State Constrained Feedback Stabilization

Abstract

A standard finite dimensional nonlinear control system is considered, along with a state constraint set S and a target set Σ. It is proven that open loop S-constrained controllability to Σ implies closed loop Sconstrained controllability to the closed δ-neighborhood of Σ, for any specified δ > 0. When the target set Σ satisfies a small time S-constrained controllability condition, conclusions on closed loop S-constrained stabilizability ensue. The (necessarily discontinuous) feedback laws in question are implemented in the sample-and-hold sense and possess a robustness property with respect to state measurement errors. The feedback constructions involve the quadratic infimal convolution of a control Lyapunov function with respect to a certain modification of the original dynamics. The modified dynamics in effect provide for constraint removal, while the convolution operation provides a useful semiconcavity property.

DOI: 10.1137/S036301290240453X

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Cite this paper

@article{Clarke2003StateCF, title={State Constrained Feedback Stabilization}, author={Francis H. Clarke and R. J. Stern}, journal={SIAM J. Control and Optimization}, year={2003}, volume={42}, pages={422-441} }