Page 695 - Mathematical Techniques of Fractional Order Systems

Index 667

Field Programmable Gate Array method, Fractional differential operators, 103 105
625 626 Fractional dynamical system, 347 348
Fitzhugh Nagumo equation, 41 43 Fractional fuzzy adaptive synchronization,
Fixed point theorem 599
Bohnenblust Karlin’s, 187 Fractional higher order stochastic
Leray Schauder, 186 187, 208 integrodifferential inclusions,
Fixed points analysis, 390 392 controllability of, 229
FO controllers, 160 161 discussion, 246
FOFSMCPD controller design, 252, 259 264, main results, 235 246
262f, 266 270, 267t preliminaries, 231 235
fractional order operator implementation, Fractional integral operator, 107
264 Fractional integration operator, 134 135
fuzzy logic control (FLC) design, 261 263 Fractional operator
Lyapunov stability criteria, stability review and approximation of, 322 325
analysis using, 260 261 Fractional order (FO) generalized discrete
FOPID, 160 maps, 375
“Forbidden” RHP sector, 82 FO generalized logistic map, 387 399
Forced-response decomposition, 75, 78 81 dynamics of generalized discrete
discussion and extensions, 95 98 fractional logistic map, 392 395
examples, 87 95 dynamics of Wu fractional logistic map,
model reduction, 85 86 388 392
approximation procedure, 85 86 generalized fractional logistic map
notation and preliminaries, 77 78 design, 399
stability conditions, 81 85 vertical scaling and zooming maps,
FOS-TVD, 134 396 399
4D integral order hyperchaotic system, FO generalized tent map, 399 403
356 357, 358f, 359 360 effects of main system parameters,
fractional order, 362 401 402
phase portraits of, 358f effects of scaling parameters, 402 403
FPGA implementations, 436 439 integer order generalized discrete maps,
Fractal geometry, 637 377 387
Fractional calculus, 1 2, 37 38, 103, maps with scaling and shaping
162 163, 185 187, 319 321, parameters, 387
347 349, 386, 561, 597 599, 625, maps with scaling parameters, 380 384
633 maps with shaping parameters, 384 387
basic definition and preliminaries for, maps with signed control parameter, 380
599 602 Fractional order 4D integral order
preliminaries of, 563 568 hyperchaotic system, 362
Fractional complex chaotic and hyperchaotic Fractional order adaptive laws (FOAL), 161,
systems, 285 167 168, 173
Fractional control, 1 2 Fractional order adaptive systems (FOAS),
Fractional derivative, 347 348 163
Caputo definition for, 323 324 Fractional order calculus preliminaries, 286
Grunwald Letnikov definition for, 323 Fractional order chaotic systems (FOCS), 321,
Gru ¨nwald Letnikov’s (GL) definition for, 350, 352, 428, 561 563
375 generalized synchronization of, 639 644
Riemann Liouville definition for, 323 topological synchronization, 641 644
Fractional differential equations (FDEs), 38, traditional methods, 639 641
185 187, 226, 229, 348 Gru ¨nwald Letnikov based FPGA
general numerical solution of, 634 636 implementation of, 438 439
Fractional differential inclusions, 185 186, HDL coder-based implementation of,
229 230 437 438