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Register a new userStability of Multi-Dimensional Switched Systems with an Application to Open Multi-Agent Systems
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Extended from the classic switched system, themulti-dimensional switched system (MDSS) allows for subsystems(switching modes) with different state dimensions. In this work,we study the stability problem of the MDSS, whose state transi-tion at each switching instant is characterized by the dimensionvariation and the state jump, without extra constraint imposed.Based on the proposed transition-dependent average dwell time(TDADT) and the piecewise TDADT methods, along with the pro-posed parametric multiple Lyapunov functions (MLFs), sufficientconditions for the practical and the asymptotical stabilities of theMDSS are respectively derived for the MDSS in the presenceof unstable subsystems. The stability results for the MDSS areapplied to the consensus problem of the open multi-agent system(MAS) which exhibits dynamic circulation behaviors. It is shownthat the (practical) consensus of the open MAS with disconnectedswitching topologies can be ensured by (practically) stabilizingthe corresponding MDSS with unstable switching modes via theproposed TDADT and parametric MLF methods.
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Consensusability is an important property for many multi-agent systems (MASs) as it implies the existence of networked controllers driving the states of MAS subsystems to the same value. Consensusability is of interest even when the MAS subsystems are physically coupled, which is the case for real-world systems such as power networks. In this paper, we study necessary and sufficient conditions for the consensusability of linear interconnected MASs. These conditions are given in terms of the parameters of the subsystem matrices, as well as the eigenvalues of the physical and communication graph Laplacians. Our results show that weak coupling between subsystems and fast information diffusion rates in the physical and communication graphs favor consensusability. Technical results are verified through computer simulations.
In this paper we investigate multi-agent discrete-event systems with partial observation. The agents can be divided into several groups in each of which the agents have similar (isomorphic) state transition structures, and thus can be relabeled into the same template. Based on the template a scalable supervisor whose state size and computational cost are independent of the number of agents is designed for the case of partial observation. The scalable supervisor under partial observation does not need to be recomputed regardless of how many agents are added to or removed from the system. We generalize our earlier results to partial observation by proposing sufficient conditions for safety and maximal permissiveness of the scalable least restrictive supervisor on the template level. An example is provided to illustrate the proposed scalable supervisory synthesis.
Due to the wide application of average consensus algorithm, its security and privacy problems have attracted great attention. In this paper, we consider the system threatened by a set of unknown agents that are both malicious and curious, who add additional input signals to the system in order to perturb the final consensus value or prevent consensus, and try to infer the initial state of other agents. At the same time, we design a privacy-preserving average consensus algorithm equipped with an attack detector with a time-varying exponentially decreasing threshold for every benign agent, which can guarantee the initial state privacy of every benign agent, under mild conditions. The attack detector will trigger an alarm if it detects the presence of malicious attackers. An upper bound of false alarm rate in the absence of malicious attackers and the necessary and sufficient condition for there is no undetectable input by the attack detector in the system are given. Specifically, we show that under this condition, the system can achieve asymptotic consensus almost surely when no alarm is triggered from beginning to end, and an upper bound of convergence rate and some quantitative estimates about the error of final consensus value are given. Finally, numerical case is used to illustrate the effectiveness of some theoretical results.
In this paper we propose a novel method to establish stability and, in addition, convergence to a consensus state for a class of discrete-time Multi-Agent System (MAS) evolving according to nonlinear heterogeneous local interaction rules which is not based on Lyapunov function arguments. In particular, we focus on a class of discrete-time MASs whose global dynamics can be represented by sub-homogeneous and order-preserving nonlinear maps. This paper directly generalizes results for sub-homogeneous and order-preserving linear maps which are shown to be the counterpart to stochastic matrices thanks to nonlinear Perron-Frobenius theory. We provide sufficient conditions on the structure of local interaction rules among agents to establish convergence to a fixed point and study the consensus problem in this generalized framework as a particular case. Examples to show the effectiveness of the method are provided to corroborate the theoretical analysis.
In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of uncertain high-order agents to the Nash equilibrium of some noncooperative game in a distributed manner. To overcome the difficulties brought by the high-order structure, unknown nonlinearities, and the regulation requirement, we first introduce a virtual player for each agent and solve an auxiliary noncooperative game for them. Then, we develop a distributed adaptive protocol by embedding this auxiliary game dynamics into some proper tracking controller for the original agent to resolve this problem. We also discuss the parameter convergence problem under certain persistence of excitation condition. The efficacy of our algorithms is verified by numerical examples.
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