The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential sta...The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of the result.展开更多
In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking erro...In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.展开更多
In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it...In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.展开更多
The design feedback controller for a problem of dynamic output class of multi-delayed neutral systems has been considered. A criterion for the existence and asymptotic stability of such controller is derived via defin...The design feedback controller for a problem of dynamic output class of multi-delayed neutral systems has been considered. A criterion for the existence and asymptotic stability of such controller is derived via defining a new integral operator. The criterion is expressed in terms of the linear matrix inequalities （LMIs）, which can be checked numerically using the effective LMI toolbox in MATLAB. One numerical example is given to illustrate the proposed design method. Numerical simulation shows that the new design method is valid.展开更多
基金supported by Sichuan Province Foundation for Applied Basic Research and Leaders of Science and Technology under Grant No.05JY029-068-2
文摘The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of the result.
基金supported by the Air Force Research Laboratory and Office of the Secretary of Defense(OSD)(FA8750-15-2-0116)the US Department of Transportation(USDOT)Research and Innovative Technology Administration(RITA)under University Transportation Center(UTC)Program(DTRT13-G-UTC47)
文摘In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.
文摘In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.
基金supported by Program for New Century Excellent Talents in University under Grant No.NCET-06-0811
文摘The design feedback controller for a problem of dynamic output class of multi-delayed neutral systems has been considered. A criterion for the existence and asymptotic stability of such controller is derived via defining a new integral operator. The criterion is expressed in terms of the linear matrix inequalities （LMIs）, which can be checked numerically using the effective LMI toolbox in MATLAB. One numerical example is given to illustrate the proposed design method. Numerical simulation shows that the new design method is valid.
