for the development of new methods that enhance the key properties of in telligent systems and improve the performance in the face of increasingly complex or uncertain conditions. The work reported in this book represents a step in this direction. A num ber of original neural network-based adaptive control designs are introduced for dealing with plants characterized by unknown functions, nonlinearity, multimodal behaviour, randomness and disturbances. The proposed schemes achieve high levels of performance by enhancing the controller's capability for adaptation, stabilization, management of uncertainty, and learning. Both deterministic and stochastic plants are considered. In the deterministic case, implementation, stability and convergence is sues are addressed from the perspective of Lyapunov theory. When compared with other schemes, the methods presented lead to more efficient use of com putational storage and improved adaptation for continuous-time systems, and more global stability results with less prior knowledge in discrete-time sys tems.

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Inhaltsverzeichnis

Frontmatter

Introduction

Frontmatter

1. Introduction

Abstract

The main goal of control engineering is to ensure that some system of interest performs according to a given specification, often under conditions of uncertainty and with as little human intervention as possible. In general, the uncertainty arises because of insufficient knowledge about the system itself or the environment in which it operates. This could be due to a highly complex plant, components that change their characteristics because of failure or drift, and the presence of unpredictable external disturbances. The specification, which need not be constant so as to accommodate for possible changes in the control objectives, defines how the variables of interest within the system are required to behave. This goal demands the system to effect some form of self-regulation. Control theory shows that in general, the most reliable way of achieving this, is by connecting a suitably designed controller in a feedback configuration with the system.

Simon G. Fabri, Visakan Kadirkamanathan

Deterministic Systems

Frontmatter

2. Adaptive Control of Nonlinear Systems

Abstract

An important attribute of intelligent control is the ability to deal with nonlinear systems that are subject to uncertainty. Hence when designing intelligent control schemes, the theoretical background that already exists in the fields of adaptive and nonlinear control should be given its due importance. In this chapter we therefore present a brief review of several aspects of nonlinear systems theory and adaptive control of nonlinear plants.

Simon G. Fabri, Visakan Kadirkamanathan

3. Dynamic Structure Networks for Stable Adaptive Control

Abstract

The local representation properties and the possibility of predetermining the basis function parameters in Gaussian RBF networks, makes them ideal candidates for implementing functional adaptive control. However these attractive features are somewhat tarnished by the curse of dimensionality problem associated with GaRBF networks when used for high dimensional spaces.

Simon G. Fabri, Visakan Kadirkamanathan

4. Composite Adaptive Control of Continuous-Time Systems

Abstract

In this chapter we introduce an improved adaptation scheme for control of functional uncertain nonlinear systems by neural networks. The proposed scheme, inspired from the composite adaptation law of Slotine and Li [233] that was originally developed for parametric uncertain systems, aims to improve the transient performance of RBF-based adaptive schemes for continuous time affine, nonlinear systems, such as those found in [204, 219, 255]. Although these papers do provide control and adaptation laws that ensure boundedness of all the system’s signals and tracking error convergence, performance issues such as rate of convergence and general improvements in the transient response are not addressed at all. Indeed this topic has been largely neglected even in the classical literature on linear adaptive control, where not many results abound [144, 182]. The few principal works dealing with this problem in the linear, parametric uncertain case are briefly described next.

Simon G. Fabri, Visakan Kadirkamanathan

5. Functional Adaptive Control of Discrete-Time Systems

Abstract

In general, Lyapunov-based adaptive designs for discrete-time systems are not a straightforward translation of their continuous-time counterpart [138]. Given a linearly parameterized model, continuous-time systems yield a Lyapunov function derivative that is linear in the derivative of the parameter estimate. By contrast, for discrete-time systems, the difference in the Lyapunov function also includes a term involving the square of the difference of the parameter estimate.

Simon G. Fabri, Visakan Kadirkamanathan

Stochastic Systems

Frontmatter

6. Stochastic Control

Abstract

In this chapter, some important techniques underpinning stochastic control theory are reviewed. Although the emphasis is on stochastic adaptive methods, i.e., those dealing with systems having unknown parameters, completeness and clarity demand that occasionally the non-adaptive case is also considered. As in most publications on stochastic control, only the discrete-time case is considered because the controller is likely to be implemented as a digital computer programme.

Simon G. Fabri, Visakan Kadirkamanathan

7. Dual Adaptive Control of Nonlinear Systems

Abstract

In this chapter, two suboptimal dual adaptive control schemes for a stochastic class of functional uncertain nonlinear systems are developed. The two schemes are based on GaRBF and sigmoidal MLP neural networks respectively. The idea of applying dual control principles within a functional adaptive context first appeared in [72]. Most other approaches typically adopt an HCE procedure that often leads to an inadequate transient response because the initial uncertainty of the unknown network parameters is large. Some of the neural network control schemes that have been put forward avoid this by performing intensive off-line training to identify the plant in open-loop and reduce the prior uncertainty of the unknown parameters [53, 193, 215]. Only later is an adaptive control phase started, with the initial network parameters set to the pre-trained values that are already substantially close to the optimal. In a certain sense this procedure defeats the main objective of adaptive control because the off-line training phase reduces most of the uncertainty existing prior to application of the control.

Simon G. Fabri, Visakan Kadirkamanathan

8. Multiple Model Approaches

Abstract

During the mid-to-late 1960’s there emerged a new state estimation and control methodology for handling the adaptive Incomplete State Information (ISI) problem [150, 166]. This methodology is known as Multiple Model Adaptive Estimation/Control (MMAE/C) or Partitioned Adaptive Filtering/Control(PAF/C). It originally appeared as a response to the fact that the reformulation of the adaptive ISI problem in terms of an augmented state (as explained in Section 6.3) yields a set of nonlinear equations, even if the original system were linear. Although this technique seems attractive, because it enables the uncertain parameters to be treated as part of the augmented state vector, estimation and control of nonlinear equations is not a simple task. This was explained in Chapter 6 when it was noted that in general, suboptimal solutions of the nonlinear ISI problem still remain computationally intensive.

Simon G. Fabri, Visakan Kadirkamanathan

9. Multiple Model Dual Adaptive Control of Jump Nonlinear Systems

Abstract

This chapter considers control of a class of nonlinear, stochastic, multimodal systems whose various mode dynamics are unknown and subject to unscheduled jumps. The practical significance of such systems includes fault-tolerant control or plants working in an unpredictable environment. The task of controlling such systems is challenging because of the presence of both mode jumps, which makes it a temporal multimodal problem, as well as the dynamic uncertainty of the modes. The latter takes into account that in a realistic situation it is difficult to formulate prior accurate models for all modes, particularly when a mode corresponds to some fault condition. The solution adopted combines ideas taken from adaptive control to handle dynamic uncertainty, and multiple model techniques to handle the multimodality. The use of multiple models also serves to make the system more “intelligent” because, as explained in Chapter 1, it furnishes it with characteristics of learning (through memorization) and not just adaptation.

Simon G. Fabri, Visakan Kadirkamanathan

10. Multiple Model Dual Adaptive Control of Spatial Multimodal Systems

Abstract

The concept of multimodality suggests an interesting way of handling systems whose dynamics are characterized by nonlinear functions. The dynamics of such systems could be interpreted as a scheduled multimodal problem, where each mode captures the dynamics within a restricted (local) range of operating conditions and the scheduling is determined by the operating conditions themselves. This method is particularly appealing for spatially complex systems because they typically exhibit very different characteristics along different zones of the operating space. A multimodal interpretation is attractive because the local modes could be individually modelled by a less complex structure than would have been the case if one higher order model was chosen to capture the global nonlinear dynamics, such as a conventional neural network. This method of treating nonlinear systems naturally lends itself to multiple model based techniques, both for control and system identification. In control, it represents the fundamental principle behind the Gain Scheduling control technique [23, 217, 226, 227]. This scenario is distinct from the jump system case considered in the previous chapter because now the mode transitions are scheduled by some measurable operating conditions, instead of being arbitrary.

Simon G. Fabri, Visakan Kadirkamanathan

Conclusions

Frontmatter

11. Conclusions

Abstract

Modern plants and processes are often characterized by highly complex structures and dynamic behaviour typified by nonlinearities, time-varying dynamics and the influence of unpredictable disturbances. Under these circumstances, knowledge about the system is usually incomplete and subject to high levels of uncertainty. The task of controlling this kind of system is therefore a considerable challenge, especially when expected to operate safely, reliably and efficiently within a wide range of operating conditions and with as little human intervention as possible. This combination of complexity coupled with strict performance specifications is not uncommon in modern aircraft, marine and aerospace systems or even industrial processes that are highly sensitive to disturbances in the environment and in the quality of the process inputs.

Simon G. Fabri, Visakan Kadirkamanathan

Backmatter

Titel: Functional Adaptive Control
verfasst von: Simon G. Fabri, PhD
Visakan Kadirkamanathan, PhD
Copyright-Jahr: 2001
Verlag: Springer London
Electronic ISBN: 978-1-4471-0319-6
Print ISBN: 978-1-4471-1090-3
DOI: https://doi.org/10.1007/978-1-4471-0319-6