Prescribed-time control of Hybrid Distributed Parameter Systems – PH-DIPSY

PH-DIPSY is a fundamental research project that focuses on the development of novel control and estimation strategies for complex physical systems modeled by Distributed Parameter Systems (DPS) subject to hybrid phenomena (such as switching dynamics). The project's ultimate goal is to achieve guaranteed prescribed-time convergence. The project aims to tackle fundamental problems in hybrid systems, design hybrid controllers and observers for DPS, and utilize time-varying tools to achieve prescribed-time stabilization and estimation. We will explore various types of DPS, including Partial Differential Equations (PDEs) of hyperbolic and parabolic types, coupled PDE-PDEs, and coupled PDE-Ordinary Differential Equations (ODEs), that may be subject to switching phenomena. To demonstrate the applicability of our methodology and theoretical results, we will apply our strategies to the problem of traffic congestion modeled by a Hybrid DPS.