Optimal Control of an Inverted Pendulum Based on the New Method of Lyapunov Exponents Estimation

This text covers optimization of an inverted pendulum control system according to the new control performance assessment criterion based on the optimal control theory. The novel control performance index is founded on the method of the Largest Lyapunov Exponent estimation. The detailed description of the new method is provided. Model of the control object is presented. A simple controller is proposed. Parameters of the controller are optimized with respect to the novel criterion by means of the Differential Evolution method. Results of numerical simulations are presented. It is shown that the new criterion can be successfully applied when the regulation time is crucial, whereas somewhat larger overshoot is acceptable.