Evolutionary multiobjective optimization based control strategies for an inverted pendulum on a cart

We report the design and implementation of three different multiobjective optimization based control strategies for the cart pole system: l) a multiobjective version of the classic quadratic regulator problem, 2) a multiobjective formulation of a standard H_infin controller and 3) a mixed norm H₂/H_infin controller design problem in a multiobjective setting. The optimization problems have been solved using an elitist Pareto dominance based multiobjective genetic algorithm developed by the authors. Input saturation and bounds on state variables have been incorporated in the problem. It is shown by way of an example that the solution to the scalarized version of multiobjective linear regulator design problem is contained in the set of solutions of the vector objective formulation of the same multiobjective design problem. Finally the validity of the solutions was tested on a real cart pole regulator system.