Heuristic Model-Free Optimal Controller Design using Gradient Based PSO

Designing nonlinear optimal controllers such as Minimum Variance Controller (MVC) has many difficulties. Main difficulties are 1) in order to design controller; the explicit relations between outputs and inputs must be executable. This relation is defined as implicitly in the nonlinear models; 2) learning controller is a high dimensional-multimodal optimization task and search space can be extremely rugged and has many local minima. In this paper, in order to overcome these disadvantages, the model-free optimal controller scheme is utilized. In a model-free controller, as the system model is not available, the gradient of the cost function cannot be executed. Instead, in this paper, a relation between gradient of the controller with gradient of the system model is derived by inverse lemma. The controller structure is selected to be neural network. Then, the gradient based PSO (GPSO) is proposed to be a learning controller. GPSO has both advantages of global searching and convergence properties. The application of the methodology to the empirical CSTR model indicates that this approach gives very credible estimates of the controller. The simulation results indicate that the proposed method can be more accurate than existing methods.