Markov jump linear systems in mixed time domain

• Grant number: 24/05642-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2024
• End date: May 31, 2026
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Eduardo Fontoura Costa
• Grantee: Hugo Gielamo Próspero
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Dynamical systems can be applied in various fields and have been extensively studied for decades. In particular, Linear Dynamical Systems with parameters subject to Markovian jumps (hereafter referred to as SLSM) are linear systems whose dynamics change abruptly, following a Markov chain, which helps to model practical situations, such as sensor or actuator failures. SLSMs feature a nice tradeoff between complexity and usefulness, allowing, e.g., to find optimal control solutions via algebraic Riccati equations. Dynamic systems have an independent variable $t$, often representing time, which can be a variable in the discrete domain (i.e., $t\in\mathbb{N}$) or continuous domain (i.e., $t\in\mathbb{R}$). SLSMs are traditionally studied separately in these domains. In an effort for a unifying framework, we recently introduced a class of SLSMs whose variable $t$ is in ``mixed-time'' (SLSM-tm for brevity), switching between continuous and discrete; for example, $t\in[0,1.5], 2,3,[3,5.2]$, with random switching instants. This work addresses the so-called linear-quadratic optimization problem for SLSM-tm. The problem formulation, expected difficulties, approach, specific objectives, and timetable are detailed in this project.