A dynamic programming approach to solving constrained linear–quadratic optimal control problems

The solution of a constrained linear–quadratic regulator problem is determined by the set of its optimal active sets. We propose an algorithm that constructs this set of active sets for a desired horizon N from that for horizon N−1. While it is not obvious how to extend the optimal feedback law itself for horizon N−1 to horizon N, a simple relation between the optimal active sets for two successive horizon lengths has recently been established. Essentially, we show how to use this recent result to improve the efficiency of existing active set enumeration algorithms.