This paper introduces several related distributed algorithms, generalised from the celebrated belief propagation algorithm for statistical learning. These algorithms are suitable for a class of computational problems in large-scale networked systems, ranging from average consensus, sensor fusion, distributed estimation, distributed optimisation, distributed control, and distributed learning. By expressing the underlying computational problem as a sparse linear system, each algorithm operates at each node of the network graph and computes iteratively the desired solution. The behaviours of these algorithms are discussed in terms of the network graph topology and parameters of the corresponding computational problem. A number of examples are presented to illustrate their applications. Also introduced is a message-passing algorithm for distributed convex optimisation.

This article investigates the distributed recursive filtering problem for discrete-time stochastic cyber–physical systems. A particular feature of our work is that we consider systems in which the state is constrained by saturation. Measurements are transmitted to nodes of a sensor network over unreliable wireless channels. We propose a linear coding mechanism, together with a distributed method for obtaining a state estimate at each node. These designs aim to minimize the state estimation error covariance. In addition, we derive a bound on this covariance, and accommodate the design parameters to minimize this bound. The resulting design depends on the packet loss probabilities of the wireless channels. This permits applying the proposed scheme to systems in which communications suffer from denial-of-service attacks, as such attacks typically affect those probabilities. Finally, we present a numerical example illustrating this application.

Sliding mode control (SMC) is a well-known robust nonlinear control method with strong robustness and fast response which has been widely used in many applications. This paper introduces the major results of SMC design methods that the authors have achieved in the last decade. Undoubtedly, our results are obtained based on many other researchers’ pioneer work in the literature which will not be discussed in detail here. Notably, our development has a main focus on tackling practical issues such that a proposed or enhanced SMC approach is effectively applicable to motion control systems. Issues on sliding function and adaptive gain designs in SMC and their control features will be both discussed in this paper. Those issues comprise fast convergent speed, predefined convergent time, input saturation restriction, chattering reduction, and unknown disturbance suppression. Lastly, conclusion and a few remarks on future research directions are presented.

This paper considers the rational expectations model with multiplicative noise and input delay, where the system dynamics rely on the conditional expectations of future states. The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model. In particular, we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case. The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.