Research Projects

Problems in optimal control theory date back to early 17th century. There are two main approaches to solve optimal control problems. First one is Bellman's ``dynamic programming'' and the other one is Pontryagin’s ``maximum principle''. Further developments of this field are made by Kalman. The works of Bellman and Kalman mark the beginning of the field of stochastic optimal control. In stochastic control applications, typically only an ideal model is assumed, or learned from available incomplete data, based on which an optimal control is designed and then applied to the actual system. This gives rise to the problem of performance loss due to the mismatch between the actual system and the assumed system. A robustness problem in this context is to show that the error due to mismatch decreases to zero as the assumed system approaches the actual system. This is a problem of major practical importance. Most of the existing works in this direction are concerned with the discrete-time Markov decision process. The literature on robustness of stochastic optimal control for continuous time system seems to be rather limited. These issues remain unresolved for continuous-time models that are partially observable, driven by general noise factors (such as wide band-width noise). A notable emerging area of interest is decentralized stochastic control, which involves multiple decision makers who must operate based solely on local information. This area not only brings a rich mathematical complexity but also offers significant applicability across numerous domains, such as energy systems, smart grids, sensor networks, and transportation systems, to name a few. While there is a substantial body of research focused on decentralized control in discrete-time frameworks, the continuous-time counterparts remain largely unexplored. Addressing this gap presents an opportunity for innovation and further understanding. Moreover, a critical focus within optimal control theory is the development of effective discrete-time approximations for continuous-time controlled models. These approximations capitalize on the well-established theories of discrete-time processes to tackle fundamental issues in continuous-time situations. Although there is a lot of studies available about fully observed models, but there is a noticeable gap when it comes to studying continuous-time models that use decentralized or partial information. This project aims to bridge critical gaps in the field of optimal control theory, delivering robust solutions and innovative ideas that can advance both theoretical understanding and practical applications in diverse real-world systems.