On the Policy Algebraic Equation in the Linear Quadratic Regulator problem

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• Mario Sassano, University of Rome "Tor Vergata"
• Thursday 16 May 2024, 14:00-15:00
• 909b.

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Abstract: To study dynamic optimization problems two main strategies have emerged in the last century: dynamic programming (DP) and Pontryagin’s minimum principle (PMP). The former characterizes the solution by shaping the dynamics in a closed loop via the selection of a feedback input, at the price however of the solution to partial differential equations in the presence of nonlinear systems. The latter instead provides extended dynamics that must be satisfied by the optimal process, for which boundary conditions should be determined. The objective of this talk is to provide a unified perspective on these two strategies, beyond the classic sensitivity conditions, by reconciling the underlying sources of information: knowledge of the complete initial condition from DP and that of the optimal dynamics from PMP . The derived conditions provide further insights on the structure of the underlying solution and on the strategies that permit its computation. In particular, the conditions allow establishing a polynomial algebraic equation, referred to as the Policy Algebraic Equation, expressed in the gain of the optimal policy alone. At the price of higher degrees, the equation has dimensions typically much smaller than the size of the classic ARE and it permits the direct computation of the optimal feedback gain (i.e. the actor) without the need for the simultaneous computation of the optimal cost (i.e. the critic).

Biography: Mario Sassano was born in Rome, Italy, in 1985. He received a Bachelor’s degree cum laude in Automation engineering and the Master’s degree cum laude in Systems and Control engineering from the University of Rome “La Sapienza”, Rome, Italy, in 2006 and 2008, respectively. In July 2012 he was awarded a Ph.D. degree in Control Theory by Imperial College London, UK, where he had been a research assistant at the Department of Electrical and Electronic Engineering (2009-2012). During this period he visited several times the Institute for Design and Control of Mechatronical Systems of the Kepler University in Linz, Austria. Since May 2022 he is an Associate Professor at the University of Rome “Tor Vergata”, Italy. He is a member of the IFAC Technical Committee 2.1 on Control Design. He serves as Associate Editor of the IEEE Control Systems Letters, of the European Journal of Control, of the IEEE CSS Conference Editorial Board and of the EUCA Conference Editorial Board.

This talk is part of the Control and Power Seminars series.

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• 909b
• Andrea Picciau's list
• Control and Power Seminars

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