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While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance. [ABSTRACT FROM AUTHOR]

In this brief, sustaining and intermittent run-to-run controllers are designed to achieve the stability of singular discrete-time neural networks with state-dependent coefficients. The controllers are designed for two reasons: 1) it is very difficult and almost impossible to only measure thein situfeedback information for the controllers and 2) the controllers may not always exist at any time. The stability is then established for singular discrete-time neural networks with state-dependent coefficients. Finally, numerical simulations are shown to illustrate the usefulness of the obtained criteria. [ABSTRACT FROM AUTHOR]

The proposed $k$ th-order filter is based on sliding modes (SMs). It exactly estimates $k$ input derivatives in the absence of noises, and is robust to noises of small magnitudes or having small average values. Estimation accuracy asymptotics are calculated. The filter is applied to the real-time accurate estimation of the equivalent control in SM control systems. [ABSTRACT FROM AUTHOR]

Zero-order holder discretization effects in sliding mode control systems with an input delay are studied. Stability conditions are formulated. Conditions for the existence of periodic solutions are derived and the existence of periodic steady states is investigated. The influence of the discretization step and the delay on the period and the amplitude of steady state oscillations is discussed. Structure of basins of attraction of periodic orbits with different switching patterns is studied. Simulation results are presented to illustrate various behaviors. [ABSTRACT FROM PUBLISHER]

In this article, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel analysis framework from both algebraic and geometric perspectives to justify the attractiveness of the synchronization manifold. Specifically, it is proven that the complementary space of the synchronization manifold can be spanned by certain subspaces constructed from the network structure. This allows to project the states of the dynamical systems onto these subspaces and transform the synchronization problem under consideration equivalently into a convergence one of the projected states in each subspace. Then, assuming the joint connectivity condition on the communication topologies, we are able to work out a unified convergence analysis for both types of dynamical systems. More specifically, for partial-state coupled generic linear systems, it is proven that synchronization can be reached if an extra condition, which is easy to verify in several cases, on the system dynamics is satisfied. For Lipschitz nonlinear systems with positive-definite inner coupling matrix, synchronization is realized if the coupling strength is strong enough to stabilize the evolution of the projected states in each subspace under certain conditions. The above claims generalize the existing results concerning both types of dynamical systems to so far the most general framework. Some illustrative examples are provided to verify our theoretical findings. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time stability (FTS) of network systems with discontinuous dynamics in the framework of signed networks. The sufficient criteria on the network interactive matrix are given to ensure the FTS of the considered systems in a unified framework. The explicit bound on the finite-time settling time is derived correspondingly. With the concept of Filippov solutions, the uniqueness of the nonsliding dynamics is shown, and the range of the sliding dynamics on the possible continuum of equilibria is given for the network systems with irreducible H-matrices. The obtained results are further applied to the network modulus consensus problems over signed digraphs. Several existing protocols are revisited and generalized with the proposed methods. Numerical examples are conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

The evolution of the target system (leader) in pinning-controlled complex networks may need to be regulated by some control inputs for performing various practical tasks, e.g., obstacle avoidance, tracking highly maneuverable target, and so on. Motivated by this observation, we shall investigate the global pinning synchronization problems for complex switching networks for which the target system is subject to nonzero control inputs. First, using the idea of unit vector function method, a discontinuous coupling law is designed. With the aid of stability theory for switched systems, it is theoretically shown that synchronization in the network under this discontinuous coupling law can be achieved by choosing sufficiently large coupling strengths if the average dwell time (ADT) is bounded below by a positive constant. Second, we use the boundary layer method to design a continuous-coupling law. It has been theoretically shown that the synchronization error is ultimately uniformly bounded (UUB) under this continuous-coupling law. The chattering effect is also avoided in real implementation by using this continuous-coupling law. Furthermore, for networks with unknown external disturbances and unmodeled dynamics, neuro-adaptive-based coupling laws are designed to ensure that the synchronization error of the networks with undirected switching communication topologies under these laws is UUB. The obtained theoretical results are finally validated by performing numerical simulation on coupling Chua’s circuit systems. [ABSTRACT FROM AUTHOR]

Multi-layer networks, which incorporate multiple subsystems and different kinds of interactions, are recently believed to have a stronger ability in modelling various real-world systems than traditional single-layer complex networks. Motivated by this observation, we try to show how to achieve node-to-node synchronization and complete synchronization in multi-layer networks under directed switching communication topologies, where the nodes have Lur’e type dynamics. First, by using the multiple Lyapunov stability theory, we show that node-to-node synchronization in two-layer networks can be achieved by choosing sufficiently large coupling strength as well as suitable feedback gain matrix if the average dwell time is bounded below by some positive constants. The result is then extended to the case of multiple layers. Furthermore, if the inner communication topologies of each layer have a directed spanning tree with a common root, we show complete synchronization in the considered network can be achieved if the control parameters and the average dwell time are appropriately chosen. Finally, the theoretical results are validated through performing numerical simulations on Chua’s circuit with double scroll attractors. [ABSTRACT FROM AUTHOR]

Many networked systems display some kind of dynamics behaving in a style with both continuous and impulsive communications. The cooperation behaviors of these networked systems with continuous connected or impulsive connected or both connected topologies of communications are important to understand. This paper is devoted to the synchronization of the networked system with continuous and impulsive hybrid communications, where each topology of communication mode is not connected in every moment. Two kind of structures, i.e., fixed structure and switching structures, are taken into consideration. A general concept of directed spanning tree (DST) is proposed to describe the connectivity of the networked system with hybrid communication modes. The suitable Lyapunov functions are constructed to analyze the synchronization stability. It is showed that for fixed topology having a jointly DST, the networked system with continuous and impulsive hybrid communication modes will achieve asymptotic synchronization if the feedback gain matrix and the average impulsive interval are properly selected. The results are then extended to the switching case where the graph has a frequently jointly DST. Some simple examples are then given to illustrate the derived synchronization criteria. [ABSTRACT FROM AUTHOR]

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from $M$ -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results. [ABSTRACT FROM PUBLISHER]