Phase Plane

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Vladimír Vašek - One of the best experts on this subject based on the ideXlab platform.

  • Non-singular fixed-time terminal sliding mode control of non-linear systems
    IET Control Theory & Applications, 2015
    Co-Authors: Zongyu Zuo, Michaela Barinova, Jiri Pecha, Petr Halamka, Karel Kolomazník, Vladimír Vašek
    Abstract:

    This study addresses a fixed-time terminal sliding-mode control methodology for a class of second-order non-linear systems in the presence of matched uncertainties and perturbations. A newly defined non-singular terminal sliding surface is constructed and a guaranteed closed-loop convergence time independent of initial states is derived based on the Phase Plane analysis and Lyapunov tools. The simulation results of a single inverted pendulum in the end are included to show the effectiveness of the proposed methodology.

Zhengrong Liu - One of the best experts on this subject based on the ideXlab platform.

  • smooth and non smooth traveling waves in a nonlinearly dispersive equation
    Applied Mathematical Modelling, 2000
    Co-Authors: Zhengrong Liu
    Abstract:

    Abstract The method of the Phase Plane is employed to investigate the solitary and periodic traveling waves in a nonlinear dispersive integrable partial differential equation. It is shown that the existence of a singular straight line in the corresponding ordinary differential equation for traveling wave solutions is the reason that smooth solitary wave solutions converge to solitary cusp wave solutions when the parameters are varied. The different parameter conditions for the existence of different kinds of solitary and periodic wave solutions are rigorously determined.

Zongyu Zuo - One of the best experts on this subject based on the ideXlab platform.

  • Non-singular fixed-time terminal sliding mode control of non-linear systems
    IET Control Theory & Applications, 2015
    Co-Authors: Zongyu Zuo, Michaela Barinova, Jiri Pecha, Petr Halamka, Karel Kolomazník, Vladimír Vašek
    Abstract:

    This study addresses a fixed-time terminal sliding-mode control methodology for a class of second-order non-linear systems in the presence of matched uncertainties and perturbations. A newly defined non-singular terminal sliding surface is constructed and a guaranteed closed-loop convergence time independent of initial states is derived based on the Phase Plane analysis and Lyapunov tools. The simulation results of a single inverted pendulum in the end are included to show the effectiveness of the proposed methodology.

Roy S Choudhury - One of the best experts on this subject based on the ideXlab platform.

  • regular and singular pulse and front solutions and possible isochronous behavior in the short pulse equation Phase Plane multi infinite series and variational approaches
    Communications in Nonlinear Science and Numerical Simulation, 2015
    Co-Authors: G Gambino, U Tanriver, Partha Guha, Ghose A Choudhury, Roy S Choudhury
    Abstract:

    Abstract In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of Phase-Plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding traveling-wave equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic/heteroclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.

Michaela Barinova - One of the best experts on this subject based on the ideXlab platform.

  • Non-singular fixed-time terminal sliding mode control of non-linear systems
    IET Control Theory & Applications, 2015
    Co-Authors: Zongyu Zuo, Michaela Barinova, Jiri Pecha, Petr Halamka, Karel Kolomazník, Vladimír Vašek
    Abstract:

    This study addresses a fixed-time terminal sliding-mode control methodology for a class of second-order non-linear systems in the presence of matched uncertainties and perturbations. A newly defined non-singular terminal sliding surface is constructed and a guaranteed closed-loop convergence time independent of initial states is derived based on the Phase Plane analysis and Lyapunov tools. The simulation results of a single inverted pendulum in the end are included to show the effectiveness of the proposed methodology.