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In this paper, we study the containment control problem with general linear dynamics under directed graph by means of centralized event-triggered control strategy. Distributed dynamic centralized event-triggered controller is proposed, which is based on the information of the relative outputs of the neighboring agents, such that the states of the followers can asymptotically converge to convex hull...
In this paper, a formation control problem is investigated for second-order discrete-time multi-agent systems with time delays and varying initial formation errors by means of consensus strategies. We derive a framework of it by using a distributed control scheme which is based on consensus with local formation errors. Through system decomposition and stability analysis, a sufficient condition is...
This study clarifies some issues regarding advances of oscillations when passage through a Hopf bifurcation is attempted. Specifically, it has been reported before that advances occur when the bifurcation parameter varies slowly through a Hopf bifurcation point. Here it is emphasized that if this variation is sufficiently slow advances are eliminated and an upper bound on the error between the system's...
In this paper, we address the differential game of pursuit and evasion between two players in the presence of an external flow field. It is assumed that the two players move on the plane at fixed but different speeds, and they are both agile. That is, they steer by choosing at each instant their direction of travel and abrupt heading changes are allowed. The external flow field is approximated by...
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradient-ascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is asymptotically...
In this paper, we examine the influence of the normalized eigenvectors of the graph Laplacian matrix on the behavior of individual agents undergoing consensus dynamics. We show that the Fielder vector can be estimated from the states of the agents and that the entries of this vector can describe the subsequent behavior of the agents. In addition, we discuss how the Fiedler vector sheds light on the...
In this paper we present a new approach of using input-output linearization to control a single input, single output, input-affine nonlinear non-minimum phase system. We will show that, if the linearized system is stabilizable, we can redefine the output of the system such that the input-output linearized system is locally asymptotically stable. Furthermore we develop an LQR technique for designing...
In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced order models by randomly choosing a subset of the inputs/outputs of the system to construct a suitable small sized Hankel matrix from the full Hankel matrix. It is...
It is now well realized [1] that two unstable dynamical systems, attempting to stabilize each other using the error between their outputs for adjusting their parameters, may not always succeed. The fact that adaptation may result in instability makes the mathematical problem a very interesting one. Since similar problems are arising in many other branches of science (e.g psychology, biology, medicine...
In this paper we investigate the problem of motion coordination of a class of multi-agent robotic systems. By means of consensus theory, we implement a decentralized control scheme which relies on the exchange of information between agents in order to obtain a coordinated motion trajectory. The key feature of this approach relies in the fact that consensus is applied to a set of exosystems (one for...
We present a design scheme for the synchronization of linear heterogeneous SISO systems by static feedback controllers. Extending some recent results, a distributed method is provided for synchronizing non-identical agents by a simple synchronization controller for homogeneous agents. In [4], it was shown that for a special condition heterogeneous agents can be synchronized by static controllers....
Chaos occurs widely in artificial and natural nonlinear systems and its irregular behavior is usually undesirable. Controlling chaos, that is, stabilization of chaotic systems, is one of major subjects in nonlinear control problems. In this paper we propose a computer-aided design method of stabilizing controllers for continuous-time chaotic systems, in which we extend our previous work so as to realize...
This paper investigates the bipartite consensus for a group of agents with a leader. The interaction topology among agents is directed, weighted, signed and structurally balanced. Some sufficient and necessary conditions are derived for the bipartite consensus of the leader-following multi-agent system. Specifically, under the assumption that the interaction graph involving the leader has a spanning...
Stability condition is considered for a class of second-order piecewise linear systems. The state space of the system is divided by partitions into some subsystems. The state trajectory evolves along with the dynamics of the subsystem in which the state exists. A necessary and sufficient condition for the system to be stable is derived. The condition is expressed via the eigenvalues of the matrices...
In this paper, we are concerned with the study of the spectrum of a periodic potential in 1D, modelling the interactions of an electron with a regular lattice of ions. The classical Bloch theory asserts that the spectrum has a band structure. In the case of a sawtooth potential, we have a very precise description and estimates of all bands and of all gaps under the potential barrier and near the minimum...
When designing a control system, it is quite important to consider different constraints in order to provide the system's degree of robustness. It is possible to design the robust systems using some conventional approaches. However, they do not make clear how to consider constraints on systems parameters, sufficient system nonlinearities, and how to provide the necessary degree of robustness. The...
The stability of a nonlinear reaction-diffusion process and its convergence rate can be determined very simply, based on an extension of the recently developed tools of contraction theory. This paper extend our earlier results [9] to the case where the diffusion term is itself nonlinear and where a convection term is also introduced. The results have applications to observer design for distributed...
The notion of a balanced realization for a general nonlinear time-varying system is introduced for state space systems that have an attracting invariant regular sub-manifold. This is viewed as a generalization of the usual case where balancing is done near a stable equilibrium point. The special case of balancing an unstable linear time-invariant systems is considered as an example.
The notions of strong and weak synchronization of chaotic systems are reviewed in the context of three coupled identical one-dimensional maps. Two possibilities exist. Either all three systems synchronize (total synchronization), or only two out of three systems synchronize (partial synchronization, or clustering). In either case, strong and weak synchronization is possible.
Given an interval matrix system with discrete- or continuous-time dynamics, the flow-invariance of an arbitrarily time-dependent rectangular set with respect to this system is introduced as a concept of geometric nature. The case of rectangular sets with exponential time-dependence is separately explored. If there exist flow-invariant rectangular sets approaching the state space origin for an infinite...
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