Optimal Adaptive Sliding Mode Control for a Class of Nonlinear Affine Systems

This paper presents an optimal robust adaptive technique for controlling a certain class of uncertain nonlinear affine systems‎. ‎The proposed approach combines sliding mode control‎, ‎a linear quadratic regulator for optimality, and gradient descent as an adaptive controller‎. ‎ The convergence of the sliding mode control process is proven using two theorems based on the Lyapunov function. Simulation results for pendulum and inverted pendulum systems demonstrate that the proposed method outperforms both the linear quadratic regulator technique and ‎the‎ ‎sliding‎ ‎mode‎ ‎control regarding reduced chattering and improved reaching time‎.