Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a ...Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.展开更多
The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to so...The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to some system of third-order differential equations.展开更多
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, whi...In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.展开更多
In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order(SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets ...In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order(SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Gr ¨unwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.展开更多
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the me...In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.展开更多
In this paper, we investigate stochastic asymptotic stability of the zero solution for certain third-order nonlinear stochastic delay differential equations by constructing Lyapunov functionals.
文摘Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.
文摘The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to some system of third-order differential equations.
文摘In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
基金supported by the Algerian Ministry of Higher Education and Scientific Research(MESRS)for CNEPRU Research Project(A01L08UN210120110001)
文摘In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order(SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Gr ¨unwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.
文摘In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.
文摘In this paper, we investigate stochastic asymptotic stability of the zero solution for certain third-order nonlinear stochastic delay differential equations by constructing Lyapunov functionals.
