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Nonlinear Control Structure Design using Grammatical Evolution and Lyapunov Equation based Optimization

A new method for the automated synthesis of nonlinear control laws for nonlinear control systems using grammatical evolution is presented. The controller structure, its parameterization and a quadratic Lyapunov function are the result of a nonlinear, nonconvex optimization process. Evolutionary algorithms based on grammatical evolution are used to find candidates for the control law. These are evaluated using a fitness function incorporating eigenvalue specifications on the linearized closed loop system and bounds on the control input signals. The guaranteed domain of attraction subject to the closed loop performance and stability specifications is maximized by evaluating the solution of the Lyapunov equation on the nonlinear system. The method is tested on two different control systems that contain different types of nonlinearities. The results show that the proposed approach is capable of outperforming state of the art methods by providing stronger stability guarantees and/or better closed loop performance while making less restrictive assumptions.