From robust model predictive control to stochastic optimal control and approximate dynamic programming: A perspective gained from a personal journey

Developments in robust model predictive control are reviewed from a perspective gained through a personal involvement in the research area during the past two decades. Various min–max MPC formulations are discussed in the setting of optimizing the “worst-case” performance in closed loop. One of the insights gained is that the conventional open-loop formulation of MPC is fundamentally flawed to address optimal control of systems with uncertain parameters, though it can be tailored to give conservative solutions with robust stability guarantees for special classes of problems. Dynamic programming (DP) may be the only general framework for obtaining closed-loop optimal control solutions for such systems. Due to the “curse of dimensionality (COD),” however, exact solution of DP is seldom possible. Approximate dynamic programming (ADP), which attempts to overcome the COD, is discussed with potential extensions and future challenges.