Decentralized H_∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition w...Decentralized H_∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition which makes the closed-loop system decentralized asymptotically stable with H_∞ performance was derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities. The method overcomes the limitations of the existing algebraic Riccati equation method. Finally, a numerical example was given to demonstrate the design procedure for the decentralized H_∞ state feedback controller.展开更多
The robust control problem for a class of underactuated mechanical systems called acrobots is addressed. The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unsta...The robust control problem for a class of underactuated mechanical systems called acrobots is addressed. The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unstable equilibrium position in the presence of parametric uncertainties and external disturbance. First, in the swing-up area, it is shown that the time derivative of energy is independent of the parameter uncertainties, but exogenous disturbance may destroy the characteristic of increase in mechanical energy. So, a swing-up controller with compensator is designed to suppress the influence of the disturbance. Then, in the attractive area, the control problem is formulated into a H~ control framework by introducing a proper error signal, and a sufficient condition of the existence of Hoo state feedback control law based on linear matrix inequality （LMI） is proposed to guarantee the quadratic stability of the control system. Finally, the simulation results show that the proposed control approach can simultaneously handle a maximum ±10% parameter perturbation and a big disturbance simultaneously.展开更多
A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe ...A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.展开更多
The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii function...The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.展开更多
文摘可分离压缩传感可以通过一定比例的额外测量有效地解决压缩成像问题中面临的测量矩阵维数过大的瓶颈.但是现有可分离压缩传感(separable compressive sensing,SCS)方法需要2个可分离的测量矩阵都必须是行归一化后的正交随机矩阵,其显著地限制了该方法的应用范围.将奇异值分解(singular value decomposition,SVD)方法引入可分离可压缩传感测量过程,可以有效地实现测量矩阵和重建矩阵的分离:在感知阶段可以更多地考虑测量矩阵物理易于实现的性质,如Toeplitz或Circulant等确定性结构的矩阵;在重建阶段,更多地考虑测量矩阵的优化.通过引入奇异值分解对重建阶段的测量矩阵进行优化,可以有效地改善重建性能,尤其是Toeplitz或Circulant矩阵在大尺度图像的压缩重建情形.数值实验结果验证了该方法的有效性.
文摘Decentralized H_∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition which makes the closed-loop system decentralized asymptotically stable with H_∞ performance was derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities. The method overcomes the limitations of the existing algebraic Riccati equation method. Finally, a numerical example was given to demonstrate the design procedure for the decentralized H_∞ state feedback controller.
基金Projects(61074112,60674044) supported by the National Natural Science Foundation of China
文摘The robust control problem for a class of underactuated mechanical systems called acrobots is addressed. The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unstable equilibrium position in the presence of parametric uncertainties and external disturbance. First, in the swing-up area, it is shown that the time derivative of energy is independent of the parameter uncertainties, but exogenous disturbance may destroy the characteristic of increase in mechanical energy. So, a swing-up controller with compensator is designed to suppress the influence of the disturbance. Then, in the attractive area, the control problem is formulated into a H~ control framework by introducing a proper error signal, and a sufficient condition of the existence of Hoo state feedback control law based on linear matrix inequality （LMI） is proposed to guarantee the quadratic stability of the control system. Finally, the simulation results show that the proposed control approach can simultaneously handle a maximum ±10% parameter perturbation and a big disturbance simultaneously.
基金Project(61104072) supported by the National Natural Science Foundation of China
文摘A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.
文摘The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.
