Error analysis of a discretization for stochastic linear quadratic control problems governed by SDEs

In this work, a time-implicit discretization for stochastic linear quadratic problems subject to stochastic differential equations with control-dependence noises is proposed, and the convergence rate of this discretization is proved. Compared to the existing results, the control variables are stochastic processes and can be contained in systems’ diffusion term. Based on this discretization, a gradient descent algorithm and its convergence rate are presented. Finally, a numerical example is provided to support the theoretical finding.

Iterative learning control for consensus of second-order multi-agent systems with interval uncertain topologies

This paper is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods.

Distributed event-triggered consensus protocols for discrete-time multiagent systems

This paper focuses on leader-following and leaderless consensus problems of discrete-time multiagent systems. A distributed observer-based consensus protocol is proposed to investigate the consensus problem for multiagent systems of general discrete-time linear dynamics. By means of the observer, the distributed control law of each agent is designed using local information to guarantee consensus, and the corresponding sufficient conditions are obtained by exploiting graph and control theory approach. A modified distributed event-triggered consensus protocol is designed to reduce communication congestion. Detailed analysis of the leaderless and the leader-following consensus is presented for both observer-based and full-information protocols. Finally, two simulation examples are provided to demonstrate the effectiveness and capabilities of the established theories.

Non-uniform ISS small-gain theorem for infinite networks

We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork while it allows for non-uniform convergence of all components. For an infinite network consisting of input-to-state stable subsystems, which do not necessarily have a uniform $\mathscr{K}\mathscr{L}$-bound on the transient behaviour, we show the following: if the gain operator satisfies the uniform small-gain condition, then the whole network is non-uniformly input-to-state stable and all its finite subnetworks are input-to-state stable.

Random matrices and controllability of dynamical systems

We introduce the concept of $\epsilon $-uncontrollability for random linear systems, i.e. linear systems in which the usual matrices have been replaced by random matrices. We also estimate the $\varepsilon $-uncontrollability in the case where the matrices come from the Gaussian orthogonal ensemble. Our proof utilizes tools from systems theory, probability theory and convex geometry.

A discrete dynamics approach to interbank financial contagion

The purpose of this paper is to describe in terms of mathematical models and systems theory the dynamics of interbank financial contagion. Such a description gives rise to a model that can be studied with mathematical tools and will provide a new framework for the study of contagion dynamics complementary to research by simulation studied so far. It provides a better understanding of such financial networks and a unifying network for the research of financial contagion. The mathematical description we present is in terms of Boolean dynamical systems and a linear operator. We relate the properties of the dynamical systems to the properties of the operator.

On the efficiency of type I censored samples

The paper revisits the entropy-based efficiency of the type-I censored sample, which was addressed by several previous works. The main purpose of this work is to provide a comprehensive definition of the efficiency function and give a general proof that the entropy of a censored sample is always less than that of the complete sample for any probability distribution and at any point of censoring. A simulation study is performed to validate our results, and a real-data example is reevaluated.

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

The global finite-time synchronization of a class of chaotic systems via the variable-substitution and feedback control

This paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper.