This article adopts a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where the drift and diffusion terms in dynamics may depend on both state control. Based Bellman’s dynamic programming principle, we presented an online RL algorithm attain optimal control with partial system information. computes control, rather than estimates...

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed....

We study a version of the Ornstein-Uhlenbeck bridge driven by spectrally-positive subordinator. Our formulation is based on Linear-Quadratic control subject to singular terminal condition. The bridge, we develop, written as limit obtained optimally controlled processes, and shown admit an explicit expression. Its extension with self-excitement also considered. condition confirmed be satisfied p...

Analysis and synthesis for linear systems with parameters that vary according to a set-valued map are investigated. It is shown that the optimal controllers are continuous and homogeneous, but not additive. A computational method based on approximating the nonquadratic cost by a piece-wise quadratic function is developed. Such an approximation determines stability nonconservatively and preserve...

We describe an implementation of an infinite-dimensional primal-dual algorithm based on the Nesterov-Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3-4 iterations) to optimal s...

In a recent paper, the authors showed how to compute performance bounds for infinite horizon stochastic control problems with linear system dynamics and arbitrary constraints, objective, and noise distribution. In this paper we extend these results to the finite-horizon case, with asymmetric costs and constraint sets. The method is based on bounding the objective with a general quadratic functi...