Polynomial LQG and H∞ controller synthesis: a genetic algorithm solution

The synthesis of linear-quadratic-Gaussian (LQG) and H _∞ optimal controllers for linear systems is discussed. Analytical solutions for these problems are available using polynomial, Wiener-Hopf and state-space techniques. An alternative, computationally simple, approach is presented. It is based on genetic algorithms. Controller parameters are encoded as binary strings, and the control parameter space is searched using the elementary string operators of reproduction, crossover and mutation. Each structure (parameter set) explored is evaluated by explicitly calculating the value of the optimization objective function