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Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques 被引量:1
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作者 LIU Minzhong KANG Lisha 《Wuhan University Journal of Natural Sciences》 EI CAS 2006年第3期520-524,共5页
We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The conver... We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems (mainly the Lorenz and Chen systems). The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems. 展开更多
关键词 dynamical evolutionary algorithm nonlinear dynamical systems RECONSTRUCTION
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Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties
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作者 Yu Kai, Zhao Chang’an & Li ShiyongDepartment of Control Science and Technology, Harbin Institute of Technology, Harbin 150001, P. R. China(Received June 28, 2001) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2002年第2期92-97,共6页
The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controller... The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective. 展开更多
关键词 Exponential stability nonlinear dynamical systems UNCERTAINTY State feedback controller.
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Nonlinear Systems Identification via an Input-Output Model Based on a Feedforward Neural Network
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作者 O. L. Shuai South China University of Technology, Gungzhou, 510641, P.R. China S. C. Zhou S. K. Tso T. T. Wong T.P. Leung The Hong Kong Polytechnic University, HungHom, Kowloon, HK 《International Journal of Plant Engineering and Management》 1997年第4期45-50,共6页
This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed m... This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model. 展开更多
关键词 nonlinear dynamic systems identification neural networks based Input Output Model identification error characteristic curve
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Comparing dynamical systems concepts and techniques for biomechanical analysis 被引量:3
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作者 Richard E.A.van Emmerik Scott W.Ducharme +1 位作者 Avelino C.Amado Joseph Hamill 《Journal of Sport and Health Science》 SCIE 2016年第1期3-13,共11页
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin... Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints. 展开更多
关键词 Adaptability Complexity Dynamical systems nonlinear dynamics Stability Variability
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Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems 被引量:1
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作者 Evgeniy Perevoznikov Olga Mikhailova 《Journal of Applied Mathematics and Physics》 2015年第5期569-576,共8页
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a... Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems. 展开更多
关键词 nonlinear Dynamical systems Stability Analysis Methods Dynamical Chaos Lorenz and Rossler Model Problems
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THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS
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作者 Linghai Zhang 《Annals of Applied Mathematics》 2016年第4期396-417,共22页
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp ra... Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall's inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980's to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established. 展开更多
关键词 nonlinear systems of fluid dynamics equations global weaksolutions decay estimates uniform energy estimates Fourier transformation Plancherel's identity Gronwall's inequality improved Fourier splitting method
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Generalised energy conservation law for chaotic phenomena 被引量:4
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作者 Jing-Tang Xing 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第6期1257-1268,共12页
Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is... Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted. 展开更多
关键词 CHAOS Generalised energy Generalised energy conservation nonlinear dynamical systems Energy flow theory
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Analysis of High Codimensional Bifurcation and Chaos for the Quad Bundle Conductor's Galloping 被引量:4
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作者 刘富豪 张琪昌 谭莹 《Chinese Physics Letters》 SCIE CAS CSCD 2010年第4期171-174,共4页
A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transforma... A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos. 展开更多
关键词 Fluid dynamics Mathematical physics Statistical physics and nonlinear systems
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Analysis of some large-scale nonlinear stochastic dynamic systems with subspace-EPC method
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作者 ER GuoKang IU VaiPan 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2011年第9期1631-1637,共7页
The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-E... The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases. 展开更多
关键词 nonlinear stochastic dynamic systems large-scale systems probability density function Fokker-Planck-Kolmogorov equation subspace-EPC
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Hybrid extended Fourier series for optimal control of nonlinear algebraic dynamical systems
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作者 Jalal NAZARZADEH Hamidreza RADMANESH 《控制理论与应用(英文版)》 EI 2011年第4期487-492,共6页
The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier se... The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature. 展开更多
关键词 Bilinear systems Hybrid extended Fourier series nonlinear algebraic dynamic systems Quadratic systems Optimal control
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The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems
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作者 Guo-Kang Er Vai Pan Iu 《Communications in Computational Physics》 SCIE 2011年第10期1241-1256,共16页
The probabilistic solutions of the nonlinear stochastic dynamic(NSD)systems with polynomial type of nonlinearity are investigated with the subspace-EPC method.The space of the state variables of large-scale nonlinear ... The probabilistic solutions of the nonlinear stochastic dynamic(NSD)systems with polynomial type of nonlinearity are investigated with the subspace-EPC method.The space of the state variables of large-scale nonlinear stochastic dynamic system excited by white noises is separated into two subspaces.Both sides of the Fokker-Planck-Kolmogorov(FPK)equation corresponding to the NSD system is then integrated over one of the subspaces.The FPK equation for the joint probability density function of the state variables in another subspace is formulated.Therefore,the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of largescale NSD systems solvable with the exponential polynomial closure method.Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases. 展开更多
关键词 nonlinear stochastic dynamic systems large-scale systems probability density function Fokker-Planck-Kolmogorov equation SUBSPACE
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Relaxation Oscillation of Thermal Convection in Rotating Cylindrical Annulus
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作者 陶建军 谭文长 《Chinese Physics Letters》 SCIE CAS CSCD 2010年第3期220-223,共4页
Chaotic thermal convection in a rapidly rotating cylindrical annulus is investigated numerically and the relaxation oscillation state is obtained under the no-slip boundary condition. The dominant frequency of the osc... Chaotic thermal convection in a rapidly rotating cylindrical annulus is investigated numerically and the relaxation oscillation state is obtained under the no-slip boundary condition. The dominant frequency of the oscillation is inherited directly from a vacillating mode, whose nonlinear interaction with another high-frequency vacillating mode leads to the chaotic state at high Rayleigh numbers through an RTN-type route. Furthermore, the effects of Coriolis parameter and Rayleigh number on the quasi-periodic burst of kinetic energy are discussed as well. 展开更多
关键词 Fluid dynamics Statistical physics and nonlinear systems
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Generalized Lorenz Equation Derived from Thermal Convection of Viscoelastic Fluids in a Loop
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作者 杨帆 朱克勤 《Chinese Physics Letters》 SCIE CAS CSCD 2010年第3期196-199,共4页
A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 (a measure of the fluid relaxation) and De2 (a measure of the ... A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 (a measure of the fluid relaxation) and De2 (a measure of the fluid retardation) appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution (limit cycle) in the system and impedes the onset of chaos while the fluid retardation (De2) tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system. 展开更多
关键词 Fluid dynamics Mathematical physics Statistical physics and nonlinear systems
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Global dynamics of a model of hepatitis B virus infection in a sub-Saharan African rural area 被引量:1
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作者 Jean Pierre II Kouenkam Joseph Mbang Yves Emvudu 《International Journal of Biomathematics》 SCIE 2020年第6期257-298,共42页
We formulate and systematically study a deterministic compartmental model of Hepatitis B.This model has some important and novel features compared with the well-known basic model in the literature.Specifically,it take... We formulate and systematically study a deterministic compartmental model of Hepatitis B.This model has some important and novel features compared with the well-known basic model in the literature.Specifically,it takes into account the differential susceptibility that follows the vaccine formulation employing three-doses schedule.It points up the HbeAg status of carriers,their levels of viral replication,the fact that treatment being not curative is recommended only to a small proportion of chronic carriers,and finally the fact that only inactive carriers are able to recover from disease.The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R0≤1 and an endemic equilibrium when R0>1.By the use of Lyapunov functions,when it exists,we prove the global asymptotic stability of the endemic equilibrium under some conditions.Using data from Tokombere,a rural area in Cameroon,numerical simulations are performed.These numerical simulations first confirm analytical results,second they suggest that a policy based on treatment could not significantly impact the course of the infection.Third,they show as it is well known that vaccination is a very effective measure to control the infection.Furthermore,they show that neonatal vaccination influences more the course of infection than mass vaccination strategy.Nevertheless,they picture how much loss between consecutive doses of vaccine could be harmful.Finally,it is suggested that for a Sub-saharan African rural area,two-thirds of expected incidence of Hepatitis B virus infection and one third of expected prevalence of chronic carriers could be averted by 2030 if the birth dose vaccination becomes systematic and if mass vaccination rate increases to up 10%. 展开更多
关键词 nonlinear dynamical systems Lyapunov methods inactive carriers differential susceptibility differential infectivity
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Nonlinear Time Series Analysis Since 1990:Some Personal Reflections 被引量:4
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作者 Howel Tong 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2002年第2期177-184,共8页
I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonpa... I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series. 展开更多
关键词 CHAOS common structure curse of dimensionality embedding dimension financial time series initial value sensitivity local polynomial smoother long memory Markov chain Monte Carlo nonlinear dynamical systems nonlinear state space models
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Aircraft-on-ground path following control by dynamical adaptive backstepping 被引量:6
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作者 Chen Bihua Jiao Zongxia Shuzhi Sam Ge 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2013年第3期668-675,共8页
The necessity of improving the air traffic and reducing the aviation emissions drives to investigate automatic steering for aircraft to effectively roll on the ground. This paper addresses the path following control p... The necessity of improving the air traffic and reducing the aviation emissions drives to investigate automatic steering for aircraft to effectively roll on the ground. This paper addresses the path following control problem of aircraft-on-ground and focuses on the task that the aircraft is required to follow the desired path on the runway by nose wheel automatic steering. The proposed approach is based on dynamical adaptive backstepping so that the system model does not have to be transformed into a canonical triangular form which is necessary in conventional backstepping design. This adaptive controller performs well despite the lack of information on the aerodynamic load and the tire cornering stiffness parameters. Simulation results clearly demonstrate the advantages and effectiveness of the proposed approach. 展开更多
关键词 Adaptive control Aircraft-on-ground BACKSTEPPING nonlinear dynamical systems Path following
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Observer-based adaptive sliding mode backstepping output-feedback DSC for spin-stabilized canard-controlled projectiles 被引量:5
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作者 Yuanchuan SHEN Jianqiao YU +3 位作者 Guanchen LUO Xiaolin AI Zhenyue JIA Fangzheng CHEN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2017年第3期1115-1126,共12页
This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles.Uniformly ultimate boundedness and tracking are achieved,exploiting a heavily coupled,bounded u... This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles.Uniformly ultimate boundedness and tracking are achieved,exploiting a heavily coupled,bounded uncertain and highly nonlinear model of longitudinal and lateral dynamics.In order to estimate unmeasurable states,an observer is proposed for an augmented multiple-input-multiple-output(MIMO) nonlinear system with an adaptive sliding mode term against the disturbances.Under the frame of a backstepping design,an adaptive sliding mode output-feedback dynamic surface control(DSC) approach is derived recursively by virtue of the estimated states.The DSC technique is adopted to overcome the problem of ‘‘explosion of complexity" and relieve the stress of the guidance loop.It is proven that all signals of the MIMO closed-loop system,including the observer and controller,are uniformly ultimately bounded,and the tracking errors converge to an arbitrarily small neighborhood of the origin.Simulation results for the observer and controller are provided to illustrate the feasibility and effectiveness of the proposed approach. 展开更多
关键词 Backstepping Dynamic surface control technique nonlinear systems Observers Sliding mode control Spin-stabilized canard controlled projectiles
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Symplectic feedback using Hamiltonian Lie algebra and its applications to an inverted pendulum
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作者 J. Lorca ESPIRO C. Munoz POBLETE 《控制理论与应用(英文版)》 EI CSCD 2013年第2期275-281,共7页
From the symplectic representation of an autonomous nonlinear dynamical system with holonomic con- straints, i.e., those that can be represented through a symplectic form derived from a Hamiltonian, we present a new p... From the symplectic representation of an autonomous nonlinear dynamical system with holonomic con- straints, i.e., those that can be represented through a symplectic form derived from a Hamiltonian, we present a new proof on the realization of the symplectic feedback action, which has several theoretical advantages in demonstrating the uniqueness and existence of this type of solution. Also, we propose a technique based on the interpretation, construction and character- ization of the pull-back differential on the symplectic manifold as a member of a one-parameter Lie group. This allows one to synthesize the control law that governs a certain system to achieve a desired behavior; and the method developed from this is applied to a classical system such as the inverted pendulum. 展开更多
关键词 Hamiltonian systems Symplectic structures Lie algebra nonlinear dynamical systems Geometric con-trol
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