Cost-to-travel functions: A new perspective on optimal and model predictive control

This paper concerns a class of functions, named cost-to-travel functions, which find applications in model-based control. For a given (potentially nonlinear) control system, the cost-to-travel function associates with any given start and end point in the state space and any given travel duration the minimum economic cost of the associated point-to-point motion. Cost-to-travel functions are a generalization of cost-to-go functions, which are often used in the context of dynamic programming as well as model predictive control. We discuss the properties of cost-to-travel functions, their relations to existing concepts in control such as dissipativity, but also a variety of control-theoretic applications of this function class. In particular, we discuss how cost-to-travel functions can be used to analyze the properties of economic model predictive control with return constraints.