We study a class of infinite horizon control problems for nonlinear systems, which includes the Linear Quadratic (LQ) problem, using the Dynamic Programming approach. Sufficient conditions for the regularity of the value function are given. The value function is compared with sub- and supersolutions of the Bellman equation and a uniqueness theorem is proved for this equation among locally Lipschitz functions bounded below. As an application it is showed that an optimal control for the LQ problem is nearly optimal for a large class of small unbounded nonlinear and non-quadratic pertubations of the same problem.
On the Bellman equation for infinite horizon problems with unbounded cost functional
DA LIO, FRANCESCA
2000
Abstract
We study a class of infinite horizon control problems for nonlinear systems, which includes the Linear Quadratic (LQ) problem, using the Dynamic Programming approach. Sufficient conditions for the regularity of the value function are given. The value function is compared with sub- and supersolutions of the Bellman equation and a uniqueness theorem is proved for this equation among locally Lipschitz functions bounded below. As an application it is showed that an optimal control for the LQ problem is nearly optimal for a large class of small unbounded nonlinear and non-quadratic pertubations of the same problem.
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