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Devansh AgrawalEmail / GitHub / Google Scholar / LinkedIn |
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Reformulations of Quadratic Programs for Lipschitz Continuity |
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Devansh Agrawal, Haejoon Lee, and Dimitra Panagou
Optimization-based controllers often lack regularity guarantees, such as Lipschitz continuity, when multiple constraints are present. When used to control a dynamical system, these conditions are essential to ensure the existence and uniqueness of the system’s trajectory. Here we propose a general method to convert a Quadratic Program (QP) into a Second-Order Cone Problem (SOCP), which is shown to be Lipschitz continuous. Key features of our approach are that (i) the regularity of the resulting formulation does not depend on the structural properties of the constraints, such as the linear independence of their gradients; and (ii) it admits a closed-form solution under some assumptions, which is not available for general QPs with multiple constraints, enabling faster computation. We support our method with rigorous analysis and examples. |
AbstractOptimization-based controllers often lack regularity guarantees, such as Lipschitz continuity, when multiple constraints are present. When used to control a dynamical system, these conditions are essential to ensure the existence and uniqueness of the system’s trajectory. Here we propose a general method to convert a Quadratic Program (QP) into a Second-Order Cone Problem (SOCP), which is shown to be Lipschitz continuous. Key features of our approach are that (i) the regularity of the resulting formulation does not depend on the structural properties of the constraints, such as the linear independence of their gradients; and (ii) it admits a closed-form solution under some assumptions, which is not available for general QPs with multiple constraints, enabling faster computation. We support our method with rigorous analysis and examples. |
Design and source code modified from Jon Barron's website. Edit here.