Value function-based approach to the scheduling of multiple controllers

Both gain scheduling and multiple model based control approaches are considered to be practical approaches for control of industrial nonlinear processes. However, the former ignores system dynamics and the latter is specific to the type of controller design and limited in its scope of application as practiced in industry. This paper proposes a value function-based strategy for switching among local controllers, thereby providing an effective global control policy for the entire operating regions. The suggested method selects the best one among a set of available control policies at each time step by evaluating the “value” function associated with the successive state when a particular control action instructed by a candidate policy is taken for a give state. The value function, which maps a state to its associated discounted infinite horizon cost-to-go, is obtained by solving the dynamic programming in an approximate way using closed-loop simulation or operational data and a function approximator. The proposed approach has the advantages that candidate controllers are general and the switching is performed not by a fixed heuristic rule but rigorously via dynamic programming. From the viewpoint of dynamic programming, the approach helps alleviate the curse of dimensionality with respect to the state space and action space. Optimal or approximately optimal switching rules can be learned without a model, which defines the state transitional rule. The approach is demonstrated on several different nonlinear control examples.