Stabilizing a linear system with saturation through optimal control

Rafal Goebel

doi:10.1109/TAC.2005.846522

2005-05-01

PRE

Rafal Goebel

DOI：10.1109/TAC.2005.846522

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摘要

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We construct a continuous feedback for a saturated system x(t) = Ax(t) + B sigma(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. The 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. Relating the saturated system, which is nonlinear, to an optimal control problem with linear dynamics is possible thanks to the monotone structure of saturation.

Keyword:

FEEDBACK STABILIZATION

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IEEE Transactions on Automatic Control

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论文数:

1.3W

被引数:

6.7W

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