STATE CONSTRAINTS, HIGHER ORDER INWARD POINTING CONDITIONS, AND NEIGHBORING FEASIBLE TRAJECTORIES

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Colombo, G (Author) Other; Khalil, NT (Author) FEUP; Rampazzo, F (Author) Other

Journal

Title: SIAM Journal on Control and Optimization

Vol. 60

Pages: 3326-3357

ISSN: 0363-0129

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 1 Citation

Other information

Authenticus ID: P-016-B7T

DOI: 10.1137/21m1468796

Abstract (EN): The classical inward pointing condition (IPC) for a control system whose state x is constrained in the closure C :- (Omega) over bar of an open set \Omega prescribes that at each point of the boundary x is an element of partial derivative Omega the intersection between the dynamics and the interior of the tangent cone (Omega) over bar at x is nonempty. Under this hypothesis, for every system trajectory x(.) on a time interval [0, T], possibly violating the constraint, one can construct a new system trajectory (x) over cap(.) that satisfies the constraint and whose distance from x(.) is bounded by a quantity proportional to the maximal deviation d := dist(Omega, x([0, T])). When IPC is violated, the construction of such a constrained trajectory is not possible in general. However, in this paper we prove that a ``higher order inward pointing condition involving Lie brackets of the dynamics' vector fields (together with a nonpositiveness curvature-like assumption) and the implementation of a suitable ``rotating control strategy allows for a novel construction of a constrained trajectory (x) over cap(.) whose distance from the reference trajectory x(.) is bounded by a quantity proportional to \surd d. As an application, we establish the continuity up to the boundary of the value function V of a connected optimal control problem, a continuity that allows one to regard V as the unique constrained viscosity solution of the corresponding Bellman equation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 32