Nonlinear and Adaptive Control Systems

Nonlinear and Adaptive Control Systems......Page 4
Contents......Page 8
Preface......Page 10
1.1 Nonlinear functions and nonlinearities......Page 12
1.2 Common nonlinear systems behaviours......Page 15
1.3 Stability and control of nonlinear systems......Page 16
2.1 Nonlinear systems and linearisation around an operating point......Page 20
2.2 Autonomous systems......Page 22
2.3 Second-order nonlinear system behaviours......Page 23
2.4 Limit cycles and strange attractors......Page 29
3 Describing functions......Page 36
3.1 Fundamentals......Page 37
3.2 Describing functions for common nonlinear components......Page 40
3.3 Describing function analysis of nonlinear systems......Page 45
4.1 Basic definitions......Page 52
4.2 Linearisation and local stability......Page 56
4.3 Lyapunov’s direct method......Page 57
4.4 Lyapunov analysis of linear time-invariant systems......Page 62
5.1 Positive real systems......Page 66
5.2 Absolute stability and circle criterion......Page 70
5.3 Input-to-state stability and small gain theorem......Page 76
5.4 Differential stability......Page 82
6.1 Input–output linearisation......Page 86
6.2 Full-state feedback linearisation......Page 94
7 Adaptive control of linear systems......Page 100
7.1 MRAC of first-order systems......Page 101
7.2 Model reference control......Page 105
7.3 MRAC of linear systems with relative degree 1......Page 110
7.4 MRAC of linear systems with high relatives......Page 113
7.5 Robust adaptive control......Page 114
8.1 Observer design for linear systems......Page 120
8.2 Linear observer error dynamics with output injection......Page 122
8.3 Linear observer error dynamics via direct state transformation......Page 131
8.4 Observer design for Lipschitz nonlinear systems......Page 133
8.5 Reduced-order observer design......Page 138
8.6 Adaptive observer design......Page 147
9.1 Integrator backstepping......Page 152
9.2 Iterative backstepping......Page 155
9.3 Observer backstepping......Page 158
9.4 Backstepping with filtered transformation......Page 163
9.5 Adaptive backstepping......Page 170
9.6 Adaptive observer backstepping......Page 178
10.1 Asymptotic rejection of sinusoidal disturbances......Page 186
10.2 Adaptive output regulation......Page 197
10.3 Output regulation with nonlinear exosystems......Page 205
10.4 Asymptotic rejection of general periodic disturbances......Page 215
11.1 Harmonics estimation and rejection in power distribution systems......Page 230
11.1.1 System model......Page 231
11.1.2 Iterative observer design for estimating frequency modes in input......Page 235
11.1.3 Estimation of specific frequency modes in input......Page 243
11.1.4 Rejection of frequency modes......Page 245
11.2 Observer and control design for circadian rhythms......Page 249
11.2.1 Circadian model......Page 250
11.2.2 Lipschitz observer design......Page 252
11.2.3 Phase control of circadian rhythms......Page 254
11.3 Sampled-data control of nonlinear systems......Page 258
11.3.1 System model and sampled-data control......Page 260
11.3.2 Stability analysis of sampled-data systems......Page 262
11.3.3 Simulation......Page 271
Bibliographical Notes......Page 274
References......Page 279
Index......Page 286