A bisection algorithm for fuzzy quadratic optimal control problems

In this paper we propose an iterative method to solve an optimal control problem, with fuzzy target and constraints. A solving method is developed for such type of problem, under quite general hypotheses. The algorithm is developed in such a way as to satisfy as best as possible both the target function and all the constraints. It consists of an iterative procedure, which modifies the admissible region with the aim to increase at each step the global performance. Even if the procedure is quite general, the algorithm can be applied only if a method exists to solve a crisp parametric sub-problem obtained by the original one. This is the case for a quadratic-linear target function with linear constraints, for which some well established solvable methods exist for the crisp associated sub-problem. The algorithm is particularized to this case, and a numerical test is proposed, showing the quick convergence to the optimal solution.