Fuzzy Adaptive Control of Uncertain MIMO Chaotic Systems with Unknown Control Direction

This paper presents an adaptive controller for MIMO chaotic systems with system uncertainties and unknown control direction. In the controller design, the matrix decomposition theory is used, and we decompose the control gain matrix into a positive matrix, a diagonal matrix whose diagonal entries are +1 or -1, and a unity upper triangular matrix. To handle the unknown control direction (i.e., the unknown sign of the control gain matrix), we use the Nussbaum-type function. In addition, we propose an adaptation law named proportional integral (PI) law to update the parameters of the fuzzy system. The stability of the controlled system is proven strictly. Finally, simulation results are presented.

Automated summary

This paper presents an adaptive controller for MIMO chaotic systems with system uncertainties and unknown control direction. Matrix decomposition theory and Nussbaum-type function are used to handle the unknown control direction, and a proportional integral (PI) law is proposed to update the parameters of the fuzzy system. The stability of the controlled system is strictly proven, and simulation results are provided.