Robust Adaptive Fault-Tolerant PID Control of MIMO Nonlinear Systems With Unknown Control Direction

This paper shows that the structurally simple and computationally inexpensive PID control, popular with single-input single-output (SISO) linear time-invariant systems, can be generalized and extended to control nonlinear multi-input multi-output (MIMO) systems with nonparametric uncertainties and actuation failures. By utilizing the Nussbaum-type function and the matrix decomposition technique, nonsquare systems with unknown control direction are also considered. Furthermore, with the proposed analytic algorithms for adaptively tuning PID gains, the resultant PID control can be made robust, adaptive, and faulttolerant, and applicable to nonlinear systems with nonvanishing uncertainties and unexpected actuation faults. Both theoretical analysis and numerical simulation verify the effectiveness and benefits of the design.