Quadratic optimal fuzzy control

Abstract

One presents a fuzzy logic approach for optimal control of discrete-time nonlinear dynamic systems with a quadratic criterion. The approach is based on Pontryagin’s Minimum Principle. It uses back-propagation from the final co-state error and gradient descent to estimate a sequence of values for the co-state variables converging to the optimal ones. This implies that the controlled variables trajectories converge to the optimal ones. The estimator is implemented through an adaptive fuzzy inference system. The approach allows one to find a solution to the optimal control problem on-line by training the system, rather than by pre computing it. The use of an adaptive fuzzy inference system will allow to incorporate a priori knowledge about the optimal behavior of the co-state variables and to track changes in the system.