Discrete Systems Analysis, Control and Optimization

More and more digital devices are being used for informa­ tion processing and control purposes in a variety of systems applications, including industrial processes, power networks, biological systems and communication networks. This trend has been helped by the advent of microprocessors and the consequent availability of cheap distributed computing power. For those applications, where digital devices are used, it is reasonable to model the system in discrete-time. In addition there are other application areas, e.g. econometric systems, business systems, certain command and control systems, environmental systems, where the underlying models are in discrete-time and here discrete-time approaches to analysis and control are the most appropriate. In order to deal with these two situations, there has been a lot of interest in developing techLiques which allow us to do analysis, design and control of discrete-time systems. This book provides a comprehensive treatment of discrete­ time dynamical systems. It covers the topics of modelling, optimization techniques and control design. The book is designed to serve as a text for teaching at the first year graduate level. The material included is organized into eight chapters.

1 Discrete Models in Systems Engineering.- 1.1 Introduction.- 1.2 Some Illustrative Examples.- 1.3 Objectives and Outline of the Book.- 1.4 References.- 2 Representation of Discrete Control Systems.- 2.1 Introduction.- 2.2 Transfer Functions.- 2.3 Difference Equations.- 2.4. Discrete State Equations.- 2.5 Modal Decomposition.- 2.6 Concluding Remarks.- 2.7 Problems.- 2.8 References.- 3 Structural Properties.- 3.1 Introduction.- 3.2 Controllability.- 3.3 Observability.- 3.4. Stability.- 3.5 Remarks.- 3.6 Problems.- 3.7 References.- 4 Design of Feedback Systems.- 4.1 Introduction.- 4.2 The Concept of Linear Feedback.- 4.3 Deadbeat Controllers.- 4.4 Development of Reduced-Order Models.- 4.5 Control Systems with Slow and Fast Modes.- 4.6 Concluding Remarks.- 4.7 Problems.- 4.8 References.- 5 Control of Systems with Inaccessible States.- 5.1 Introduction.- 5.2 State Reconstruction Schemes.- 5.3 Observer-Based Controllers.- 5.4 Two-Level Observation Structures.- 5.5 Discrete Two-Time-Scale Systems.- 5.6 Concluding Remarks.- 5.7 Problems.- 5.8 References.- 6 State and Parameter Estimation.- 6.1 Introduction.- 6.2 Random Variables and Gauss-Markov Processes.- 6.3 Linear Discrete Models with Random Inputs.- 6.4 The Kalman Filter.- 6.5 Decentralised Computation of the Kalman Fikter.- 6.6 Parameter Estimation.- 6.7 Problems.- 6.8 References.- 7 Adaptive Control Systems.- 7.1 Introduction.- 7.2 Basic Concepts of Model Reference Adaptive Systems.- 7.3 Design Techniques.- 7.4 Self-Tuning Regulators.- 7.5 Concluding Remarks.- 7.6 Problems.- 7.7 References.- 8 Dynamic Optimisation.- 8.1 Introduction.- 8.2 The Dynamic Optimisation Problem.- 8.3 Linear-Quadratic Discrete Regulators.- 8.4 Numerical Algorithms for the Discrete Riccati Equation.- 8.5 Hierarchical Optimization Methodology.- 8.6 Decomposition-Decentralisation Approach.- 8.7 Concluding Remarks.- 8.8 Problems.- 8.9 References.