Title | Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation |
Publication Type | Conference Paper |
Year of Publication | 2006 |
Authors | Oishi, M., I. Mitchell, C. Tomlin, and P. Saint-Pierre |
Conference Name | Decision and Control, 2006 45th IEEE Conference on |
Pagination | 3801 -3807 |
Date Published | dec. |
Keywords | aircraft 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 |
URL | http://dx.doi.org/10.1109/CDC.2006.377614 |
DOI | 10.1109/CDC.2006.377614 |