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This paper is concerned with the linear delayed forward–backward stochastic differential equations (D-FBSDEs). The existence of time delay leads to the infinite-dimensional problem which makes the explicit solvability more challenging. The main contribution is to propose a discretisation approach which gives the explicit solution of the D-FBSDEs and consists of the following three steps: first, we transform the continuous-time D-FBSDEs into the discrete-time form with the aid of interval partition. Second, we derive the solution of the discrete-time D-FBSDEs by applying backward iterative induction. Finally the explicit solution of the continuous-time D-FBSDEs is obtained by taking the limit to the solution of discrete-time form which is also strictly proved under continuous-time framework. The proposed approach is applicable for more general FBSDEs with delay, which would provide a complete solution to the stochastic LQ control with time delay. [ABSTRACT FROM AUTHOR]

In this paper, we study the team optimal decentralized estimation with partial history sharing information structure. There exist N$$ N $$ agents that have their own observations and share partial history observations to each other. The main contributions include two aspects: One is to give the iterative equations of the common estimation, which is the conditional expectation of state with respect to the common information for all agents and the innovation of the local information for each agent; the other is to provide the structure of the team optimal decentralized estimation, that is, the linear combination of the common estimation and the innovation of the local information. The novelty lies in that the estimation can be obtained at one time by defining an augmented state. In particular, the result is reduced to the well‐known centralized estimation when all the information is sharing for all the agents. [ABSTRACT FROM AUTHOR]

This paper considers a linear‐quadratic mean field control problem involving a major agent and N minor agents. We aim to optimize a social cost as a weighted sum of the individual costs under decentralized information. Firstly, the forward‐backward stochastic difference equations (FBSDEs) are obtained for this problem by variational analysis. Then, by decoupling the FBSDEs, we design the decentralized control laws, which are further shown to be asymptotically optimal. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the team optimal decentralized state estimation problem where the state is transmitted to a remote agent with packet dropouts and is observed by N$$ N $$ local agents with additive noises. In particular, the information of the remote agent is available to all local agents with hierarchical relationships, which leads to an asymmetric information structure. The main contribution is to derive the analytical expressions for the team optimal decentralized state estimation. Different from the existing decentralized estimation results, the novelty of the paper is to comprehensively investigate the influence of packet dropouts and additive noises, which occur frequently in networked control systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the linear quadratic optimal control problem for the time-delay stochastic system with partial information. The main contribution is to derive the equivalent solvability condition and give the explicitly optimal controller under partial information in terms of the Riccati equations. The key is to explicitly solve the forward and backward stochastic difference equations with partial information, which is derived from the stochastic maximum principle. [ABSTRACT FROM AUTHOR]