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Anytime solution of constrained nonlinear programs via control barrier functions
A. Allibhoy, J. Cortés
IEEE Conference on Decision and Control, Austin, Texas, 2021, pp. 6520-6525

Abstract

This paper considers the problem of designing a dynamical system to solve constrained nonlinear optimization problems such that the feasible set is forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning that it is guaranteed to return a feasible solution regardless of when it is terminated. Such property is of critical importance in feedback control since controllers are often implemented as solutions to constrained programs that must be solved in real time. The proposed design builds on the basic insight of following the gradient flow of the objective function while keeping the state evolution within the feasible set using techniques from the theory of control barrier functions. We show that the resulting closed-loop system can be interpreted as a continuous approximation of the projected gradient flow, establish the monotonic decrease of the objective function along the feasible set, and characterize the asymptotic convergence properties to the set of critical points. Various examples illustrate our results.

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