Exact penalizations for optimal control problems

Abstract: This talk presents a novel technique to solve optimal control problems with state constraints. 
The main approaches that have been introduced to study optimal control problems (e.g. Pontryagin’s Maximum Principle and Dynamic Programming) in their simplest formulations, deal with problems with no static constraints on the state. However, many control and optimization applications are naturally formulated using constraints.
We draw analogies with the theory of exact penalty functions, used in mathematical programming, to construct a systematic procedure to transform two classes of infinite horizon continuous time problems with state constraints to equivalent penalized unconstrained problems. We focus on a special class of systems with as many states as controls and subject to a set of equality constraints which reduces the ”control authority”, both in the case of linear and nonlinear control-affine systems. We present two approaches, discussing differences, advantages, and drawbacks.

Biography: Mr. Riccardo Grimaldi received his B.S. in Information Engineering and his M.S. in Control Systems Engineering from the University of Padova, Italy, in 2024. During his studies, he spent a term as a visiting student at Imperial College London, where he conducted research for his thesis on constrained optimal control, supervised by Prof. Alessandro Astolfi. His primary research interests include optimal control and nonlinear control theory.