Mathematical Control Theory - An Introduction

Preface to the first edition
Preface to the second edition
Contents
Introduction
	0.1 Problems of mathematical control theory
	0.2 Specific models
	Bibliographical notes
Part I Elements of Classical Control Theory
1 Controllability and observability
	1.1 Linear differential equations
	1.2 The controllability matrix
	1.3 Rank condition
	1.4 A classification of control systems
	1.5 Kalman decomposition
	1.6 Observability
	Bibliographical notes
2 Stability and stabilizability
	2.1 Stable linear systems
	2.2 Stable polynomials
	2.3 The Routh theorem
	2.4 Stability, observability and Lyapunov equation
	2.5 Stabilizability and controllability
	2.6 Hautus lemma
	2.7 Detectability and dynamical observers
	Bibliographical notes
3 Controllability with vanishing  energy
	3.1 Characterization theorems
	3.2 Orbital Transfer Problem
	3.3 NCVE and generalized Liouville's theorem
	Bibliographical notes
4 Systems with constraints
	4.1 Bounded sets of parameters
	4.2 Positive systems
	Bibliographical notes
5 Realization theory
	5.1 Impulse response and transfer functions
	5.2 Realizations of the impulse response function
	5.3 The characterization of transfer functions
	Bibliographical notes
Part II Nonlinear Control Systems
6 Controllability and observability  of nonlinear systems
	6.1 Nonlinear differential equations
	6.2 Controllability and linearization
	6.3 Lie brackets
	6.4 The openness of attainable sets
	6.5 Observability
	Bibliographical notes
7 Stability and stabilizability
	7.1 Differential inequalities
	7.2 The main stability test
	7.3 Linearization
	7.4 The Lyapunov function method
	7.5 La Salle's theorem
	7.6 Topological stability criteria
	7.7 Exponential stabilizability and the robustness problem
	7.8 Necessary conditions for stabilizability
	7.9 Stabilization of the Euler equations
	Bibliographical notes
8 Realization theory
	8.1 Input–output maps
	8.2 Partial realizations
	Bibliographical notes
Part III Optimal Control
9 Dynamic programming
	9.1 Introductory comments
	9.2 Bellman equation and the value function
	9.3 The linear regulator problem  and the Riccati equation
	9.4 The linear regulator and stabilization
	Bibliographical notes
10 Viscosity solutions  of Bellman equations
	10.1 Viscosity solution
	10.2 Dynamic programming principle
	10.3 Regularity of the value function
	10.4 Existence of the viscosity solution
	10.5 Uniqueness of the viscosity solution
	Bibliographical notes
11 Dynamic programming  for impulse control
	11.1 Impulse control problems
	11.2 An optimal stopping problem
	11.3 Iterations of convex mappings
	11.4 The proof of Theorem 11.1
	Bibliographical notes
12 The maximum principle
	12.1 Control problems with fixed terminal time
	12.2 An application of the maximum principle
	12.3 The maximum principle for impulse control problems
	12.4 Separation theorems
	12.5 Time-optimal problems
	Bibliographical notes
13 The existence of optimal  strategies
	13.1 A control problem without an optimal solution
	13.2 Filippov's theorem
	Bibliographical notes
Part IV Infinite-Dimensional Linear Systems
14 Linear control systems
	14.1 Introduction
	14.2 Semigroups of operators
	14.3 The Hille–Yosida theorem
	14.4 Phillips' theorem
	14.5 Important classes of generators
	14.6 Specific examples of generators
	14.7 The integral representation of linear systems
	14.8 Delay systems
	14.9 Existence of solutions to delay equation
	14.10 Semigroup approach to delay systems
	14.11 State space representation of delay systems
	Bibliographical notes
15 Controllability
	15.1 Images and kernels of linear operators
	15.2 The controllability operator
	15.3 Various concepts of controllability
	15.4 Systems with self-adjoint generators
	15.5 Controllability of the wave equation
	Bibliographical notes
16 Stability and stabilizability
	16.1 Various concepts of stability
	16.2 Spectrum determined growth assumptions
	16.3 Stability of delay equations
	16.4 Lyapunov's equation
	16.5 Stability of abstract hyperbolic systems
	16.6 Stabilizability and controllability
	Bibliographical notes
17 Linear regulators in Hilbert  spaces
	17.1 Introduction
	17.2 The operator Riccati equation
	17.3 The finite horizon case
	17.4 Regulator problem for delay systems
	17.5 The infinite horizon case: Stabilizability and detectability
	Bibliographical notes
18 Boundary control systems
	18.1 Semigroup approach to boundary control systems
	18.2 Boundary systems with general controls
	18.3 Heating systems
	18.4 Approximate controllability of the heating systems
	18.5 Null controllability for a boundary control system
	Bibliographical notes
Appendix
	A.1  Measurable spaces
	A.2  Metric spaces
	A.3  Banach spaces
	A.4  Hilbert spaces
	A.5  Bochner's integral
	A.6  Spaces of continuous functions
	A.7  Spaces of measurable functions
References
Index