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. Using back propagation from the final co-state error and gradient descent, a method is devised which allows for training an adaptive fuzzy inference system to estimate values for the co-state variables converging to the optimal ones. In turn this implies that the controlled variables trajectories also converge to the optimal ones.
The approach allows finding a solution to the optimal control problem on-line, by training of the system, rather than by pre computing it. In particular, the use of an adaptive fuzzy inference system also will allow incorporating a priori knowledge about the optimal behavior of the co-state variable and track changes in the system.
