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It is shown that a certain set is positively invariant for the return map associated with the Chua's circuit. The set contains the intersection of the numerically observed double-scroll attractor and the planes defining the return map. The proof is based on rigorous numerics.
Mode-based clustering approaches such as mean-shift and its variants are extremely successful. They are also computationally expensive due to their iterative hill-climbing strategy when determining cluster labels for samples. We identify the fact that mode-based cluster boundaries exhibit themselves as minor surfaces of the data distribution. Based on this observation, we develop a mode-based clustering...
This paper studies practical consensus (PC) problem for linear multi-agent systems (MAS) under a fixed, connected, and undirected communication network. PC means that the difference between any two agents remains in an arbitrarily chosen neighborhood of the origin after some time by using a suitable control law. All the agents, which are heterogeneous first-order linear time-varying (LTV) systems,...
This paper considers the distributed containment control problem for multi-agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and not available to any follower. It is assumed that the communication graph among the followers is undirected, there exists at least one leader that has a directed path to each follower, and the leaders' control inputs...
In this paper we study control under input saturation and disturbances of neutrally stable and critically unstable linear systems. It is shown that a feedback controller can be designed so that the closed-loop states remain bounded for disturbances which belong to two different classes depending on the specific system structure and the equilibrium is globally asymptotically stable.
We study the robustness to external disturbances of large 1-D network of double-integrator agents with distributed control. We provide precise quantitative comparison of certain H∞ norm between two common control architectures: predecessor-following and symmetric bidirectional. In particular, we show that the scaling laws of the H∞ norm for predecessor-following architecture is O(αN) (α > 1), but...
We study the sensitivity properties of non-linear dynamical systems subject to disturbances, when disturbance parameters are near critical values. In particular, in seeking to explain recent experimental and simulation results, we give an explanation for why the inverses of response-time sensitivities to disturbance parameters often display an affine dependence on the parameters near critical points...
We study in this paper the control of discrete-time neutrally stable and critically unstable linear systems subject to input saturation and disturbances. It is shown that a feedback controller can be designed so that the closed-loop states remain bounded for two classes of disturbances and the equilibrium is globally asymptotically stable. This paper is a companion of [7].
In this paper, we consider three problems, namely, the output consensus problem, the model-reference output consensus problem, and the regulation of output consensus problem, for a network of non-identical right-invertible linear agents. The network provides each agent with a linear combination of multiple agents' outputs. We assume that all the agents are introspective, meaning that they have access...
This article is devoted to the synchronization of heterogeneous, and hence non-identical, linear systems. The proposed solution results in a fully distributed control law solely relying on local measurements. In order to achieve this, it is shown that the problem can be decomposed into three sub-problems: First, the synchronization of identical exosystems provides a feasible trajectory which turns...
Attitude control systems naturally evolve on nonlinear configurations, such as S2 and SO(3). The nontrivial topological properties of these configurations result in interesting and complicated nonlinear dynamics when studying the corresponding closed loop attitude control systems. In this paper, we review some global analysis and simulation techniques that allow us to describe the global nonlinear...
Distributed synchronization has gradually gained importance over the last two decades. The ad-hoc nature of new applications has increased the need for robust and scalable distributed algorithms that are capable of generating high precision timing information. However, current solutions usually produce phase errors when the frequencies are heterogeneous. This paper proposes a distributed synchronization...
A combination of dual Lyapunov analysis and properties of decentralized navigation function based controllers is used to check the stability properties of a certain class of decentralized controllers for navigation and collision avoidance in multi-agent systems. The derived results yield a less conservative condition from previous approaches, which relates to the negativity of the sum of the minimum...
A class of discontinuous vector fields is investigated, where equilibria are generically positioned in an interval in the phase space, and equilibria are not isolated points. The dynamics near such an equilibrium set is studied, and it is shown that the structural stability of trajectories near the equilibrium sets is determined by the local dynamics near the endpoints of this interval. Based on this...
We propose a method for designing switching rules that can drive the state of the switched dynamic system to a desired equilibrium point. The method deals with the class of switched systems where each sub-system has an affine vector field. The results are given in terms of linear matrix inequalities and they guarantee global asymptotic stability of the tracking error dynamics even if sliding motion...
In this paper exponential stabilizability of continuous-time positive switched systems is investigated. It is proved that, when dealing with two-dimensional systems, exponential stabilizability can be achieved if and only if there exists an Hurwitz convex combination of the (Metzler) system matrices. However, for systems of higher dimension this is not true. In general, exponential stabilizability...
The task of synchronising autonomous agents is solved by a networked controller that steers the agents towards a common trajectory. This paper extends existing analysis and design methods for sets of linear agents with individual dynamics. To formulate the basic condition under which agents can be synchronised, the notion of system inclusion is introduced. It is shown that the agents can be synchronised...
We present in this paper preliminary results and research directions concerning the output regulation problem for over-actuated linear systems. The focus of the paper is on the characterization of the solution of the full-information regulator problem for systems which are right-invertible but not left-invertible, where the input operator is injective. The intrinsic redundancy in the plant model is...
A method of state-space partitioning that stabilizes piecewise nonlinear homogeneous systems is developed. Specifically, given available system matrices, partition of the state space is determined in a graphical manner. Finally, we show several illustrative examples to demonstrate efficacy of the proposed approach.
Roving patrol plays a very important role in strengthening safety within campuses or communities through their patrol around the target. In fact, there maybe exist some patrolmen who do not work efficiently. Therefore, it is useful to quantitatively evaluate their roving effectiveness. The widespread use of global positioning system (GPS) and GPS data logger have generated huge amount of trajectory...
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