Convex dynamic programming for hybrid systems

Sven Hedlund, Lund Institute of Technology, Sweden, Department of Automatic Control

This talk presents a method for optimal control of hybrid systems. The Bellman equation is extended to a hybrid version that covers discrete and continuous dynamics. The equalities are replaced by inequalities such that every solution to these inequalities gives a lower bound on the optimal value function.

A discretization of these "hybrid Bellman inequalities" leads to a convex optimization problem in terms of finite-dimensional linear programming. From the solution, a value function that preserves the lower bound property can be constructed. An approximation of the optimal feedback control law is given and tried on some examples.