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Robust Control Design: An Optimal Control Approach

Robust Control Design: An Optimal Control Approach

Feng Lin

ISBN: 978-0-470-05956-2

Sep 2007

378 pages



Comprehensive and accessible guide to the three main approaches to robust control design and its applications

Optimal control is a mathematical field that is concerned with control policies that can be deduced using optimization algorithms. The optimal control approach to robust control design differs from conventional direct approaches to robust control that are more commonly discussed by firstly translating the robust control problem into its optimal control counterpart, and then solving the optimal control problem.

Robust Control Design: An Optimal Control Approach offers a complete presentation of this approach to robust control design, presenting modern control theory in an concise manner. The other two major approaches to robust control design, the H_infinite approach and the Kharitonov approach, are also covered  and described in the simplest terms possible, in order to provide a complete overview of the area. It includes up-to-date research, and offers both theoretical and practical applications that include flexible structures, robotics, and automotive and aircraft control.

Robust Control Design: An Optimal Control Approach will be of interest to those needing an introductory textbook on robust control theory, design and applications as well as graduate and postgraduate students involved in systems and control research. Practitioners will also find the applications presented useful when solving practical problems in the engineering field.



1 Introduction.

1.1 Systems and Control

1.2 Modern Control Theory

1.3 Stability

1.4 Optimal Control

1.5 Optimal Control Approach

1.6 Kharitonov Approach

1.7 H_ and H2 Control

1.8 Applications

1.9 Use of This Book

2 Fundamentals of Control Theory.

2.1 State Space Model

2.2 Responses of Linear Systems

2.3 Similarity Transformation

2.4 Controllability and Observability

2.5 Pole Placement by State Feedback

2.6 Pole Placement Using Observer

2.7 Notes and References

2.8 Problems

3 Stability Theory.

3.1 Stability and Lyapunov Theorem

3.2 Linear Systems

3.3 Routh–Hurwitz Criterion

3.4 Nyquist Criterion

3.5 Stabilizability and Detectability

3.6 Notes and References

3.7 Problems

4 Optimal Control and Optimal Observers.

4.1 Optimal Control Problem

4.2 Principle of Optimality

4.3 Hamilton–Jacobi–Bellman Equation

4.4 Linear Quadratic Regulator Problem

4.5 Kalman Filter

4.6 Notes and References

4.7 Problems 

5  Robust Control of Linear Systems.

5.1 Introduction

5.2 Matched Uncertainty

5.3 Unmatched Uncertainty

5.4 Uncertainty in the Input Matrix

5.5 Notes and References

5.6 Problems

6 Robust Control of Nonlinear Systems.

6.1 Introduction

6.2 Matched Uncertainty

6.3 Unmatched Uncertainty

6.4 Uncertainty in the Input Matrix

6.5 Notes and References

6.6 Problems

7 Kharitonov Approach.

7.1 Introduction

7.2 Preliminary Theorems

7.3 Kharitonov Theorem

7.4 Control Design Using Kharitonov Theorem

7.5 Notes and References

7.6 Problems

8 H and H2 Control.

8.1 Introduction

8.2 Function Space

8.3 Computation of H2 and H_ Norms

8.4 Robust Control Problem as H2 and H_ Control


8.5 H2/H_ Control Synthesis

8.6 Notes and References

8.7 Problems

9 Robust Active Damping.

9.1 Introduction

9.2 Problem Formulation

9.3 Robust Active Damping Design

9.4 Active Vehicle Suspension System

9.5 Discussion

9.6 Notes and References

10 Robust Control of Manipulators.

10.1 Robot Dynamics

10.2 Problem Formulation

10.3 Robust Control Design

10.4 Simulations

10.5 Notes and References

11 Aircraft Hovering Control.

11.1 Modelling and Problem Formulation

11.2 Control Design for Jet-borne Hovering 

11.3 Simulation

11.4 Notes and References

Appendix A: Mathematical Modelling of Physical Systems.

References and Bibliography.