Explicit solution to a linear-quadratic optimal control problem with an arbitrary terminal
The author presents an explicit solution to an optimal stochastic control problem in which the optimized system is described by a linear stochastic differential equation with Wiener disturbances and the performance index is a sum of a quadratic integral functional and arbitrary terminal term. The line of reasoning goes through the Hamilton-Jacobi-Bellman equation ``linearized'' by the logarithmic transformation of the cost-to-go function. This equation could be solved by a solution to a Cauchy problem for an evolutionary equation [\textit{R. Cordero-Soto} et al., Ann. Phys. 325, No. 9, 1884--1912 (2010; Zbl 1198.81084)] with a special elliptic part. The solution can be expressed through solutions of ordinary differential equations and it leads to an explicit formula for the optimal control.
scientific article; zbMATH DE number 6845975