Convex optimization in fuzzy predictive control

Fuzzy predictive control combines conventional model-based predictive control with techniques from fuzzy multicriteria decision making. Information regarding the (fuzzy) goals and the (fuzzy) constraints of the control problem is combined by using a decision function from the fuzzy set theory. The selection of this function is important as it reflects the goals of the optimization and the requirements of the system expressed by system designers and process operators. Moreover,the system response can be improved significantly by a proper selection of the decision function. However, many of these functions give rise to a non-convex optimization problem which is not tractable by conventional optimization techniques. Thus, the technique remains applicable only to processes with slow dynamics and large sampling time. This paper presents a set of conditions for linear systems for which the fuzzy predictive control problem results in a convex optimization problem whose solution can be found with low computational effort. It is shown that the use of triangular membership functions on the predicted error and their aggregation using the Yager t-norm results in a convex optimization problem. Under these conditions, fuzzy predictive control can be applied to a broader class of systems with faster dynamics than conventional predictive control.