Session: Dynamic Optimization: Deterministic and Stochastic Continuous-time Models II
Chair: Cristopher Hermosilla
Cluster: Multi-agent Optimization and Games
Talk 1: Average Cost Problems Subject to State Constraints
Speaker: Nathalie Khalil
Abstract: Control systems with unknown parameters provide a natural framework for modeling uncer- tainties in various applications. In this work, we focus on pathwise state-constrained optimal control problems where these unknown parameters affect the system’s dynamics, cost function, endpoint constraint, and state constraint. The objective is to minimize a cost criterion expressed in integral form, the so-called “average cost”, with the cost function evaluated relative to a refer- ence probability measure defined over the set of unknown parameters. For this class of problems, we derive necessary optimality conditions. By using an average cost criterion, this approach offers an alternative to traditional minimax or robust optimization methods.
Talk 2: Degeneration in Optimal Control Problems with Non-regular Mixed Constraints
Speaker: Karla Cortez
Abstract: In this talk we will discuss the emergence of the degeneration phenomenon in the necessary conditions derived in recent literature on optimal control problems with non-regular mixed constraints. We will examine how the lack of regularity in these constraints can lead to trivial multipliers, hindering the applicability of classical optimality conditions. To address this issue, we will present non-degeneration conditions that ensure the existence of non-trivial multipliers in these problems and we will illustrate their potential through examples and preliminary results. The talk will conclude with a discussion on future directions for extending and validating these findings.
Talk 3: Uniqueness of Multipliers in Optimal Control Problems
Speaker: Jorge Becerril
Abstract: In this talk, we explore conditions for the uniqueness of multipliers in optimal control problems across different settings. We start with the simplest case involving only isoperimetric constraints, highlighting the connection between uniqueness and key concepts such as regularity and normality. Next, we examine optimal control problems with regular mixed constraints, focusing on piecewise continuous controls. In this context, the continuity assumption allows us to relate uniqueness to the observability of a certain no-input linear system. Under additional assumptions, using results from viability theory, we can establish a one-to-one correspondence between the set of Lagrange multipliers and the initial value of certain set-valued function. Lastly, we discuss ongoing efforts to extend these findings to the case of essentially bounded controls.
