Control of Nonlinear Dynamical Systems (eBook)

Preface 6
Contents 8
Introduction 13
Optimal control 22
1.1 Statement of the optimal control problem 22
1.2 The maximum principle 27
1.3 Open-loop and feedback control 32
1.4 Examples 34
Method of decomposition (the first approach) 41
2.1 Problem statement and game approach 41
2.2 Control of the subsystem and feedback control design 47
2.3 Weak coupling between degrees of freedom 64
2.4 Nonlinear damping 77
2.5 Applications and numerical examples 92
Method of decomposition (the second approach) 112
3.1 Problem statement and game approach 112
3.2 Feedback control design and its generalizations 121
3.3 Applications to robots 140
Stability based control for Lagrangian mechanical systems 155
4.1 Scleronomic and rheonomic mechanical systems 155
4.2 Lyapunov stability of equilibrium 159
4.3 Lyapunov’s direct method for autonomous systems 159
4.4 Lyapunov’s direct method for nonautonomous systems 161
4.5 Stabilization of mechanical systems 161
4.6 Modification of Lyapunov’s direct method 163
Piecewise linear control for mechanical systems under uncertainty 164
5.1 Piecewise linear control for scleronomic systems 164
5.2 Applications to mechanical systems 177
5.3 Piecewise linear control for rheonomic systems 206
Continuous feedback control for mechanical systems under uncertainty 220
6.1 Feedback control for scleronomic system with a given matrix of inertia 220
6.2 Control of a scleronomic system with an unknown matrix of inertia 236
6.3 Control of rheonomic systems under uncertainty 244
Control in distributed-parameter systems 251
7.1 System of linear oscillators 251
7.2 Distributed-parameter systems 258
7.3 Solvability conditions 269
Control system under complex constraints 280
8.1 Control design in linear systems under complex constraints 280
8.2 Application to oscillating systems 286
8.3 Application to electro-mechanical systems 308
Optimal control problems under complex constraints 332
9.1 Time-optimal control problem under mixed and phase constraints 333
9.2 Time-optimal control under constraints imposed on the rate of change of the acceleration 345
9.3 Time-optimal control under constraints imposed on the acceleration and its rate of change 359
Time-optimal swing-up and damping feedback controls of a nonlinear pendulum 371
10.1 Optimal control structure 372
10.2 Swing-up control 376
10.3 Damping control 384
References 392
Index 397