Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation
Oishi, M.
Mitchell, I.
Tomlin, C.
Saint-Pierre, P.
Dept. of Electr. & Comput. Eng., British Columbia Univ., Vancouver, BC;
This paper appears in: Decision and Control, 2006 45th IEEE Conference on
Publication Date: 13-15 Dec. 2006
On page(s): 3801-3807
Location: San Diego, CA,
ISBN: 1-4244-0171-2
INSPEC Accession Number: 9408915
Digital Object Identifier: 10.1109/CDC.2006.377614
Current Version Published: 2007-05-07
Abstract
We consider feedback linearizable systems subject to bounded control input and nonlinear state constraints. In a single computation, we synthesize 1) parameterized nonlinear controllers based on feedback linearization, and 2) the set of states over which this controller is valid. This is accomplished through a reachability calculation, in which the state is extended to incorporate input parameters. While we use a Hamilton-Jacobi formulation, a viability approach is also feasible. The result provides a mathematical guarantee that for all states within the computed set, there exists a control law that simultaneously satisfy two separate goals: envelope protection (no violation of state constraints), and stabilization despite saturation. We apply this technique to two real-world systems: the longitudinal dynamics of a civil jet aircraft, and a two-aircraft, planar collision avoidance scenario. The result, in both cases, is a feasible range of input parameters for the nonlinear control law, and a corresponding controlled invariant set
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