Robust Passivity Cascade Technique-Based Control Using RBFN Approximators for the Stabilization of a Cart Inverted Pendulum

Abstract

This paper proposes a novel passivity cascade technique (PCT)-based control for nonlinear inverted pendulum systems. Its main objective is to stabilize the pendulum’s upward states despite uncertainties and exogenous disturbances. The proposed framework combines the estimation properties of radial basis function neural networks (RBFNs) with the passivity attributes of the cascade control framework. The unknown terms of the nonlinear system are estimated using an RBFN approximator. The performance of the closed-loop system is further enhanced by using the integral of angular position as a virtual state variable. The lumped uncertainties (NN—Neural Network approximation, external disturbances and parametric uncertainty) are compensated for by adding a robustifying adaptive rule-based signal to the PCT-based control. The boundedness of the states is confirmed using the passivity theorem. The performance of the proposed approach was assessed using a nonlinear inverted pendulum system under both nominal and disturbed conditions.