TE-03: Optimal Control and Applications I
Stream: Optimal Control and Applications
Room: Nash
Chair(s): Theodore Trafalis

Optimal control problems on stratified spaces
Othmane Jerhaoui
We are interested in control problems on stratified spaces. In such problems, the state variable space is partitioned in different manifolds with boundary glued together along their boundaries. Each manifold is associated with a compact control set, a controlled dynamics and a cost function. We are interested in analyzing the set of trajectories, and in characterizing the value function. Moreover, we will discuss some numerical schemes for such control problems. Finally, we discuss some generalizations of this problem on some metric spaces resembling this setting called Aleksandrov spaces.

Zero-Sum Deterministic Differential Game in Infinite Horizon with Continuous and Impulse Controls
HAFID LALIOUI
We consider a zero-sum deterministic differential game with two players adopting both continuous and impulse controls in infinite time horizon. The form of impulses supposed to be of general term (depends on non linear functions) and the cost of impulses being arbitrary (depends on the state of the system). We use the dynamic programming principle (DPP) and the viscosity solution approach to prove that the value function turns out to be, under Isaacs condition, the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman-Isaacs (HJBI) variational inequalities (QVIs).

Mixed Zero-Sum Stochastic Differential Game and Doubly Reflected BSDEs with a Specific Generator.
Nacer OURKIYA
This paper studies the mixed zero-sum stochastic differential game problem. We allow the functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. We show the existence of solution for this doubly reflected BSDEs and we prove the existence of a saddle-point of the game. Moreover, in the Markovian framework we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation.

Learning-Based Nonlinear H-infinity Control via Game-Theoretic Differential Dynamic Programming
Wei Sun, Theodore Trafalis
We present a learning-based nonlinear H-inf control algorithm that guarantees system performance under learned dynamics and disturbance estimate. The Gaussian Process regression is utilized to update the dynamics of the system and provide disturbance estimate based on data gathered by the system. A soft-constrained differential game associated with the disturbance attenuation problem in nonlinear H-inf control is then formulated to obtain the nonlinear H-inf controller. The differential game is solved through the Game-Theoretic Differential Dynamic Programming algorithm in continuous time.