Fuzzy Optimal Control for Multistage Fuzzy Systems

In the case that a system is affected by fuzzy factors, a fuzzy optimal-control problem is proposed. A fuzzy optimal-control problem for a multistage fuzzy system is considered to optimize the expected value of a fuzzy objective function subject to a multistage fuzzy system where, at every stage, the system is disturbed by a fuzzy variable. Based on Bellman´s Principle of Optimality, a recurrence equation for the problem is presented. A linear quadratic fuzzy optimal-control problem is shown to have an exact solution by the recurrence equation if the system is affected by triangular fuzzy variables. For general cases, two methods, the hybrid intelligent algorithm and the finite-search method, are established to approximate the solutions of the problem. Finally, an example is used to show that these two methods are effective to solve a fuzzy optimal-control problem for a multistage fuzzy system.