Publications

This chapter describes mathematical representation, approximation, and identification of, in most cases, nonlinear systems. An ideal representation of a real system is generally impossible, so that system approximation becomes necessary in practice. Intuitively, approximation is always possible. However, the key issues are what kind of approximation is good, where the sense of "goodness" must first be defined, of course, and how to find such a good approximation. The fundamental issue in representing a physical system by a mathematical formulation, called a mathematical model, is its correct symbolization, accurate quantization, and strong ability to illustrate and reproduce important properties of the original system. A higher level mathematical model is needed to provide a qualitative and quantitative representation of the real physical circuit. Mathematical modeling via differential equations and via state-space descriptions are the most basic mathematical representation methods.

In this paper, the problem of making a stable nonlinear autonomous system chaotic or enhancing the existing chaos of an originally chaotic system by using a small-amplitude feedback controller is studied. The designed controller is a linear feedback controller composed with a nonlinear modulo or sawtooth function, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, thereby yielding chaotic dynamics. We mathematically prove that the controlled system is indeed chaotic in the sense of Li and Yorke. A few potential applications of the new chaotification algorithm are briefly discussed.

In this paper, the state controllability of networked higher-dimensional linear time-invariant dynamical systems is considered, where communications are performed through one-dimensional connections. The influences on the controllability of such a networked system are investigated, which come from a combination of network topology, node-system dynamics, external control inputs and inner interactions. Particularly, necessary and sufficient conditions are presented for the controllability of the network with a general topology, as well as for some special settings such as cycles and chains, which show that the observability of the node system is necessary in general and the controllability of the node system is necessary for chains but not necessary for cycles. Moreover, two examples are constructed to illustrate that uncontrollable node systems can be assembled to a controllable networked system, while controllable node systems may lead to uncontrollable systems even for the cycle topology.This article is part of the themed issue 'Horizons of cybernetical physics'.

Abundant collective motion patterns of animal groups have different kinds of functions like migration, predator avoidance and foraging. To explore the phase transition mechanism behind such charming collective behaviors, some self-propelled particle models have been proposed, most of which however have isotropic inter-particle interactions and hence could not reproduce sophisticated natural collective patterns. As a remedy, this letter develops an anisotropic self-propelled particle model. By slightly tweaking the vision range and inter-particle attraction, the proposed model demonstrate transitions between four distinct collective motion patterns, i.e. , torus, dumbbell, twist, and worm. To investigate more insightfully into the phase transition nature, quantitative analysis is carried out, revealing the relationship of visual angle-based inter-agent interactions and abundant pattern transitions existing in large numbers of natural, social and artificial grouping behaviors. From the industrial application point of view, the present study can help adjust the formation of multiple unmanned systems by simply tweaking a couple of vision-related parameters in their models.

Article Free Access Share on Performance analysis of fuzzy proportional-derivative control systems Authors: Huaidong Li Instiute of Space Systems Operations, University of Houston Instiute of Space Systems Operations, University of HoustonView Profile , Heidar Malki Instiute of Space Systems Operations, University of Houston Instiute of Space Systems Operations, University of HoustonView Profile , Guanrong Chen Instiute of Space Systems Operations, University of Houston Instiute of Space Systems Operations, University of HoustonView Profile Authors Info & Claims SAC '94: Proceedings of the 1994 ACM symposium on Applied computingApril 1994 Pages 115–119https://doi.org/10.1145/326619.326679Online:06 April 1994Publication History 2citation754DownloadsMetricsTotal Citations2Total Downloads754Last 12 Months2Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper introduces a novel fourth-order double-torus chaotic circuit. Based on this basic circuit, a systematic theoretical design approach is proposed for generating 1-D <formula formulatype="inline"><tex>$n$</tex></formula> torus, 2-D <formula formulatype="inline"><tex>$n\times m$</tex></formula>–torus, 3-D <formula formulatype="inline"><tex>$n\times m\times l$</tex></formula> torus, and 4-D <formula formulatype="inline"><tex>$n \times m \times l \times p$</tex> </formula> torus chaotic attractors. This is the first autonomous circuit reported in the literature for generating multidirectional multi-torus (MDMT) chaotic attractors. The dynamical behaviors of these MDMT chaotic systems are further investigated, including equilibrium points, bifurcations, Lyapunov exponents, and PoincarÉ maps. Theoretical analysis shows that the MDMT chaotic attractors can be generated by switching and displacing a basic linear circuit. Finally, a block circuit diagram is designed for hardware implementation of the MDMT chaotic attractors. This is also the first time in the literature to experimentally verify a maximal 1-D 20–torus, a maximal 2-D 5<formula formulatype="inline"><tex>$\,\times \,$</tex></formula>5 torus, and a maximal 4-D 5<formula formulatype="inline"><tex>$\,\times \,$</tex></formula>5<formula formulatype="inline"><tex>$\,\times \,$</tex></formula>3<formula formulatype="inline"> <tex>$\,\times \,$</tex></formula>3 torus chaotic attractors. </para>

No abstract is provided for this article.

We propose a variable structure control method which is another innovative technique for suppressing beam halo-chaos in the periodic focusing channels of high-current proton beam accelerator, which belongs to a high-tech field. The analysis and numerical results show that the method is effective for controlling beam halo-chaos. Physical implementation of such a kind of control strategy remains an important and open issue for further applications.

In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means that the network synchronizes faster with lower-overshoot. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an optimal controller is designed, according to the so-called LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network.

By employing the finite-time control method, the consensus control algorithm for higher-order multiagent systems is designed in this paper. Under a neighbor-based rule, a higher-order finite-time consensus algorithm is explicitly constructed, which only uses local information. The finite-time consensus control algorithm can guarantee that the state consensus is achieved in a finite time. In addition, for multiagent systems having a leader-following structure, the consensus algorithm is also designed. Finally, two examples are presented to show the effectiveness.

With the wide application of AI services in the era of big data, federated learning models that can solve the data silo problem without sharing sensitive data in different devices have received much attention. Research in recent years has shown that private information can still be inferred by analyzing model parameters localized in federated learning models. To address this risk, differential privacy techniques have been applied to federated learning models due to their unique privacy-preserving approach to protect customers’ private data. However, the proposed joint learning models based on differential privacy still have flaws. Firstly, the heterogeneity of the gradient parameters is not taken into account which affects the convergence of the model and the quality of the training parameters, because the gradient cropping thresholds used in the model training are the same, and it is not possible to adaptively adjust the amount of added noise. Secondly the way of client selection in the model is a random selection method, which is not conducive to ensuring that excellent clients are selected to participate in model aggregation in each round of training. Based on the above problems, this paper proposes a federated learning model with aggregated gradient adaptive cropping technique and client self-selection, which adapts to adjust the amount of noise by means of adaptive gradient cropping of different clients in different rounds, and combines roulette and elite retention client sampling methods to accelerate the convergence of the model. Experiments demonstrate that our proposed model is able to improve the classification accuracy of the final model by 5.1% under the same level of privacy constraints compared to the traditional joint learning model. In terms of convergence speed, the number of rounds required for our model to enter the convergence state is reduced by $\mathbf{1 0 - 1 5}$ rounds compared to the traditional approach.