Functional Adaptive Control

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.

I. Introduction.- 1. Introduction.- 1.1 Intelligent Control Systems.- 1.2 Approaches to Intelligent Control.- 1.2.1 Contribution of Adaptive Control.- 1.2.2 Contribution of Artificial Intelligence.- 1.2.3 Confluence of Adaptive Control and AI: Intelligent Control.- 1.3 Enhancing the Performance of Intelligent Control.- 1.3.1 Multiple Model Schemes: Dealing with Complexity.- 1.3.2 Stochastic Adaptive Control: Dealing with Uncertainty.- 1.4 The Objectives and their Rationale.- II. Deterministic Systems.- 2. Adaptive Control of Nonlinear Systems.- 2.1 Introduction.- 2.2 Continuous-time Systems.- 2.2.1 Control by Feedback Linearization.- 2.2.2 Control by Backstepping.- 2.2.3 Adaptive Control.- 2.3 Discrete-time Systems.- 2.3.1 Affine Approximations and Feedback Linearization.- 2.3.2 Adaptive Control.- 2.4 Summary.- 3. Dynamic Strueture Networks for Stahle Adaptive Control.- 3.1 Introduction.- 3.2 Problem Formulation.- 3.3 Fixed-structure Network Solutions.- 3.4 Dynamic Network Structure.- 3.5 The Control Law and Error Dynamies.- 3.6 The Adaptive System.- 3.7 Stability Analysis.- 3.8 Evaluation of Control Parameters and Implementation.- 3.8.1 The Disturbanee Bound.- 3.8.2 Choice of the Boundary Layer.- 3.8.3 Comments.- 3.8.4 Implementation.- 3.9 Simulation Examples.- 3.9.1 Example 1.- 3.9.2 Example 2.- 3.10 Summary.- 4. Composite Adaptive Control of Continuous-Time Systems.- 4.1 Introduetion.- 4.2 Problem Formulation.- 4.3 The Neural Networks.- 4.4 The Control Law.- 4.5 Composite Adaptation.- 4.5.1 The Identifieation Model.- 4.5.2 The Adaptation Law.- 4.6 Stability Analysis.- 4.7 Determination of the Disturbanee Bounds.- 4.8 Simulation Examples.- 4.8.1 Example 1.- 4.8.2 Example 2.- 4.9 Summary.- 5. Funetional Adaptive Control of Discrete-Time Systems.- 5.1 Introduetion.- 5.2 Problem Formulation.- 5.3 The Neural Network.- 5.4 The Control Law.- 5.5 The Adaptive System.- 5.6 Stability Analysis.- 5.7 Traeking Error Convergenee.- 5.8 Simulation Examples.- 5.8.1 Example 1.- 5.8.2 Example 2.- 5.9 Extension to Adaptive Sliding Mode Control.- 5.9.1 Definitions of a Discrete-time Sliding Mode.- 5.9.2 Adaptive Sliding Mode Control.- 5.9.3 Problem Formulation.- 5.9.4 The Control Law.- 5.9.5 The Adaptive System.- 5.9.6 Stability Analysis.- 5.9.7 Sliding and Tracking Error Convergence.- 5.9.8 Simulation Example.- 5.10 Summary.- III. Stochastic Systems.- 6. Stochastic Control.- 6.1 Introduction.- 6.2 FUndamental Principles.- 6.3 Classes of Stochastic Control Problems.- 6.4 Dual Control.- 6.4.1 Degrees of Interaction.- 6.4.2 Solutions to the Implementation Problem.- 6.5 Conclusions.- 7. Dual Adaptive Control of Nonlinear Systems.- 7.1 Introduction.- 7.2 Problem Formulation.- 7.3 Dual Controller Design.- 7.3.1 GaRBF Dual Controller.- 7.3.2 Sigmoidal MLP Dual Controller.- 7.3.3 Analysis of the Control Laws.- 7.4 Simulation Examples and Performance Evaluation.- 7.4.1 Example 1.- 7.4.2 Example 2.- 7.5 Summary.- 8. Multiple Model Approaches.- 8.1 Introduction.- 8.2 Basic Formulation.- 8.2.1 Multiple Model Adaptive Contro!..- 8.2.2 Jump Systems.- 8.3 Adaptive IO Models.- 8.3.1 Scheduled Mode Transitions.- 8.4 Summary.- 9. Multiple Model Dual Adaptive Control of Jump Nonlinear Systems.- 9.1 Introduction.- 9.2 Problem Formulation.- 9.3 The Estimation Problem.- 9.3.1 Known Mode Case.- 9.3.2 Unknown Mode Case.- 9.4 Self-organized Allocation of Local Models.- 9.5 The Control Law.- 9.5.1 Known Mode Case.- 9.5.2 Unknown Mode Case.- 9.6 Simulation Examples and Performance Evaluation.- 9.6.1 Example 1.- 9.6.2 Example 2.- 9.7 Summary.- 10. Multiple Model Dual Adaptive Control of Spatial Multimodal Systems.- 10.1 Introduction.- 10.2 Problem Formulation.- 10.3 The Modular Network.- 10.4 The Estimation Problem.- 10.4.1 Local Model Parameter Estimation.- 10.4.2 Validity Function Estimation.- 10.5 The Control Law.- 10.5.1 Known System Case.- 10.5.2 Unknown System Case.- 10.6 Simulation Examples and Performance Evaluation.- 10.6.1 Example 1.- 10.6.2 Example 2.- 10.6.3 Performance Evaluation.- 10.7 Summary.- IV. Conclusions.- 11. Conclusions.- References.