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Inverse Parametric Programming and Control of Hybrid Systems


A.B. Hempel

ANU Canberra, Australia, Systems and Control Series

Many applications use ideas from the inverse optimization literature, for example expert learning and economic policy analysis. The main assumption is that a given function is assumed to be the explicit solution to a parametric optimization problem. The goal in inverse optimization is then to identify the generating problem data from the given function. We consider the case of piecewise affine (PWA) functions, which are of particular interest because the explicit solutions to parametric linear and quadratic programs have this structure. In this talk, we show that every PWA function can be obtained by a simple linear transformation from the solution to a linear or quadratic program and how the generating problem data can be found. The main step in the construction is the decomposition of the given PWA function into a convex and a concave part. This result expands our previous contributions considerably and enables us to model every PWA dynamical system in terms of an optimization problem. Using this optimization model for control input computations seems to be beneficial when compared to currently standard approaches.


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