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Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation

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4 Author(s)
Oishi, M. ; Dept. of Electr. & Comput. Eng., British Columbia Univ., Vancouver, BC ; Mitchell, I.M. ; Tomlin, C. ; Saint-Pierre, P.

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

Published in:

Decision and Control, 2006 45th IEEE Conference on

Date of Conference:

13-15 Dec. 2006