2020/04/07 by Sachin Shivakumar, Amritam Das, Shivakumar, Sachin +5
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2004.03638
openalex publication_date 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a convex formulation of H∞-optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE) system and show that stability and H∞ performance of the PIE system implies that of the ODE-PDE system. We then construct a dual PIE system and show that asymptotic stability and H∞ performance of the dual system is equivalent to that of the primal PIE system. Next, we pose a convex dual formulation of the stability and H∞-performance problems using the Linear PI Inequality (LPI) framework. LPIs are a generalization of LMIs to Partial Integral (PI) operators and can be solved using PIETOOLS, a MATLAB toolbox. Next, we use our duality results to formulate the stabilization and H∞-optimal state-feedback control problems as LPIs. Finally, we illustrate the accuracy and scalability of the algorithms by constructing controllers for several numerical examples.