This study addresses the problem of parameter estimation for a one-dimensional reaction-diffusion equation, involving both unknown domain parameters and unknown boundary parameters. The proposed approach utilizes the ...This study addresses the problem of parameter estimation for a one-dimensional reaction-diffusion equation, involving both unknown domain parameters and unknown boundary parameters. The proposed approach utilizes the least-squares method to design an adaptive law for parameter estimation. The convergence analysis demonstrates that under persistent excitation conditions, the adaptive law converges exponentially to zero, indicating that the estimated parameters converge exponentially to their true values. Numerical simulations confirm the effectiveness. Furthermore, it is shown that within a certain range of the reaction coefficient, the auxiliary system acts as a state observer, providing an accurate estimate of the system state at an exponential rate. .展开更多
This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigat...This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design. Motivated by the related literature, an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one, from which the control design becomes much convenient. It is worthwhile pointing out that, since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded, the desirable kernel functions are more difficult to derive than those of the closely related literature. Then, by Lyapunov method and a dynamics compensated technique, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. Finally, a simulation example is provided to validate the proposed method.展开更多
We consider the stabilisation of discrete-time nonlinear systems that are actuated through a pair of transport partial difference equation(PdE)systems that convect in the opposite directions from one another.An explic...We consider the stabilisation of discrete-time nonlinear systems that are actuated through a pair of transport partial difference equation(PdE)systems that convect in the opposite directions from one another.An explicit feedback law that compensates the discrete PdE dynamics is designed.Global asymptotic stability of the closedloop system is proved with the aid of a Lyapunov function.The feedback design is illustrated through an example.The proposed design in this paper allows the delay to be arbitrarily long and time-varying.Furthermore,our predictor feedback law in discrete time is explicit as the predictor state is computed by an algebraic equation.展开更多
文摘This study addresses the problem of parameter estimation for a one-dimensional reaction-diffusion equation, involving both unknown domain parameters and unknown boundary parameters. The proposed approach utilizes the least-squares method to design an adaptive law for parameter estimation. The convergence analysis demonstrates that under persistent excitation conditions, the adaptive law converges exponentially to zero, indicating that the estimated parameters converge exponentially to their true values. Numerical simulations confirm the effectiveness. Furthermore, it is shown that within a certain range of the reaction coefficient, the auxiliary system acts as a state observer, providing an accurate estimate of the system state at an exponential rate. .
基金supported by the National Natural Science Foundations of China under Grant Nos.61403327,61325016,61273084 and 61233014
文摘This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design. Motivated by the related literature, an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one, from which the control design becomes much convenient. It is worthwhile pointing out that, since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded, the desirable kernel functions are more difficult to derive than those of the closely related literature. Then, by Lyapunov method and a dynamics compensated technique, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. Finally, a simulation example is provided to validate the proposed method.
基金This work is supported by the National Natural Science Foundation of China[grant numbers 61074011 and 61374077].
文摘We consider the stabilisation of discrete-time nonlinear systems that are actuated through a pair of transport partial difference equation(PdE)systems that convect in the opposite directions from one another.An explicit feedback law that compensates the discrete PdE dynamics is designed.Global asymptotic stability of the closedloop system is proved with the aid of a Lyapunov function.The feedback design is illustrated through an example.The proposed design in this paper allows the delay to be arbitrarily long and time-varying.Furthermore,our predictor feedback law in discrete time is explicit as the predictor state is computed by an algebraic equation.
