Robustness of Stochastic Optimal Control to Approximate Diffusion Models Under Several Cost Evaluation Criteria
成果类型：
Article
署名作者：
Pradhan, Somnath; Yueksel, Serdar
署名单位：
Queens University - Canada
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2022.0134
发表日期：
2024
页码：
2049-2077
关键词：
markov decision-processes
multidimensional diffusions
MAXIMUM PRINCIPLE
ergodic control
CONVERGENCE
STABILITY
Iteration
systems
摘要：
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss because of the mismatch between the true and assumed models. A robustness problem in this context is to show that the error because of the mismatch between a true and an assumed model decreases to zero as the assumed model approaches the true model. We study this problem when the state dynamics of the system are governed by controlled diffusion processes. In particular, we discuss continuity and robustness properties of finite and infinite horizon alpha-discounted/ergodic optimal control problems for a general class of nondegenerate controlled diffusion processes as well as for optimal control up to an exit time. Under a general set of assumptions and a convergence criterion on the models, we first establish that the optimal value of the approximate model converges to the optimal value of the true model. We then establish that the error because of the mismatch that occurs by application of a control policy, designed for an incorrectly estimated model, to a true model decreases to zero as the incorrect model approaches the true model. We see that, compared with related results in the discrete-time setup, the continuous-time theory lets us utilize the strong regularity properties of solutions to optimality (Hamilton-Jacobi-Bellman) equations, via the theory of uniformly elliptic partial differential equations, to arrive at strong continuity and robustness properties.