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Robinson's counterexample and regularity properties of optimization-based controllers
P. Mestres, A. Allibhoy, J. Cortés
Systems and Control Letters, submitted

Abstract

Robinson's counterexample shows that, even for relatively well-behaved parametric optimization problems, the corresponding optimizer might not be locally Lipschitz with respect to the parameter. In this brief note, we revisit this counterexample here motivated by the use of optimization-based controllers in closed-loop systems, where the parameter is the system state and the optimization variable is the input to the system. We show that controllers obtained from optimization problems whose objective and constraints have the same properties as those in Robinson's counterexample enjoy regularity properties that guarantee the existence (and in some cases, uniqueness) of solutions of the corresponding closed-loop system.

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