Stabilizing linear systems with saturation through optimal control

R. Goebel
2004 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)  
We construct a continuous feedback for a saturated systemẋ(t) = Ax(t) + Bσ(u(t)). The feedback renders the system asymptotically stable on the whole set of states that can be driven to 0 with an open-loop control. Trajectories of the resulting closed-loop system are optimal for an auxiliary optimal control problem with a convex cost and linear dynamics. The value function for the auxiliary problem, which we show to be differentiable, serves as a Lyapunov function for the saturated system.
more » ... ng the saturated system, which is nonlinear, to an optimal control problem with linear dynamics is possible thanks to the monotone structure of saturation.
doi:10.1109/cdc.2004.1429686 fatcat:guygsgbvozfuhiqzm5ude3ttzq