State reachability analysis of fuzzy models

For a discrete-time system modeled by fuzzy implications, a state xf is reachable from another state x0 if there exists a sequence of control signals to drive the fuzzy model from x0 to xf at some final time instant. It will be shown that if the product-operation rule, the exponential shape membership functions, and the center-of-area defuzzification method are used, then the state reachability problem of fuzzy models can be resolved by solving a sequence of nonlinear programming problems. If the objective function of any of the nonlinear programming problems is found to be zero, then the state xf is reachable from the state x0 and the corresponding control signals can be determined. Otherwise, xf is unreachable from x0 and there exists no control signals to drive the fuzzy model from x0 to xf.