INVERTED PENDULUM ANGLE TRACKING CONTROL SUBJECT TO UNCERTAINTIES AND STOCHASTIC PERTURBATIONS

The tracking control problem of an inverted pendulum on a cart, operating under modelling uncertainties and stochastic perturbations is addressed. Suitable neural network designs and adaptive bounding algorithms are used to approximate all the unknown nonlinear uncertainties and stochastic disturbances. This scheme is integrated into the proposed nonlinear controller in order to achieve the angle tracking on a desired reference function. Stability analysis based on Lyapunov functions proves that all the error variables are bounded in probability; simultaneously, the mean square tracking error enters in finite-time in an arbitrarily selected small region around the origin wherein it remains thereafter. The controller performance is evaluated by simulation results. Furthermore, the design procedure and the effect of its parameters' selection are discussed.