Abstract

Bellman’s Dynamic Programming is a powerful theory for addressing multi-stage decision making problems, and has been used to solve the optimal control problem. However, its well-known shortcoming is the so-called ‘curse of dimensionality’, and optimal controllers designed rely on the solution of certain HJB equation, a PDE which is very hard, if not impossible, to solve for general nonlinear systems. Approximate/adaptive dynamic programming (ADP) has been introduced to overcome the curse of dimensionality and recently utilized in optimal controller design.

In this talk, we present a data-driven, non-model-based framework for optimal nonlinear control design using data collected from the control plan in question. Specifically, we present a novel methodology called ‘robust adaptive dynamic programming’ (robust-ADP), that aims to generalize ADP theory to nonlinear systems with both parametric and dynamic uncertainties. Linear and nonlinear controllers are designed with guaranteed robust stability and optimality. Examples from computational neuroscience and electric power systems are presented to illustrate the potentially wide applicability of the robust-ADP theory.