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This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to establish two new types of rough set structures associated with the Marcus–Wyse (MW -, for brevity) topology, such as an M -rough set and an MW -topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in Z 2 , where Z is the set of integers. These two rough set structures are related to each other via an M -digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (LFC -, for short) space (U , C) and a subset X of U , we firstly introduce a new neighborhood system on U related to X. Next, we formulate the lower and upper approximations with respect to X , where all of the sets U and X (⊆ U) need not be finite and the covering C is locally finite. Actually, the notion of M -digitization of a 2-dimensional Euclidean space plays an important role in developing an M -rough and MW -topological rough set structures. Further, we prove that M -rough set operators have a duality between them. However, each of MW -topological rough set operators need not have the property as an interior or a closure from the viewpoint of MW -topology. [ABSTRACT FROM AUTHOR]

This paper studies the rendezvous strategy for a group of unicycle systems with connectivity preservation and collision avoidance. Based on the method of potential functions, a novel distributed control algorithm is proposed for all unicycles. By tuning the design parameters, the unicycles finally aggregate so that the average of the distances is bounded by a pre-specified positive number. It is proved that the connectivity of a minimum spanning tree in the initial topology is guaranteed. The result is then extended to multiple unicycles with heterogenous input disturbances. Potential function is further modified to handle the disturbances. Illustrative example is presented to show the improvements and effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Highlights: [•] The tracking consensus analysis method for stochastic MASs is novel. [•] The asymmetric communication delays is focused on in this paper. [•] The delays is time-varying, and one derives its upper bound. [•] This paper also focuses on noise, directed topology, and nonlinear dynamics. [ABSTRACT FROM AUTHOR]

This paper is concerned with collision-free second-order vehicle formation control when the inter-vehicle network topology is time-varying. The proposed control law has two parts: one for converging to a desired formation (no collision avoidance considered); the other for achieving collision avoidance. Unlike existing works, the proposed control law uses a fixed (so easy-to-implement) set of time-invariant control gains for achieving the desired formation and the gradient of a distance-based edge-tension function for collision avoidance. This simple combination of the two parts provably allows for collision-free formation control under time-varying network topologies. Theoretical and numerical evidences are provided to justify the effectiveness of the developed control law. [ABSTRACT FROM AUTHOR]