Cooperative Linear-Quadratic Mean Field Control and Hamiltonian Matrix Analysis
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In this thesis, we present a new methodology to investigate the existence and uniqueness of the solution of the Social Certainty Equivalence (SCE) equation system related to social optima in mean field linear-quadratic-Gaussian (LQG) control problems. The methodology involves Hamiltonian matrices and continuous-time algebraic Riccati equations (CARE), and it avoids the restrictive contractive assumption typically used in a fixed point approach. For computing the stabilizing solution of CARE, we also develop a computational method related to generalized eigenvectors and Schur vectors. We further extend our method to solve a linear-quadratic mean field game.Keywords:SCE Equation System; Hamiltonian Matrices; Continuous-time Algebraic Riccati Equations
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Copyright © 2017 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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chen-cooperativelinearquadraticmeanfieldcontrol.pdf | 2023-05-05 | Public | Download | |
chen-cooperativelinearquadraticmeanfieldcontrol-supplemental.zip | 2023-05-05 | Public | Download |