Model reference control, nonadaptivecontrol schemes, 3±4 Morse, A.S., 84 Multi-input multi-output MIMO systems, 287±306 direct adaptive control, 289±96 indirect adaptive control, 296±9 S
Trang 1partial adaptive pole placement, 10, 13,
14, 18
See also Model reference adaptive
control (MRAC)
Chatteringbehaviour, 56
Cholesky decomposition, 69, 71
Concave covers, 223±8
de®nitions, 223
examples of, 224±8
properties of, 223±4
Concave functions, 217, 221±3
de®nitions, 221
properties of, 221±3
Continuous-time Lyapunov design,
268±9
Control Lyapunov function (clf), 188
Controlled Dungequations, 135±6
Converging-output converging-state
(COCS) function, 128, 132
Converse Lyapunov Theorem, 130
Convex functions, 217, 221±3
de®nition, 221
properties of, 221±3
Dead zone based methods, 23±5, 260±2,
267, 277
inverse of dead zone characteristic, 264
ordinary direct adaptive control with
dead zone, 27±8
robust direct adaptive control, 28±31
See also Actuator compensation
Deadbeat control strategy, 67, 160, 163,
166
Dense search method, 83±4
Didinsky, G., 186
Direct adaptive control, 28±31
multi-input multi-output systems,
289±96
with dead zone, 27±8
Direct localization principle, 89±101
localization in the presence of
unknown disturbance, 99±101
optimal localization, 94±9
Discrete-time nonlinear systems:
active identi®cation, 159±82
avoidance of nonlinear parametrization, 164±6
®nite duration, 178 input selection for identi®cation, 173±8, 179, 180
pre-computation of projections, 168±73, 180
problem formulation, 161±6 second-order example, 162±4 adaptive stabilization, 80±115, 245 direct localization principle, 89±101 indirect localization principle, 101±8 problem statement, 86±9
simulation examples, 108±12 See also Nonlinear systems Dungequations, 135±6 Dynamic feedback, 187, 204, 209 Dynamic normalization technique, 151±5 Feedback passivation, see Adaptive passivation
Finite escape time, 162, 166 Freeman, R.A., 185 Friction models, 236±40 Fuzzy systems, 287 applications, 299±305 two-link robot arm, 301±5 direct adaptive control, 290±2 indirect adaptive control, 297±9 Globally adaptively stabilizable systems,
128, 129 Globally uniformly asymptomatically stable (GUAS) systems, 124 Gradient projection adaptive law, 266±8
H2optimal control:
adaptive internal model control schemes, 11, 13±14 simulation example, 18±19 nonadaptive control schemes, 4±5
H1optimal control:
adaptive internal model control schemes, 11±12, 13, 14 simulation example, 18±19 nonadaptive control schemes, 5±6
Trang 2Hamilton±Jacobi±Bellman (HJB) pde,
184, 185
Hurwitz polynomial of degree, 7±8, 9
Hysteresis, 260±2, 277
inverse, 264
See also Actuator compensation
Hysteresis switching, 11, 84
Identi®cation scheme, see Active
identi®cation scheme
Indirect adaptive control, 63±79
adaptive control law, 69±74
properties of identi®cation scheme,
69±70
strategy, 70±4
adaptive control scheme, 68±9
multi-input multi-output systems,
296±9
problem formulation, 65±7
simulation examples, 74±8
system with noise, 75±8
system without noise, 74±5
Indirect localization principle, 101±8
localization in the presence of
unknown disturbance, 108
Input-to-output practically stable (IOpS)
systems, 125, 126
Input-to-output stable (IOS) systems, 125
Input-to-state practically stable (ISpS)
systems, 125, 126
Input-to-state stable (ISS) systems, 120,
124±5
Internal model control (IMC) schemes,
1±2
IMC ®lter, 5, 11
known parameters, 2±7
H2optimal control, 4±5
H1 optimal control, 5±6
model reference control, 3±4
partial pole placement control, 3
robustness to uncertainties, 6±7
See also Adaptive internal model
control schemes
Inverse optimal control, 185±6
inverse optimal adaptive tracking, 197±
202
inverse optimality via backstepping, 202±5
See also Actuator compensation, adaptive inverse approach Ioannou, P.A., 201
Isidori, A., 123, 136 Kharitonov Theory, 10 Kokotovic, P.V., 185, 186 Krstic, M., 185, 186, 196±7, 205±8, 210 Kuhn Tucker theorem, 249
Lagrangian function, 249 LaSalle's theorem, 191 Levy±Desplanques theorem, 298 Linear-quadratic-regulator (LQR), 201 Linearly parametrized systems, 215±16 Localization method, 80, 85
direct localization principle, 89±101 localization in the presence of unknown disturbance, 99±101 optimal localization, 94±9 indirect localization principle, 101±8, 111±12
localization in the presence of unknown disturbance, 108 simulation examples, 108±12 constant parameters, 109±10 indirect localization, 111±12 parameter jumps, 110±11
LU decomposition, 69 Magnetic bearing system, 242±5 adaptive control based on nonlinear parametrization, 243±5 Martensson, B., 81±3
Min-max optimization, 215, 217, 245 Model reference adaptive control (MRAC), 10±11, 41 output feedback design, 272 simulation example, 18 stability and robustness analysis, 13, 14 variable structure MRAC system, 41±3 MRAC based error model, 44±6 See also Adaptive variable structure control
Trang 3Model reference control, nonadaptive
control schemes, 3±4
Morse, A.S., 84
Multi-input multi-output (MIMO)
systems, 287±306
direct adaptive control, 289±96
indirect adaptive control, 296±9
See also Fuzzy systems
Multivariable systems, 275±80
nonlinearity model and its inverse,
277
output feedback designs, 280
state feedback designs, 278±80
Neural networks, 216, 287
See also Fuzzy systems
Newton±Raphson method, 227
Nonadaptive control schemes, 2±7
H2optimal control, 4±5
H1optimal control, 5±6
model reference control, 3±4
partial pole placement control, 3
robustness to uncertainties, 6±7
See also Internal model control (IMC)
schemes
Nonlinear gain, 124±7
input-to-state stable (ISS) systems,
124±5
nonlinear small gain theorems, 125±7
Nonlinear parametrization (NP), 216±18,
258, 277
avoidance of, 164±6
active identi®cation, 165
orthogonalized projection
estimation, 166
projection measurements, 165
regressor subspace, 164±5
concave covers, 223±8
de®nitions, 223
examples of, 224±8
properties of, 223±4
concave/convex functions, 220±3
de®nitions, 221
properties of, 221±3
problem statement, 218±20
stable adaptive NP systems, 228±35
adaptive controller, 230±4 adaptive observer, 234±5 extensions to the vector case, 229 low-velocity friction model, 236±40 magnetic bearing system, 242±5 new error model, 228±9 scalar error model with linear parameters, 229±30 stirred tank reactors (STRs), 240±2 structure of adaptive controller, 218±20
See also Nonlinear systems Nonlinear systems:
adaptive robust control for uncertain dynamical systems, 308±27 adaptive robust control with -modi®cation, 312±17 application to PM synchronous motors, 317±20
problem formulation, 310±12 nonsmooth nonlinearities, 260±1 designs for, 281±4
See also Actuator compensation, adaptive inverse approach optimal adaptive tracking, 184±213 adaptive backstepping, 193±7 adaptive trackingcontrol Lyapunov function (atclf), 188±93
design for strict-feedback systems, 205±9
inverse optimal adaptive tracking, 197±202
inverse optimality via backstepping, 202±5
problem statement, 186±8 transient performance, 209±10 See also Adaptive passivation; Discrete-time nonlinear systems; Nonlinear parametrization; Small gain techniques
Nonsmooth nonlinearities, 260±1 designs for, 281±4
See also Actuator compensation, adaptive inverse approach; Nonlinear systems Nussbaum, R.D., 81±2
Trang 4Orthogonalized projection scheme, 160,
166
algorithm, 169±70
for output-feedback systems, 170±1
Output feedback systems, 271±5
adaptive output feedback passivation,
136±8
for multivariable systems, 280
inverse control, 269±71
adaptive law, 271
error model, 270±1
reference system, 269±70
model reference design, 272
orthogonalized projection for,
170±1
parametric-output-feedback form,
161±2
PID design, 273±5
pole placement design, 272±3
Overparametrization, 216
Pan, Z., 186
Parametric strict-feedback system, 139,
185±6, 205±9, 281
Parametric-output-feedback form, 161±2
Parseval's Theorem, 4
Partial pole placement control:
adaptive internal model control
schemes, 10, 13, 14
simulation example, 18
nonadaptive control schemes, 3
Passivation, 120, 123
See also Adaptive passivation
Passivity, 121±3
strict passivity, 122
Pendulum example, 147±51
Permanent magnet synchronous (PMS)
motor example, 309±10, 317±20
control design, 318±20
model of PMS motor, 317±18
simulation study, 320
PID design, 273±5
Piecewise-linear characteristic, 260±2, 277
inverse, 264
See also Actuator compensation
Polar decomposition, 65, 69
Pole placement design, 272±3 Polynomial dierential operators, 81 Recursive adaptive passivation, 1315 Riccati equations, 184, 185, 201 Robots, 289
two-link robot arm, 301±5 Robust adaptive control:
for nonlinear uncertain dynamical systems, 308±27
adaptive robust control with -modi®cation, 312±17 application to PM synchronous motors, 317±20
problem formulation, 310±12 with less prior knowledge, 23±38 direct adaptive control, 28±31 problem formulation, 25±7 simulation example, 36±8 with least prior knowledge, 32±6 Robustness, 261
adaptive internal control schemes, 9± 10
adaptive algorithms, 81 robust adaptive law design, 7±9, 313±14
robustness analysis, 12±18 adaptive variable structure control, 47±
8, 52±5 nonadaptive control schemes, 6±7 Saturation function, 221
Self-excitation technique, 64 Separable sets, 95±6 Separation Principle, 148 Sepulchre, R., 185 Singular value decomposition (SVD), 65, 69
Small control property, 190 Small gain techniques, 6±7, 119±20, 138± 55
adaptive controller design, 139±45 initialization, 139±40
recursive steps, 140±4 small gain design step, 144±5 class of uncertain systems, 138±9
Trang 5examples and discussions, 14755
pendulum example, 14751
robusti®cation via dynamic
normalization, 151±5
nonlinear small gain theorems, 125±7
stability analysis, 146±7
Smooth control law, 203
Sontag, E.D., 188, 189±90, 196, 200, 202
Stability analysis, 12±18
adaptive variable structure control,
47±8, 52±5
small gain approach, 146±7
Stabilization, 185
See also Adaptive stabilization
Stabilizingsets, 101±2
State feedback designs, 265±9, 278±80
continuous-time Lyapunov design,
268±9
error model, 265±6
gradient projection adaptive law,
266±8
multivariable systems, 278±80
Stirred tank reactors (STRs), 240±2
adaptive control based on nonlinear
parametrization, 241±2
Strict passivity, 122
Strict-feedback systems, 139, 185±6, 205±
9
Sun, J., 201
Supervisory control, 84, 89
Switchingcontrol, 80±6
algorithms, 81
conventional switchingcontrol, 88±9
direct localization principle, 89±101
localization in the presence of
unknown disturbance, 99±101
optimal localization, 94±9
indirect localization principle, 101±8 localization in the presence of unknown disturbance, 108 problem statement, 86±9 simulation examples, 108±12 constant parameters, 109±10 indirect localization, 111±12 parameter jumps, 110±11 supervisory switchingcontrol, 84, 89 Sylvester resultant matrix, 64±5 Takagi±Sugeno fuzzy systems, see Fuzzy systems
Trackingperformance, adaptive variable structure control, 47±9, 52±6 See also Nonlinear systems Trajectory initialization, 210 Tuningfunctions, 120, 186, 191, 233 adaptive backsteppingwith, 120, 127, 193±7
Unboundedness observable (UO) function, 128
Uncertain discrete-time systems, see Discrete-time nonlinear systems Variable structure design (VSD), 41±2 See also Adaptive variable structure control
Willems, J.C., 123 Youla parameter, 3 Young's inequality, 137 Zero-state detectability, 122