A Simple Approximate Dynamic Programing Based on Integral Sliding Mode Control for Unknown Linear Systems with Input Disturbance

This work presents an adaptive optimal control algorithm based integral sliding mode control law for a class of continuous-time systems with input disturbance or uncertain and unknown parameters. The main objective is to find a general form of integral sliding mode control law can assure that the system states are forced to reach a sliding surface in the initial finite time. Then, an adaptive optimal control based on the approximate dynamic programming method is responsible for the robust stability of the closed-loop system. Finally, the theoretical analysis and simulation results demonstrate the performance of the proposed algorithm for a wheel inverted pendulum system.