Stabilization and Optimal Control of Interconnected SDE - Scalar PDE System

Abstract: In this talk, I will present my work on the optimal control and stabilization of a system composed of an interconnected Stochastic Differential Equation (SDE) and a Scalar Partial Differential Equation (PDE), with control applied at the boundary of the PDE. Such systems can be found in practical scenarios, such as in temperature control of a building where heat must be transmitted from a distance. I will begin with an introduction to boundary control of PDEs, emphasizing the backstepping method—a powerful technique for designing boundary controllers that stabilize PDEs. In particular, we will see how backstepping can be employed to stabilize a system of coupled hetero-directional transport equations. Next, we will examine the complete system where this PDE is connected with an SDE at the boundary. I will show how backstepping transforms this problem into an equivalent control problem for an input-delayed SDE, making it more tractable. Finally, I will discuss the implications of input delays in controlling SDEs with additive noise, particularly how these delays impact system performance and the strategies we can use to mitigate these effects.

numerical analysisoptimization and control

Audience: researchers in the topic

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CAM seminar

Series comments: Online streaming via zoom on exceptional cases if requested. Please contact the organizers at the latest Monday 11:45.