In this paper, we study state-feedback controller design for controlling the Lyapunov exponents of an n-dimensional dynamical system. We examine some theoretical results and perform numerical simulations for systems with and without noise influence. The controlled Lyapunov exponents are asymptotically normally distributed if the system has noisy inputs. Computer simulations on finite samples are all consistent with the theoretical results.
This paper studies the dynamics of traveling wave solutions to a shallow water wave model with a large-amplitude regime in phase space. The corresponding traveling wave system is a singular planar dynamical system with two singular straight lines. By using the method of dynamical systems, bifurcation diagrams are obtained. The existence of solitary wave solutions, periodic wave solutions, peakon, pseudo-peakon solution, periodic peakon solutions and compacton solutions are determined under different parameter conditions.
In this paper, the controllability problem is addressed for temporally switching networks and the associated temporally switching systems. The state controllability criterion of temporally switching systems is firstly obtained, which stands for structural controllability of temporally switching networks with the same structure. With a new temporal interpretation of the dilation and intersection concepts, some algebraic and graphic criteria are precisely derived. Specifically, it reveals that the essence for the structural controllability is the existence of n temporally independent walks (the n-walk theory), which generalizes the classical concept of cactus in graph theory to temporal networks. Furthermore, from the perspective of the new n-walk theory, its uniqueness makes the notion of strong structural controllability more precise and clearer for temporal networks. This comprehension of the (strong) structural controllability concept not only is of particular advantage for more in-depth studies of network control problems, but also provides useful guidance for constructing controllable temporal networks.
In this article, the constrained optimization problem with its global objective function being the sum of convex local cost functions and the constraint being a closed convex set is researched. The aim of this study is to solve the researched problem in a distributed manner, that is, using only local computations and local information exchanges. Toward this end, two gradient-tracking-based distributed optimization algorithms are designed for the considered problem over weight-balanced and weight-unbalanced graphs, respectively. Since the classical projection method is unsuitable to handle the closed convex set constraint under the gradient-tracking framework, a new indirect projection method is employed in this article to deal with the involved closed convex set constraint. Furthermore, two time scales are introduced to complete the convergence analyses. In addition, under the condition that all local cost functions are strongly convex and L -smooth, it is proved that the algorithms with well-selected fixed step sizes have linear convergence rates.
No abstract is provided for this article.
This paper is concerned with a novel four-dimensional continuous autonomous hyperchaotic system, which is obtained by adding a simple dynamical state-feedback controller to a Lorenz-like three-dimensional autonomous chaotic system. This new system contains three parameters and each equation of the system has one quadratic cross-product term. Some basic properties of the system are studied first. Its complex dynamic behaviors are then analyzed by means of Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits and Poincaré sections. It is shown that the system has several large hyperchaotic regions. When the system is evolving in a hyperchaotic region, the two positive LEs are both large, which can be larger than 1 if the system parameters are taken appropriately. The pitchfork bifurcation of the system is finally analyzed by using the center manifold theorem.
In this paper, the adaptive filtering problem for unknown genetic regulatory networks with disturbance attenuation is investigated based on Lyapunov method and adaptive techniques. A new regulatory network and several adaptive laws are designed to ensure the stochastic stability of the error states between the unknown and the estimated networks. The designed adaptive laws are independent of the unknown system states and parameters, where the only required information is the structure of the network. A simulation example is given to verify the theoretical results.
In coordinative control of a network of multi-agent systems, to guarantee the stability of the coordinated motion, a basic assumption typically is that the underlying topology of the network can maintain its connectivity frequently enough during the motion evolution. However, for a given set of initial conditions, this assumption is very difficult to satisfy and verify. In particular, the connectivity of the initial network generally cannot guarantee the connectivity of the network throughout the evolution. In this paper, we propose a rendezvous protocol with double-integrator dynamics, which combines the functions of motion control and connectivity preservation. This protocol can enable the group of mobile agents to converge to the same position and move with the same velocity while preserving the connectivity of the whole network during the evolution if the initial network is connected. We find that there is a trade-off between the maximum overshoot and the settling time of the velocity convergence. Furthermore, we investigate the rendezvous protocol with a virtual leader and show that all agents can asymptotically attain a desired velocity even if only one agent in the team has information about the virtual leader. We finally show some numerical simulations to verify and illustrate the theoretical results.
In this paper, the problem of making a stable map chaotic by using smooth small-amplitude high-frequency feedback control is studied. The controlled map is mathematically proven to be chaotic in the sense of Li and Yorke. To demonstrate the practical usefulness of the proposed method, it is applied to a feedback boost switching regulator model operating in discontinuous mode. Copyright © 2000 John Wiley & Sons, Ltd.
This work presents an efficient approach for computing the slow invariant manifold of the fourth-order canonical memristor-based Chua circuits using the flow curvature method. First, the magnetic-flux and charge characteristic curve is generated from the classical circuit with a piecewise-linear function. Then, the characteristic curve is generated from the circuit with the piecewise-linear function replaced by a cubic function. Further, the duality principle is applied to studying such memristor-based circuits in the three-dimensional flux-linkage and charge phase space and then in the four-dimensional current–voltage phase space. It is demonstrated that the slow invariant manifolds of these fourth-order memristor-based chaotic circuits can be more directly computed for the first case than the second.
