Classical Solutions of Linear Regulatorfor Degenerate Diffusions
نویسنده
چکیده
The usual framework of control is the one given in probably the most studied control problem, stochastic regulator control problem, which deals with minimizing a performance index of a system governed by a set of differential equations. The stochastic linear regulator problem has been studied by many authors including Bensoussan [4], Fleming and Soner [9] for nondegenerate diffusions. Da Prato [8] gives the solution to the stochastic linear regulator for the degenerate systems related to Riccati equations (i.e., any ordinary differential equation) for the quadratic case with infinite horizon. But he has not established the existence of a classical solution of the Hamilton-Jacobi-Bellman (HJB) equation (i.e., a partial differential equation in the optimal control theory) to the linear regulator control problem. Here we have studied an extended stochastic control problem of the linear regulator for the degenerate diffusions by considering the general case with infinite horizon. We are concerned with the stochastic control problem to minimize the discounted expected cost:
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