Speed gradient control of chaotic continuous-time systems

Abstract

Abstruct-The problems of synchronization and control of chaotic systems with uncertain parameters are considered as those of nonlinear adaptive control. To solve these problems for continuous-time systems the so called speed-gradient method is applied. As an example the problem of master-slave synchronization of the two forced Duffing's systems is considered.

Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations

“…The first idea of synchronizing two identical chaotic systems with different initial conditions was introduced by Pecora and Carroll [6], and the method was realized in electronic circuits. The methods for synchronization of the chaotic systems have been widely studied in recent years, and many different methods have been applied theoretically and experimentally to synchronize chaotic systems, such as feedback control [7][8][9][10][11][12], adaptive control [13][14][15][16][17], backstepping [18] and sliding mode control [19,20]. Recently, the theory of incremental input-to-state stability to the problem of synchronization in a complex dynamical network of identical nodes, using chaotic nodes as a typical platform was studied in [21].…”

Swinging Up a Pendulum by Energy Control *

“…the pendulum, see Furuta and Yamakita (1991), Furuta, Yamakita and Kobayashi (1992), Wiklund, Kristenson and A s stroK m (1993), Yamakita, Nonaka and Furuta (1993), Yamakita, Nonaka, Sugahara and Furuta (1994), Spong (1995), Spong and Praly (1995), Chung and Hauser (1995), Yamakita, Iwashiro, Sugahara and Furuta (1995), Wei, Dayawansa and Levine (1995), Borto! (1996), Lin, Saberi, Gutmann and Shamash (1996), Fradkov and Pogromsky (1996), Fradkov, Makarov, Shiriaev and Tomchina (1997), Lozano and Fantoni (1998). Pendulums are also excellently suited to illustrate hybrid systems (Guckenheimer, 1995;A s stroK m, 1998) and control of chaotic systems (Shinbrot, Grebogi & Wisdom, 1992).…”

Adaptive neuro-genetic control of chaos applied to the attitude control problem

“…Traditional adaptive control theory is based mainly around the model reference adaptive control method [6][7][8][9]. Despite the above, one must not underestimate or ignore conventional control (and adaptive control) theory, since it offers perhaps the only way of providing theoretical stability guarantees for the control of certain classes of nonlinear (even chaotic) dynamic systems (for example, see Refs [10][11][12][13]). This work and other work in the neurocontrol area aims to achieve control of dynamic systems for which existing control theory finds difficulties.…”