Visible to the public Dynamical Systems

SoS Newsletter- Advanced Book Block

Dynamical Systems

Research into dynamical systems cited here focuses on non-linear and chaotic dynamical systems and in proving abstractions of dynamical systems through numerical simulations. The first paper was presented at HOT SoS 2014, the Symposium and Bootcamp on the Science of Security (HotSoS), a research event centered on the Science of Security held April 8-9, 2014 in Raleigh, North Carolina.

  • Mitra, S. "Proving Abstractions of Dynamical Systems through Numerical Simulations" HOT SoS 2014 (To be published 2014 in Journals of the ACM.) (ID#:14-1362) Available at: A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether or not the ideal system is an abstraction of the attacked system. A quantitative variation of this question can capture how much the attacked system deviates from the ideal. Thus, algorithms for deciding abstraction relations can help measure the effect of attacks on cyberphysical systems and to develop attack detection strategies. In this paper, we present a decision procedure for proving that one nonlinear dynamical system is a quantitative abstraction of another. Directly computing the reach sets of these nonlinear systems are undecidable in general and reach set over-approximations do not give a direct way for proving abstraction. Our procedure uses (possibly inaccurate) numerical simulations and a model annotation to compute tight approximations of the observable behaviors of the system and then uses these approximations to decide on abstraction. We show that the procedure is sound and that it is guaranteed to terminate under reasonable robustness assumptions. Keywords: cyberphysical systems, adversary, simulation, verification, abstraction.
  • Dong Juny; Li Donghai, "Nonlinear robust control for complex dynamical systems," Control Conference (CCC), 2013 32nd Chinese , vol., no., pp.5509,5514, 26-28 July 2013. (ID#:14-1363) Available at: The plants of complex dynamical systems consist of real part and imaginary part and there exits strong coupling between them. In this paper, the nonlinear robust controller is applied in the control of six typical complex dynamical systems expressed in differential equations. Two control schemes of the systems are designed. One scheme treats the real part and imaginary part of the complex dynamical systems as a whole to design a single-input single-output control system, another scheme independently deals with the real part and imaginary part to design a two-input two-output control system. The simulated results show that the nonlinear robust controller can achieve effective control for complex dynamical systems, and that the two control schemes can achieve same control performance on the premise of the same initial system states and controller parameters. Keywords: control system synthesis; differential equations; large-scale systems; nonlinear control systems; robust control; time-varying systems; complex dynamical systems; control system design; differential equations; nonlinear robust control; single-input single-output control system; two-input two-output control system; Control systems; Electronic mail; Frequency modulation; Power system dynamics; Robust control; Robustness; Thermal engineering; complex dynamical systems; nonlinear robust controller; the imaginary part; the real part
  • Brito Palma, L.; Costa Cruz, J.; Vieira Coito, F.; Sousa Gil, P., "Interactive demonstration of a java-based simulator of dynamical systems," Experiment@ International Conference ('13), 2013 2nd, vol., no., pp.176,177, 18-20 Sept. 2013 (ID#:14-1364) Available at: In this paper, an interactive demonstration of a java-based simulator of dynamical systems is presented. This simulator implements linear low-order process models (first order, second order and third order). Open-loop control and closed-loop tests can be done with the application. The main contribution is a Java application that can be used by the instructor / user in a blended learning environment to teach / learn the basic notions of dynamical systems, in open-loop control and also in closed-loop control, running on all the most popular operating systems. Keywords: Java ;closed loop systems; computer aided instruction; control engineering computing; control engineering education; digital simulation; interactive systems; open loop systems; Java-based simulator; automatic control; blended learning environment; closed-loop control; closed-loop tests; dynamical systems; interactive demonstration; linear low-order process models; open-loop control; operating systems; Control systems; Java; Remote laboratories; Software; Time factors; Transfer functions; automatic control; dynamical systems; engineering education ; learning systems; simulation
  • Kim, K.-K.K.; Shen, D.E.; Nagy, Z.K.; Braatz, R.D., "Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives]," Control Systems, IEEE , vol.33, no.5, pp.58,67, Oct. 2013. (ID#:14-1365) Available at: One purpose of the "Historical Perspectives" column is to look back at work done by pioneers in control and related fields that has been neglected for many years but was later revived in the control literature. This column discusses the topic of Norbert Wiener's most cited paper, which proposed polynomial chaos expansions (PCEs) as a method for probabilistic uncertainty quantification in nonlinear dynamical systems. PCEs were almost completely ignored until the turn of the new millennium, when they rather suddenly attracted a huge amount of interest in the noncontrol literature. Although the control engineering community has studied uncertain systems for decades, all but a handful of researchers in the systems and control community have ignored PCEs. The purpose of this column is to present a concise introduction to PCEs, provide an overview of the theory and applications of PCE methods in the control literature, and to consider the question of why PCEs have only recently appeared in the control literature. Keywords: chaos; control system analysis; nonlinear control systems; nonlinear dynamical systems; polynomials; probability; uncertain systems; PCE; Wiener polynomial chaos expansion; nonlinear dynamical system analysis; nonlinear dynamical system control; probabilistic uncertainty quantification; uncertain systems; Approximation methods; Computational modeling; History; Mathematical model; Nonlinear systems; Probabilistic logic; Random variables; Uncertainty
  • Masuda, Kazuaki, "A method for finding stable-unstable bifurcation points of nonlinear dynamical systems by using a Particle Swarm Optimization algorithm," SICE Annual Conference (SICE), 2013 Proceedings of , vol., no., pp.554,559, 14-17 Sept. 2013. (ID#:14-1506) Available at: In this paper, we propose a method for finding stable-unstable bifurcation points of nonlinear dynamical systems by using a Particle Swarm Optimization (PSO) algorithm. Since the structure of systems can change suddenly at such points, it is desired to find them in advance for the purpose of engineering such as design, control, etc. We formulate a mathematical optimization problem to find a particular type of bifurcation points of nonlinear black-box systems, and we solve it numerically by employing a Particle Swarm Optimization (PSO) algorithm. Practicality of the proposed method is investigated by numerical experiments. Keywords: Aerospace electronics; Bifurcation; Linear programming; Nonlinear dynamical systems; Optimization; Trajectory; Vectors; Nonlinear dynamical systems; Particle Swarm Optimization (PSO); bifurcation; constrained optimization; multiple optimal solutions search
  • Wenwu Yu; Guanrong Chen; Ming Cao; Wei Ren, "Delay-Induced Consensus and Quasi-Consensus in Multi-Agent Dynamical Systems," Circuits and Systems I: Regular Papers, IEEE Transactions on , vol.60, no.10, pp.2679,2687, Oct. 2013. (ID#:14-1507) Available at: This paper studies consensus and quasi-consensus in multi-agent dynamical systems. A linear consensus protocol in the second-order dynamics is designed where both the current and delayed position information is utilized. Time delay, in a common perspective, can induce periodic oscillations or even chaos in dynamical systems. However, it is found in this paper that consensus and quasi-consensus in a multi-agent system cannot be reached without the delayed position information under the given protocol while they can be achieved with a relatively small time delay by appropriately choosing the coupling strengths. A necessary and sufficient condition for reaching consensus in multi-agent dynamical systems is established. It is shown that consensus and quasi-consensus can be achieved if and only if the time delay is bounded by some critical value which depends on the coupling strength and the largest eigenvalue of the Laplacian matrix of the network. The motivation for studying quasi-consensus is provided where the potential relationship between the second-order multi-agent system with delayed positive feedback and the first-order system with distributed-delay control input is discussed. Finally, simulation examples are given to illustrate the theoretical analysis. Keywords: {delays; eigenvalues and eigen functions; feedback; graph theory; multi-agent systems; protocols; Laplacian matrix; delayed position information; delayed positive feedback; distributed-delay control input; eigenvalue; linear consensus protocol; multiagent dynamical systems; periodic oscillations; quasiconsensus; second-order dynamics; time delay; Algebraic graph theory; delay-induced consensus; multi-agent system; quasi-consensus
  • Zhaoyan Wu; Xinchu Fu, "Structure identification of uncertain dynamical networks coupled with complex-variable chaotic systems," Control Theory & Applications, IET , vol.7, no.9, pp.1269,1275, June 13 2013. (ID#:14-1508) Available at: This paper recognizes the inability to predetermine all topological structures of uncertain dynamical networks in practical applications. Proposed is a structure identification method for uncertain dynamical methods associated with complex-variable chaotic systems. The proposed method is based on the Barbalatis lemma, and is verified in this paper with numerical simulations. Keywords: chaos; complex networks; nonlinear dynamical systems; numerical analysis; topology; uncertain systems; Barbalat's lemma; complex-variable chaotic systems; network estimators; node dynamics; numerical simulations; uncertain dynamical networks; uncertain topological structure.


Articles listed on these pages have been found on publicly available internet pages and are cited with links to those pages. Some of the information included herein has been reprinted with permission from the authors or data repositories. Direct any requests via Email to SoS.Project (at) for removal of the links or modifications to specific citations. Please include the ID# of the specific citation in your correspondence.