Inverse Parametric Optimization with an Application to Hybrid System Control

Andreas B. Hempel (hempelcontrol.ee.ethz.ch)
Paul J. Goulart (pgoulartcontrol.ee.ethz.ch)
John Lygeros (lygeroscontrol.ee.ethz.ch)

Abstract: We present a number of results on inverse parametric optimization and its application to hybrid system control. We show that any function that can be written as the difference of two convex functions can also be written as a linear mapping of the solution to a convex parametric optimization problem. We exploit these results in application to the control of systems with piecewise affine dynamics, and show that it is possible to model such systems as optimizing processes. Optimal control problems for such systems can be remodeled as bilevel optimization problems and solved with existing techniques.

Keywords: Optmization, Hybrid Systems

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering (Control Applications )

Category 3: Complementarity and Variational Inequalities

Citation: A slightly shorter version to appear in IEEE Transactions on Automatic Control vol. 60, no. 1, Jan. 2015

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Entry Submitted: 07/30/2013
Entry Accepted: 07/30/2013
Entry Last Modified: 07/23/2014

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