PI adaptive LS-SVR control scheme with disturbance rejection for a class of uncertain nonlinear systems

Developing controller for uncertain nonlinear systems in the presence of disturbances is an important and still challenging problem. Adaptive control method asserts to adapt system parameters against uncertainties, if only uncertainties change sufficiently slowly. Alternatively, if uncertainties stay in known bounds, robust control approaches claim to ensure system stability. In this paper, a Proportional–Integral (PI) indirect adaptive Least Squares Support Vectors Regression (LS-SVR) control scheme for a class of uncertain nonlinear system in the presence of large and fast disturbances is proposed. The LS-SVR is used to approximate the nonlinear uncertainty which must be bounded, whereas in comparison to robust control methodologies no requirement needs for bounds to be known. The asymptotic stability of the control scheme is proved by using Lyapunov synthesis. The simulation study is performed on a second-order inverted pendulum system in the presence of fast against slow and large against small disturbances to demonstrate the effectiveness of the proposed control scheme.