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

TitleComputing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation
Publication TypeConference Paper
Year of Publication2006
AuthorsOishi, M., I. Mitchell, C. Tomlin, and P. Saint-Pierre
Conference NameDecision and Control, 2006 45th IEEE Conference on
Pagination3801 -3807
Date Publisheddec.
Keywordsaircraft control, aircraft planar collision avoidance, civil jet aircraft longitudinal dynamics, controlled invariant set, feedback, feedback linearizable system, feedback linearization, feedback linearizing control law, Hamilton-Jacobi formulation, linearisation techniques, nonlinear control law, nonlinear control systems, nonlinear state constraint, parameterized nonlinear controller, reachability analysis, reachability calculation, reachable set, viability approach, viable set
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

URLhttp://dx.doi.org/10.1109/CDC.2006.377614
DOI10.1109/CDC.2006.377614

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