Stochastic Gradient-Based Optimization of Control Parameters for Uncertain Linear Systems with Sliding Mode Control and LQR

The objective of this article is to investigate the efficacy of an optimal control method for linear systems using first-order sliding mode control, along with the incorporation of a Linear Quadratic Regulator (LQR), in controlling the behavior of a pendulum. Our focus is on developing a control law that is both optimal and robust, capable of ensuring precision, convergence, speed, and asymptotic stabilization of the system even in the presence of uncertainties and perturbations, while minimizing chattering. To validate our proposed control strategy, we present simulation results that demonstrate its usefulness and effectiveness.