Min–max control using parametric approximate dynamic programming

This study presents a computationally efficient approximate dynamic programming approach to control uncertain linear systems based on a min–max control formulation. The optimal cost-to-go function, which prescribes an optimal control policy, is estimated using piecewise parametric quadratic approximation. The approach requires simulation or operational data only at the bounds of additive disturbances or polyhedral uncertain parameters. This strategy significantly reduces the computational burden associated with dynamic programming and is not limited to a particular form of performance criterion as in previous approaches.