Online Optimal Controller Design using Evolutionary Algorithm with Convergence Properties

Many real-world applications require minimization of a cost function. This function is the criterion that figures out optimally. In the control engineering, this criterion is used in the design of optimal controllers. Cost function optimization has difficulties including calculating gradient function and lack of information about the system and the control loop. In this article, for the first time, gradient memetic evolutionary programming is proposed for minimization of non-convex cost functions that have been defined in control engineering. Moreover, stability and convergence of the proposed algorithm are proved. Besides, it is modified to be used in online optimization. To achieve this, the sign of the gradient function is utilized. For calculating the sign of the gradient, there is no need to know the cost-function’s shape. The gradient functions are estimated by the algorithm. The proposed algorithm is used to design a PI controller for nonlinear benchmark system CSTR (Continuous Stirred Tank Reactor) by online and offline approaches. KEYWORD: Nonlinear Optimal Controller, GMEP (Gradient Memetic Evolutionary Programming), Sign of Gradient Function, Online Optimization, Nonlinear Benchmark CSTR.