Nonlinear control of dynamical systems from time series

被引:17
作者
Petrov, V
Showalter, K
机构
[1] Department of Chemistry, West Virginia University, Morgantown, WV
关键词
D O I
10.1103/PhysRevLett.76.3312
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Feedback control of multidimensional, nonlinear single-input single-output systems is formulated in terms of an invariant hypersurface in the delayed state space of a system observable and a control parameter. The surface is created directly from the response of the system to random perturbations, providing a model-independent nonlinear control algorithm. The algorithm can be used to stabilize unstable states or to drive a system to any particular objective state in a minimum number of steps.
引用
收藏
页码:3312 / 3315
页数:4
相关论文
共 19 条
[11]   CONTROL OF CHAOS IN AN ELECTROCHEMICAL-CELL [J].
PARMANANDA, P ;
SHERARD, P ;
ROLLINS, RW ;
DEWALD, HD .
PHYSICAL REVIEW E, 1993, 47 (05) :R3003-R3006
[12]   TRACKING UNSTABLE PERIODIC-ORBITS IN THE BELOUSOV-ZHABOTINSKY REACTION [J].
PETROV, V ;
CROWLEY, MJ ;
SHOWALTER, K .
PHYSICAL REVIEW LETTERS, 1994, 72 (18) :2955-2958
[13]   TRACKING UNSTABLE TURING PATTERNS THROUGH MIXED-MODE SPATIOTEMPORAL CHAOS [J].
PETROV, V ;
METENS, S ;
BORCKMANS, P ;
DEWEL, G ;
SHOWALTER, K .
PHYSICAL REVIEW LETTERS, 1995, 75 (15) :2895-2898
[14]   STABILIZING AND CHARACTERIZING UNSTABLE STATES IN HIGH-DIMENSIONAL SYSTEMS FROM TIME-SERIES [J].
PETROV, V ;
MIHALIUK, E ;
SCOTT, SK ;
SHOWALTER, K .
PHYSICAL REVIEW E, 1995, 51 (05) :3988-3996
[15]   CONTROLLING CHAOS IN THE BELOUSOV-ZHABOTINSKY REACTION [J].
PETROV, V ;
GASPAR, V ;
MASERE, J ;
SHOWALTER, K .
NATURE, 1993, 361 (6409) :240-243
[16]   DYNAMIC CONTROL OF A CHAOTIC LASER - EXPERIMENTAL STABILIZATION OF A GLOBALLY COUPLED SYSTEM [J].
ROY, R ;
MURPHY, TW ;
MAIER, TD ;
GILLS, Z ;
HUNT, ER .
PHYSICAL REVIEW LETTERS, 1992, 68 (09) :1259-1262
[17]   CONTROLLING CHAOS IN THE BRAIN [J].
SCHIFF, SJ ;
JERGER, K ;
DUONG, DH ;
CHANG, T ;
SPANO, ML ;
DITTO, WL .
NATURE, 1994, 370 (6491) :615-620
[18]   USING SMALL PERTURBATIONS TO CONTROL CHAOS [J].
SHINBROT, T ;
GREBOGI, C ;
OTT, E ;
YORKE, JA .
NATURE, 1993, 363 (6428) :411-417
[19]   CONTROLLING CHAOS USING TIME-DELAY COORDINATES VIA STABILIZATION OF PERIODIC-ORBITS [J].
SO, P ;
OTT, E .
PHYSICAL REVIEW E, 1995, 51 (04) :2955-2962