A Tutorial on Quantized Feedback Control

In this tutorial paper, we explore the field of quantized feedback control, which has gained significant attention due to the growing prevalence of networked control systems. These systems require the transmission of feedback information, such as measurements and control signals, over digital networks, presenting novel challenges in estimation and control design. Our examination encompasses various topics, including the minimal information needed for effective feedback control, the design of quantizers, strategies for quantized control design and estimation,achieving consensus control with quantized data, and the pursuit of high-precision tracking using quantized measurements.

Exact controllability of rational expectations model with multiplicative noise and input delay

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.

Distributed computations for large-scale networked systems using belief propagation

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 largescale 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.

Convergence Rate Analysis of Gaussian Belief Propagation for Markov Networks

Gaussian belief propagation algorithm(GaBP) is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density functions from a high dimensional joint density function over a Markov network in a finite number of iterations when the underlying Gaussian graph is acyclic. It is also known more recently that the algorithm produces correct marginal means asymptotically for cyclic Gaussian graphs under the condition of walk summability(or generalised diagonal dominance). This paper extends this convergence result further by showing that the convergence is exponential under the generalised diagonal dominance condition,and provides a simple bound for the convergence rate. Our results are derived by combining the known walk summability approach for asymptotic convergence analysis with the control systems approach for stability analysis.

Input-to-state stability and gain computation for networked control systems

This paper studies the stability problem for networked control systems.A general result,called network gain theorem,is introduced to determine the input-to-state stability(ISS)for interconnected nonlinear systems.We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS.For the case of linear networked systems,a complete characterisation of the stability condition is provided,together with two distributed algorithms for computing the network gain:the classical Jacobi iterations and a message-passing algorithm.For the case of nonlinear networked systems,characterisation of the ISS condition can be done using M-functions,and Jacobi iterations can be used to compute the network gain.

Collaborative target tracking in WSNs using the combination of maximum likelihood estimation and Kalman filtering

Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach in wire- less sensor networks using the combination of maximum likelihood estimation and the Kalman filter. The cluster leader converts the received nonlinear distance measurements into linear observation model and approximates the covariance of the converted measurement noise using maximum likelihood estimation, then applies Kalman filter to recursively update the target state estimate using the converted measurements. Finally, a measure based on the Fisher information matrix of maximum likelihood estimation is used by the leader to select the most informative sensors as a new tracking cluster for further tracking. The advantages of the proposed collaborative tracking approach are demonstrated via simulation results.