NDLI: Existence of feasible approximating trajectories for differential inclusions with obstacles as state constraints

Content Provider	IEEE Xplore Digital Library
Author	Bettiol, P. Vinter, R.
Copyright Year	2009
Description	Author affiliation: Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, SW7 2BT, UK (Bettiol, P.; Vinter, R.)
Abstract	In the analysis of optimal control problems with state constraints, a key step (establishing ‘metric regularity’) is to show that an arbitrary state trajectory can be approximated by a feasible state trajectory, whose distance from the original state trajectory is linearly related to the state constraint violation. It is then possible, for example, to give conditions for the state constraint Maximum Principle to apply in normal form (the cost multiplier can be taken non-zero), to establish regularity properties of the value function and to characterize it as the unique viscosity solution of the Hamilton Jacobi Bellman equation. While a great deal of attention has been given in the literature to conditions for metric regularity, cases in which the state constraint region is the complement of a collection of boxes with corners has not previous treated. Such cases are important because they arise in the optimal control of AUVs which are required to avoid box regions in the state space. This paper provides conditions for metric regulariy that cover such situations.
Starting Page	8624
Ending Page	8629
File Size	962922
Page Count	6
File Format	PDF
ISBN	9781424438716
ISSN	01912216
DOI	10.1109/CDC.2009.5400266
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-12-15
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimal control Viscosity Jacobian matrices Equations State-space methods Cost function Control systems Sufficient conditions Extraterrestrial measurements
Content Type	Text
Resource Type	Article

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