A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system ...A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given.Finally, simulation results show the effectiveness of the proposed method.展开更多
In this paper,the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method.First,a transformation is introduced.Thus,the system is transformed into ...In this paper,the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method.First,a transformation is introduced.Thus,the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal.Then,by applying the preview control theory,an augmented system for the non-delayed system is derived,and a controller with preview function is designed,assuming that the reference signal is previewable.Finally,the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.Numerical simulations are provided to verify the presented results.展开更多
An HIV infection model with saturated infection rate and double delays is investigated. First, the existence of the infection-free equilibrium E0, the immune-exhausted equilibrium E1 and the infected equilibrium E2 wi...An HIV infection model with saturated infection rate and double delays is investigated. First, the existence of the infection-free equilibrium E0, the immune-exhausted equilibrium E1 and the infected equilibrium E2 with immunity in different conditions is shown. By analyzing the characteristic equation, we study the locally asymptotical stability of the trivial equilibrium, and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold. Then with suitable Lyapunov function and LaSalle＇s invariance principle, the global stability of the three equilibriums is obtained. Finally, numerical simulations are presented to illustrate the main mathematical results.展开更多
基金Supported by the National Natural Science Foundation of China(61174209)
文摘A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given.Finally, simulation results show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(61174209).
文摘In this paper,the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method.First,a transformation is introduced.Thus,the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal.Then,by applying the preview control theory,an augmented system for the non-delayed system is derived,and a controller with preview function is designed,assuming that the reference signal is previewable.Finally,the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.Numerical simulations are provided to verify the presented results.
基金This work was supported by National Natural Science Foundation of China （61174209, 11471034）.
文摘An HIV infection model with saturated infection rate and double delays is investigated. First, the existence of the infection-free equilibrium E0, the immune-exhausted equilibrium E1 and the infected equilibrium E2 with immunity in different conditions is shown. By analyzing the characteristic equation, we study the locally asymptotical stability of the trivial equilibrium, and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold. Then with suitable Lyapunov function and LaSalle＇s invariance principle, the global stability of the three equilibriums is obtained. Finally, numerical simulations are presented to illustrate the main mathematical results.
