Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Optimization-based safe stabilizing feedback with guaranteed region of attraction
P. Mestres, J. Cortés
IEEE Control Systems Letters 7 (2023), 367-372
Abstract
This paper proposes an optimization with penalty-based
feedback design framework for safe stabilization of
control affine systems. Our starting point is the
availability of a control Lyapunov function (CLF) and a
control barrier function (CBF) defining
affine-in-the-input inequalities that certify,
respectively, the stability and safety objectives for
the dynamics. Leveraging ideas from penalty methods for
con- strained optimization, the proposed design
framework imposes one of the inequalities as a hard
constraint and the other one as a soft constraint. We
study the properties of the closed-loop system under the
resulting feedback controller and identify conditions on
the penalty parameter to eliminate undesired equilibria
that might arise. Going beyond the local stability
guarantees available in the literature, we are able to
provide an inner approximation of the region of
attraction of the equilibrium, and identify conditions
under which the whole safe set belongs to
it. Simulations illustrate our results.
pdf
Mechanical and Aerospace Engineering,
University of California, San Diego
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cortes at ucsd.edu
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