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How did your education and early career lead to your initial and continuing interest in the control field?

In this article, we mainly study an integrated networked control system operating over multipath routing networks, where the delivered control signal in each path experiences both transmission delay and packet loss. These imperfections significantly compromise system performance and may even cause instability. For such a system, we derive, for the first time, the necessary and sufficient stabilization condition utilizing a delay-dependent algebraic Riccati equation. Different from many previous works, one significant contribution is that our control policy is designed as the feedback of an extended state that contains the current available state and relevant past control information. Furthermore, we introduce an existence and uniqueness theorem for the maximum packet loss rate in symmetric systems. Notably, we derive its closed-form expression specifically in the scalar case.

This article is concerned with linear quadratic regulation (LQR) and stabilization problems for discrete-time stochastic systems with multiple input channels and input delays. In comparison with single-input-channel problems, a key difficulty, induced by the different delays in different input channels, is that the information sets for multiple controllers are required to be asymmetric and coupled. A novel technique, referred to as orthogonal decomposition–reorganization, is proposed to conquer the coupling between channels. After the technique is used, a new method based on some refined decompositions is provided to solve the delayed forward–backward stochastic difference equations, which overcomes the asymmetry and amounts to finding the solvability condition of the underlying LQR problems. The complete solutions of the finite- and infinite-horizon LQR problems are given by newly developing Riccati-type equations. Also, a necessary and sufficient stabilizing condition is obtained for the system restricted by a performance index. Finally, the effectiveness of the results is evaluated by a numerical example.

This article studies the stabilization control of the Stackelberg game-based system (SGBS) which involves a leader and a follower under continuous time. There are two main contributions: first, the explicit Stackelberg strategy and the optimal performance index under finite horizon are derived based on Riccati equations (REs). Second, the equivalent condition for the SGBS to be stabilizable is obtained, meanwhile, the corresponding Stackelberg strategy and optimal index under this condition are given by REs. Different from the previous works, in the optimization process of the leader, we obtain the linear Stackelberg strategy based on state feedback by applying the matrix maximum principle. Our key technique is solving forward–backward differential equations obtained from the maximum principle.

In this article, we consider the discrete-time rational expectations model with state delays. In particular, the dynamic equation relies both on the history of states and the conditional expectation of the future states. The novelty of this article lies in transforming the solvability of the rational expectations model to that of the forward and backward stochastic difference equations (FBSDEs). The main contribution is to obtain the (unique) solvability and the explicit solutions for the FBSDEs in both finite horizon and infinite horizon. This accordingly gives the explicit solution of the rational expectations model. The key technology is to establish a nonhomogeneous relationship between forward and backward processes of the FBSDEs.