Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of th...Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.展开更多
This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems posses...This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems possess two important characteristics: (i) The uncertain nonlinear terms meet the linearly unmeasurable-states dependent growth with the growth rate being an unknown function of the input and output. (ii) There exist input matching uncertainty and unknown measurement sensitivity. By introducing a single dynamic gain and employing a cleverly devised event-triggering mechanism (ETM), we design a new gain-based event-triggered output-feedback controller, which globally regulates all states of the considered systems and maintains global boundedness of the closed-loop system. Furthermore, the estimation of input matching uncertainty achieves convergence towards its actual value, and Zeno behavior does not happen. Two simulation examples including a practical one show that the proposed approach is effective.展开更多
An efficient and accurate spectral method is presented for scattering problems with rough surfaces.A probabilistic framework is adopted by modeling the surface roughness as random process.An improved boundary perturba...An efficient and accurate spectral method is presented for scattering problems with rough surfaces.A probabilistic framework is adopted by modeling the surface roughness as random process.An improved boundary perturbation technique is employed to transform the original Helmholtz equation in a random domain into a stochastic Helmholtz equation in a fixed domain.The generalized polynomial chaos(gPC)is then used to discretize the random space;and a Fourier-Legendre method to discretize the physical space.These result in a highly efficient and accurate spectral algorithm for acoustic scattering from rough surfaces.Numerical examples are presented to illustrate the accuracy and efficiency of the present algorithm.展开更多
文摘Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.
基金supported by the fund of Beijing Municipal Commission of Education(KM202210017001 and 22019821001)the Natural Science Foundation of Henan Province(222300420253).
文摘This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems possess two important characteristics: (i) The uncertain nonlinear terms meet the linearly unmeasurable-states dependent growth with the growth rate being an unknown function of the input and output. (ii) There exist input matching uncertainty and unknown measurement sensitivity. By introducing a single dynamic gain and employing a cleverly devised event-triggering mechanism (ETM), we design a new gain-based event-triggered output-feedback controller, which globally regulates all states of the considered systems and maintains global boundedness of the closed-loop system. Furthermore, the estimation of input matching uncertainty achieves convergence towards its actual value, and Zeno behavior does not happen. Two simulation examples including a practical one show that the proposed approach is effective.
基金supported in part by NSF grants DMS-0243191 and DMS-0311915.
文摘An efficient and accurate spectral method is presented for scattering problems with rough surfaces.A probabilistic framework is adopted by modeling the surface roughness as random process.An improved boundary perturbation technique is employed to transform the original Helmholtz equation in a random domain into a stochastic Helmholtz equation in a fixed domain.The generalized polynomial chaos(gPC)is then used to discretize the random space;and a Fourier-Legendre method to discretize the physical space.These result in a highly efficient and accurate spectral algorithm for acoustic scattering from rough surfaces.Numerical examples are presented to illustrate the accuracy and efficiency of the present algorithm.
