2,312 publications from this institution
A single-link flexible-joint manipulator is considered. An analytic closed-form optimal solution is obtained for the nonlinear constrained optimal trajectory planning problem. The optimal solution turns out to be exact in the sense that no approximation is applied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
In this paper, the commonly concerned issue of synchronization regions of complex dynamical networks is investigated, for the case when the synchronous state is an equilibrium point. Some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form ( - ∞ , α 1 ) are established, where α 1 is a constant. In addition, a sufficient condition for the existence of a bounded synchronization region of the form ( α 2 , α 3 ) is derived, where α 2 and α 3 are constants, by using the parameter-dependent Lyapunov function method. Furthermore, some effective controller design methods are presented that can change the synchronization regions, thereby managing the synchronizability of the network. Finally, some numerical examples are given to show that a dynamical network may have disconnected synchronization regions, particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of ( - ∞ , α 1 ) ∪ ( α 2 , α 3 ) .
Journal Article Minimum-Energy Optimal Control of a Steady-State Distributed Harmonic System with State Constraints Get access GUANRONG CHEN GUANRONG CHEN Department of Electrical and Computer Engineering, Rice UniversityHouston, Texas 77251, U.S.A. Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Mathematical Control and Information, Volume 6, Issue 1, 1989, Pages 63–70, https://doi.org/10.1093/imamci/6.1.63 Published: 01 March 1989 Article history Received: 25 April 1988 Published: 01 March 1989
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This study uses seven four-dimensional four-variable polynomial chaotic maps without equilibria in combination with generalized chaos synchronization (GCS) theorem to construct eight-dimensional bidirectional discrete generalized chaos synchronization (8DBDGCS) systems without equilibria. By combining the 8DBDGCS system with the GCS theorem, a 12-dimensional GCS system is designed. Numerical simulation verifies the chaotic dynamics of the 12-dimensional GCS system, which is used to design a 2 16 -word chaotic pseudorandom number generator (CPRNG). The SP-8002 test suite is used to test the randomness of four 100-key streams consisting of 1 000 000 bits generated respectively by the CPRNG, a six-dimensional GCS-based CPRNG, the RC4 algorithm and the ZUC algorithm. The results show that the randomness performances of the two CPRNGs are promising, suggesting that there are no significant correlations between the key stream and the perturbed key streams generated via the 2 16 -word CPRNG. In addition, theoretically the key space of the CPRNG is larger than 2 1195 . The CPRNG is used with an avalanche-encryption scheme to encrypt an RGB balloon image, demonstrating that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal 2 16 -word CPRNGs.
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This paper presents the Chen system as a controlled weather model. Mathematically, the Chen system is dual to the Lorenz system via time reversal. Physically, the Chen system can be viewed as a controlled weather model from the anti-control perspective. This paper illustrates the physical principle of this controlled weather model, and develops an engineering design of the model for real indoor climate (temperature-humidity) regulation, with a perspective on outdoor weather control application.
In this paper, a simple control method that combines a linear state-feedback with a nonlinear mod-operation is proposed for making an arbitrarily given, deterministic, discrete-time dynamical systems chaotic. The given system can be arbitrary in the sense that it can be either linear or nonlinear, lower or higher-dimensional, asymptotically stable, unstable, or chaotic. The resulting controlled system is chaotic in the sense that the controlled map (1) has sensitive dependence on initial conditions, (2) is topologically transitive, and (3) has a dense set of periodic points.
Network robustness is critical for various industrial and social networks against malicious attacks, which has various meanings in different research contexts and here it refers to the ability of a network to sustain its functionality when a fraction of the network fail to work due to attacks. The rapid development of complex networks research indicates special interest and great concern about the network robustness, which is essential for further analyzing and optimizing network structures towards engineering applications. This comprehensive survey distills the important findings and developments of network robustness research, focusing on the a posteriori structural robustness measures for single-layer static networks. Specifically, the a posteriori robustness measures are reviewed from four perspectives: 1) network functionality, including connectivity, controllability and communication ability, as well as their extensions; 2) malicious attacks, including conventional and computation-based attack strategies; 3) robustness estimation methods using either analytical approximation or machine learning-based prediction; 4) network robustness optimization. Based on the existing measures, a practical threshold of network destruction is introduced, with the suggestion that network robustness should be measured only before reaching the threshold of destruction. Then, a posteriori and a priori measures are compared experimentally, revealing the advantages of the a posteriori measures. Finally, prospective research directions with respect to a posteriori robustness measures are recommended.
Recently, an effective method for realizing linearly separable Boolean functions via Cellular Neural Networks (CNN), called the threshold bifurcation method, was introduced, with a CNN gene bank of four variables established [Chen & Chen, 2005]. Based on this success, the present paper is to further explore the realization of all linearly separable Boolean functions of five variables via CNN with von Neumann neighborhoods. This paper provides: (i) important and essential relations among the genes (or templates) and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set, (ii) a neat truth table of uncoupled CNN with five input variables, (iii) 94572 linearly separable Boolean functions (LSBF) in the family of 2 25 = 4.294967296 × 10 9 Boolean functions of five variables, realizable by a single CNN, and (iv) all 94572 CNN linearly separable Boolean genes (LSBG), which can be determined to form the CNN gene bank of five variables.
This paper is concerned with a leader–follower problem for a multi-agent system with a switching interconnection topology. Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time. Some dynamic neighbor-based rules, consisting of distributed controllers and observers for the autonomous agents, are developed to keep updating the information of the leader. With the help of an explicitly constructed common Lyapunov function (CLF), it is proved that each agent can follow the active leader. Moreover, the tracking error is estimated even in a noisy environment. Finally, a numerical example is given for illustration.
A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.
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In the last two years, we have developed some new ideas and techniques for the control of chaotic nonlinear systems using conventional feedback controllers design methods, for both discrete-time and continuous-time systems [1-4], where the target position is either an (unstable) equilibrium point or an (unstable) limit cycle of the chaotic system. In this paper, we further provide a rigorous mathematical theory to support these new ideas and techniques, for a particular yet representative case: the well-known continuous-time chaotic Duffing system.
