Simplified robust adaptive control of a class of time‐varying chaotic systems

Abstract

Purpose

To develop a simplified robust control scheme for a class of nonlinear time‐varying uncertain chaotic systems.

Design/methodology/approach

By means of input‐to‐state stability theory, a new robust adaptive control scheme is designed, which is simpler than the one proposed by Li et al. and applicable to a larger class of nonlinear systems. Only one parameter is adjusted in the controller and the scheme assures that all the signals remain bounded. The behavior of the proposed control scheme is also analyzed through simulations on the Rössler system.

Findings

By adjusting only one parameter in the controller and imposing only one mild assumption on the time‐varying parameters, the proposed control algorithm assures that all the signal remain bounded and that the state of the original system will follow a desired trajectory defined either by the trajectory and its first time derivative, or given by a reference model.

Research limitations/implications

The results are limited to a particular class of nonlinear systems where the dimension of the input vector is equal to the order of the system (dimension of the state vector).

Practical implications

The main advantage of the proposed method is that the modification introduced leads to a substantially simpler adaptive robust controller whose practical implementation will be easier.

Originality/value

The contribution of the proposed method is in the simplification of the control algorithm applied to a class of nonlinear time‐varying uncertain chaotic systems. This will be useful for control engineers to control complex industrial plants.

Citation

Estrada, J.L., Duarte‐Mermoud, M.A., Travieso‐Torres, J.C. and Beltrán, N.H. (2008), "Simplified robust adaptive control of a class of time‐varying chaotic systems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 2, pp. 511-519. https://doi.org/10.1108/03321640810847797