TY - CHAP

T1 - Robust adaptive control design for chaotic continuous-time systems

AU - Ohmori, Hiromitsu

AU - Ito, Yoshinobu

AU - Sano, Akira

PY - 1996/12/1

Y1 - 1996/12/1

N2 - This paper presents a new nonlinear robust adaptive control design for continuous-time chaos systems in the presence of disturbances. The scheme of adaptation is based on the concept of dynamic certainty equivalence (DyCE) and incorporates the design of a fixed(non-adaptive) compensator in the error feedback loop. The fixed compensator is used to realize the high performance of a tracking. The key features of our control design are: (1) use of H∞ minimization design for the fixed compensator, and (2) use of a robust high-order estimator with dead-zone. By using our proposed nonlinear adaptive controller, it can be shown that the chaotic signal of the system dynamics tends to be driven into a well controlled periodic state or a steady state, and conversely, the periodic signal asymptotically converges to chaotic signal. Then it can be seen that our scheme is one of the unified approaches for controlling chaos. The mathematical proof of stability for the total closed loop system is guaranteed. Finally in order to verify the effectiveness of the proposed method, numerical simulations are shown.

AB - This paper presents a new nonlinear robust adaptive control design for continuous-time chaos systems in the presence of disturbances. The scheme of adaptation is based on the concept of dynamic certainty equivalence (DyCE) and incorporates the design of a fixed(non-adaptive) compensator in the error feedback loop. The fixed compensator is used to realize the high performance of a tracking. The key features of our control design are: (1) use of H∞ minimization design for the fixed compensator, and (2) use of a robust high-order estimator with dead-zone. By using our proposed nonlinear adaptive controller, it can be shown that the chaotic signal of the system dynamics tends to be driven into a well controlled periodic state or a steady state, and conversely, the periodic signal asymptotically converges to chaotic signal. Then it can be seen that our scheme is one of the unified approaches for controlling chaos. The mathematical proof of stability for the total closed loop system is guaranteed. Finally in order to verify the effectiveness of the proposed method, numerical simulations are shown.

UR - http://www.scopus.com/inward/record.url?scp=0030377881&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030377881&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0030377881

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2355

EP - 3592

BT - Proceedings of the IEEE Conference on Decision and Control

A2 - Anon, null

T2 - Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4)

Y2 - 11 December 1996 through 13 December 1996

ER -