This paper develops the mean-square exponential input-to-state stability(exp-ISS) of the Euler-Maruyama(EM) method for stochastic delay control systems(SDCSs).The definition of mean-square exp-ISS of numerical m...This paper develops the mean-square exponential input-to-state stability(exp-ISS) of the Euler-Maruyama(EM) method for stochastic delay control systems(SDCSs).The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.展开更多
In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lya...In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.展开更多
For input saturated Hammerstein systems, the two-step predictive control strategy is adopted. The first step calculates the desired intermediate variable applying unconstrained linear modal and predictive control. The...For input saturated Hammerstein systems, the two-step predictive control strategy is adopted. The first step calculates the desired intermediate variable applying unconstrained linear modal and predictive control. The second step obtains the real-time control action by solving algebraic equation and desaturation. The case of immeasurable state is considered where the observer gain matrix is solved by Sylvester equation. The sufficient closed-loop stability condition is given and the designing and tuning algorithm for the domain of attraction is proposed. The theoretical results are validated by an example.展开更多
为了提高伺服电机系统的动态响应速度、抗干扰能力,解决输入饱和的问题,课题组基于扩张状态观测器(extended state observer,ESO)和抗饱和输入(anti-saturation input,ASI)辅助系统设计了伺服电机的运动控制方案。首先,建立了伺服电机...为了提高伺服电机系统的动态响应速度、抗干扰能力,解决输入饱和的问题,课题组基于扩张状态观测器(extended state observer,ESO)和抗饱和输入(anti-saturation input,ASI)辅助系统设计了伺服电机的运动控制方案。首先,建立了伺服电机的数学模型,将系统阻尼和系统不确定性归为扰动,将扰动设为系统的扩张状态;然后在等效反步滑模控制(backstepping sliding mode control,BSMC)的基础上,引入了ASI辅助系统和ESO,解决输入饱和问题,并抑制内、外干扰;采用双曲正切饱和函数替换符号函数以减小滑模控制的抖振;通过李雅普诺夫稳定性方法检验所提出控制器的稳定性。最后,将基于ESO和ASI的等效反步滑模控制与比例积分微分(proportional integral differential,PID)控制、滑模控制(sliding mode control,SMC)进行仿真对比。结果表明:相较于传统PID和SMC控制器,课题组所设计的控制器可以实现伺服电机的无超调快速响应,解决了输入饱和问题,并具有较好的抗干扰能力和减小输入冲击的作用。展开更多
Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating ...Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.展开更多
近年来,电网换相换流器型高压直流输电(line commutated converter based on high voltage direct current,LCC-HVDC)系统的稳定性问题得到广泛关注,多位专家学者建议采用谐波状态空间(harmonic state space,HSS)等线性周期时变建模方...近年来,电网换相换流器型高压直流输电(line commutated converter based on high voltage direct current,LCC-HVDC)系统的稳定性问题得到广泛关注,多位专家学者建议采用谐波状态空间(harmonic state space,HSS)等线性周期时变建模方法对其分析。然而,HSS不可避免地提高了建模的复杂度与维数,在面对大规模交直流系统时具有局限性。同时,LCC-HVDC包含多类型谐波耦合,各部分耦合对稳定性的影响大小尚未得到充分论证。为此,文中以HSS为底层理论建立LCC-HVDC的耦合阻抗矩阵,揭示高压直流输电系统内部的谐波耦合机理。进一步,通过多频电路等效思想,提出三相系统多维阻抗的降维方法,将耦合阻抗矩阵无损降维成单入单出阻抗,以此分析不同次数的谐波耦合对阻抗特性与稳定性的影响。结果表明,考虑到13次谐波截断可以有效提升高压直流输电系统阻抗模型精度,但对稳定性分析结果的影响小于忽略工况变化、简化逆变侧带来的误差。展开更多
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical) stoch...In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical) stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.展开更多
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
基金supported by the National Natural Science Foundation of China(6127312660904032)the Natural Science Foundation of Guangdong Province(10251064101000008)
文摘This paper develops the mean-square exponential input-to-state stability(exp-ISS) of the Euler-Maruyama(EM) method for stochastic delay control systems(SDCSs).The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.
基金supported by National Natural Science Foundation of China (No. 60874006)Natural Science Foundation of Hei-longjiang Province for Youth (No. QC2009C99)
文摘In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.
基金Supported by National Natural Science Foundation of China (60872046) the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
文摘For input saturated Hammerstein systems, the two-step predictive control strategy is adopted. The first step calculates the desired intermediate variable applying unconstrained linear modal and predictive control. The second step obtains the real-time control action by solving algebraic equation and desaturation. The case of immeasurable state is considered where the observer gain matrix is solved by Sylvester equation. The sufficient closed-loop stability condition is given and the designing and tuning algorithm for the domain of attraction is proposed. The theoretical results are validated by an example.
基金supported by the National Natural Science Foundation of China (Grant Nos 50977047 and 50907038)
文摘Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.
文摘近年来,电网换相换流器型高压直流输电(line commutated converter based on high voltage direct current,LCC-HVDC)系统的稳定性问题得到广泛关注,多位专家学者建议采用谐波状态空间(harmonic state space,HSS)等线性周期时变建模方法对其分析。然而,HSS不可避免地提高了建模的复杂度与维数,在面对大规模交直流系统时具有局限性。同时,LCC-HVDC包含多类型谐波耦合,各部分耦合对稳定性的影响大小尚未得到充分论证。为此,文中以HSS为底层理论建立LCC-HVDC的耦合阻抗矩阵,揭示高压直流输电系统内部的谐波耦合机理。进一步,通过多频电路等效思想,提出三相系统多维阻抗的降维方法,将耦合阻抗矩阵无损降维成单入单出阻抗,以此分析不同次数的谐波耦合对阻抗特性与稳定性的影响。结果表明,考虑到13次谐波截断可以有效提升高压直流输电系统阻抗模型精度,但对稳定性分析结果的影响小于忽略工况变化、简化逆变侧带来的误差。
基金the National Natural Science Foundation of China (No.60221301, No.60428304).
文摘In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical) stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.