Page 697 - Mathematical Techniques of Fractional Order Systems

Index 669

problem formulation, 325 326 Fractional stochastic differential equation
recent work, 322 (FSDE)
review and approximation of fractional single-valued, by using analytic resolvent
operator, 322 325 operators
stability of fractional order systems, 326 mild solution, existence of, 212 222
system description, 327 329 optimal control, existence of, 222 225
simulation results, 581 preliminaries, 209 225
system description, 568 569 single-valued and multivalued, 187 208
Fractional order integral (FOI) operators, 162 multivalued fractional stochastic integro-
Fractional order Liouvillian chaotic systems, differential equation, controllability of,
284 285 187 201
Fractional order Liu system, 413 414 solvability and optimal control results for
Fractional order Lorenz hyperchaotic system, FSDEs, 202 208
362 363 Fractional stochastic integro-differential
Fractional order Lorenz’s systems, 644 648 equation, 208 210
algorithm of topological synchronization of, Fractional theory, 37 38
648 651 Fractional-order Newton Leipnik system,
Fractional order Lu hyperchaotic system, 354 355
352 354, 356 357, 362 Fractional-order Volta’s System, 354
Fractional order models of motors, 440 Frequency-domain methods, 138
Fractional order nonlinear dynamical system, Fubini theorem, 201
stability of, 566 568 Fuzzy adaptive control method, 626 627
Fractional order operator implementation, 264 Fuzzy adaptive robust H ~ control, 603 607
Fractional order PMSM models. Fuzzy logic (FL), 250 251, 602 603
See Permanent magnet synchronous Fuzzy logic control (FLC) design, 260 263,
motor (PMSM) 263t, 264f
Fractional order Qi system, 352 354
Fractional order Riemann Liouville integral,
230 G
Fractional order Ro ¨ssler’s systems, 651 654 Gain scheduling, 249 250
algorithm of topological synchronization of, Gamma function, 119, 286, 490
655 656 Gao system, fractional order hyperchaotic,
Fractional order time-varying-delay systems, 327 328, 329f, 330f
133 Gauss map, 404
approximation of fractional order Gaussian distribution, 534 535
derivatives and consistent Generalized chaotic susceptible infected
initialization, 151 recovered epidemic model, 431 432
feedback stabilization, 148 150 Generalized discrete fractional logistic map,
based on time-delay-dependent stability dynamics of, 392 395
condition, 149 150 fixed points and range of ρ, 393
based on time-delay-independent stability stability analysis, 394 395
condition, 148 149 Generalized fractional logistic map design,
numerical examples, 151 154 399
preliminary results, 135 137 Generalized integer order sliding surface for
problem formulation, 137 138 second order plant, 259
stability analysis in presence of time- Generalized synchronization, 419, 626 627,
varying delays, 138 147 641
time-delay-dependent stability, 143 147 of fractional order chaotic systems,
time-delay-independent stability, 639 644
139 143 Genetic algorithm (GA), 252
Fractional predictor-corrector algorithm, 324 flow chart of, 265f