Page 696 - Mathematical Techniques of Fractional Order Systems

668 Index

Fractional order chaotic systems (FOCS) when disturbance is injected at controller
(Continued) output, 270 272
simulation of, 413 415 when disturbance is injected at plant
Fractional order Chen hyperchaotic system, output, 273 274
362 363 FOFSMCPD controller design, 259 264
Fractional order complex Chen chaotic fractional order operator implementation,
system, stabilization of, 294 295 264
Fractional order complex hyperchaotic fuzzy logic control (FLC) design,
systems, identical synchronization of, 261 263
299 301 stability analysis using Lyapunov
Fractional order complex Lorenz hyperchaotic stability criteria, 260 261
system, stabilization of, 296 297 genetic algorithm (GA), optimization of
Fractional order derivatives (FODs), 162 controller gains by, 265 269
approximation of, 151 description of GA, 265 266
Fractional order differential equations tuning of controller for trajectory
(FODE), 412 413, 564 tracking task, 266 269
numerical solution of, 565 566 IOSMCPD controller design, 257 259,
Fractional order diffusion and reaction model, 261f
38 manipulator system, dynamic model of,
Fractional order dynamic systems, 348 349 252 256
Fractional order error models (FOEMs) with robustness testing
parameter constraints, 159 uncertainty in length, 275
additional tools for the analysis of FOS, uncertainty in mass, 275 276
164 Fractional order hyperchaotic Gao system,
analysis of FOEM3 with parameter 327 328
constraints, 169 173 2-D phase portraits of, 330f
FOEM3 with parameter constraints, 3-D phase portraits of, 329f
170 172 Fractional order hyperchaotic Rossler system
fractional order error model 3, 169 170 2D phase portrait of, 329f
stability analysis of FOEM3 with 3D phase portrait of, 328f
parameter constraints, 172 173 Fractional order hyperchaotic system,
analysis of fractional order error model 2 284 285
with parameter constraints, 164 169 active backstepping technique, 576 581
FOEM2 with parameter constraints, controller design for stabilization,
166 168 576 579
fractional order error model 2, 165 166 synchronization using, 579 581
stability analysis of FOEM2 with backstepping technique, 569 576
parameter constraints, 168 169 controller design for stabilization,
fractional calculus, 162 163 570 574
simulation examples, 173 178 controller design for synchronization,
ideal conditions, 174 176 574 576
noisy environment, 176 178 chaotic systems, 559 561
simulation specifications, 173 174 circuit realization of, 284
stability of fractional order systems, 163 discussions, 582 586
Fractional order form of system with infinite fractional calculus, 561
equilibria, 488 493 preliminaries of, 563 568
Fractional order fuzzy sliding mode controller fractional order differential equations,
design for nonlinear complex systems, numerical solution of, 565 566
249 fractional order nonlinear dynamical
design and implementation of sliding mode system, stability of, 566 568
controllers, 257 multiswitching synchronization of, 319
disturbance rejection complete synchronization, 330 339