一般广义时变系统的容许性和二次容许性

针对一般广义时变系统, 采用广义Lyapunov 不等式和受限等价变换的分析方法, 提出了一般广义时变系统容许性和二次容许性的概念, 建立了一般广义时变系统的Lyapunov 不等式. 将一般广义时变系统容许性问题转化为求解Lyapunov 不等式问题, 获得了该类系统容许和二次容许的充要条件, 所得结论是广义系统容许性研究成果向一般广义时变系统的自然推广. 最后, 通过数值算例验证了所得结论的有效性.     

广义不确定周期时变系统具有完整性的二次稳定

研究带有不确定项的广义周期时变系统的二次稳定及其完整性问题。引入广义不确定周期时变系统二次稳定的概念,用广义代数Riccati不等式,给出广义不确定周期时变系统在状态和输出反馈作用下所构成的闭环系统二次稳定,并且当传感器或执行器出现故障时仍能具有完整性二次稳定的充分必要条件。所得结论是广义系统完整性研究成果向一般广义周期时变系统的扩展。最后,通过数值算例验证了所得结论的有效性。     

线性时变广义系统的能控性与能观性问题

讨论了线性时变系统和线性时变广义系统的两个基本问题, 得到了两种判定时变系统能控性与能观性的必要条件, 该判定条件只依赖于系统矩阵A(t)和输入矩阵B(t), 不必计算系统的系统状态转移矩阵, 使得判别时变系统能控性与能观性易于实现. 说明了本文结论是线性定常系统相应结论的自然扩展. 对进一步深入研究时变系统和时变广义系统具有实际启发作用.     

广义不确定周期时变系统的鲁棒稳定性分析

研究广义不确定周期时变系统的鲁棒稳定性问题.基于广义周期时变系统Lyapunov不等式,提出了广义不确定周期时变系统鲁棒稳定的概念,采用矩阵不等式(LMI)方法,得到了该类系统鲁棒稳定的充分必要条件;然后,进一步研究了在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法;最后,引入了广义周期时变系统二次稳定的概念,并讨论了二次稳定性与鲁棒稳定性之间的关系.     

广义时变脉冲系统的时域稳定

研究了状态依赖广义时变脉冲系统的时域稳定问题.基于微分矩阵不等式 (Differential matrix inequalities, DMI) 和S-procedure理论, 给出了两类状态依赖广义时变脉冲系统时域稳定的充分条件.接下来, 根据给出的充分条件设计了状态反馈控制器, 使得闭环系统时域稳定.最后, 给出数值算例来验证结论的有效性.     

不确定广义线性时变系统的鲁棒稳定和二次稳定

针对不确定广义线性时变系统,采用矩阵不等式的分析方法,提出不确定广义线性时变系统鲁棒稳定和二次稳定的概念.建立该类系统的矩阵不等式,将该类系统的鲁棒控制问题转化为求解矩阵不等式问题,得到该类系统鲁棒稳定和二次稳定的充分必要条件,并给出一种状态反馈鲁棒镇定控制器的设计方法.最后,通过数值算例表明了所提出方法的可行性.     

广义时变脉冲系统的输入输出时域稳定

研究了广义时变脉冲系统的输入输出时域稳定问题.基于矩阵微分不等式(Differential matrix inequalities,DMI),给出了两个上述系统输入输出时域稳定的充分条件分别对应 L2干扰输入和 L∞干扰输入.这样的条件要求矩阵微分不等式解的存在性.接下来根据给出的充分条件设计了控制器,使得闭环系统输入输出时域稳定.本文的结果对于一般情况下的广义时变系统同样适用.最后,给出了两个算例来验证结果的有效性.     

一般广义周期时变系统的H∞控制

针对一般广义周期时变系统的H∞控制问题,采用Lyapunov函数理论和线性矩阵不等式(LMI)相结合的分析方法,通过分析正常周期时变系统和一般广义周期时变系统允许的充分必要条件,得到了一般广义周期时变系统允许且满足H∞控制性能指标的充分必要条件.所得结论将广义系统H∞控制问题研究成果推广到一般广义周期时变系统的控制性能,奠定了广义时变系统H∞控制问题的研究基础.     

广义系统具有完整性的鲁棒二次稳定

考虑带有Frobenius范数界的不确定广义系统,具有完整性的鲁棒二次稳定问题.用 Riccati不等式给出不确定广义系统在状态反馈和输出反馈作用下所构成的闭环系统二次稳定, 并且当执行器出现故障时,不确定广义系统仍能保持二次稳定的充分条件,即不确定广义系统 具有完整性的鲁棒二次稳定的充分条件.     

广义预测控制在非线性系统中的应用研究

本文研究了一类非线性系统的广义预测控制,将其等效为时变线性系统,然后在线辨识时变参数,进行广义预测控制。给出了两种辨识时变参数的方法,并以二容液位系统为模型,进行了仿真研究,结果表明,此方法计算量小,工作点变化时跟踪速度快．具有较好的控制效果。     

Optimal control of time-varying singular systems using the RK–Butcher algorithm

The problem of optimal control of time-varying linear singular systems with quadratic performance index has been studied using the Runge–Kutta–Butcher algorithm. The results obtained using the Runge–Kutta (RK) method based on the arithmetic mean (RKAM) and the RK–Butcher algorithms are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the result obtained using the RK–Butcher algorithm is closer to the true solution of the problem. Stability regions for the RKAM algorithm, the single-term Walsh series method and the RK–Butcher algorithms are presented. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the RK–Butcher algorithm. This algorithm can easily be implemented using a digital computer. An additional advantage of this method is that the solution can be obtained for any length of time for this type of optimal control of time-varying linear singular systems.     

线性参变过驱动系统鲁棒控制分配策略

针对一类具有不确定时变参量的线性参变(linear parameter-varying,LPV)过驱动系统的控制分配问题,考虑系统的不确定参量扰动和执行器物理约束,利用伪控指令分配误差和控制量误差的1--范数,建立了含有时变不确定因子的控制分配优化模型.根据鲁棒优化思想,采用矢量变换技术处理时变不确定因子,得到了一种基于有约束锥二次凸优化模型的鲁棒控制分配算法,实现对LPV过驱动系统伪控指令的在线优化分配.最后,对某4轮电动汽车时变二自由度转向过驱动控制系统的对比仿真实验表明,相比常规4WS和伪逆控制分配方法,本文的鲁棒控制分配算法有效地降低了系统参变量不确定扰动的影响,得到更合理的控制分配解,有效改善了车辆的操纵稳定性.     

线性离散奇异系统的不定二次最优控制问题: Krein空间方法

The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter. Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.     

针对时变轨迹的非线性仿射系统的鲁棒近似最优跟踪控制

针对非线性连续系统难以跟踪时变轨迹的问题,本文首先通过系统变换引入新的状态变量从而将非线性系统的最优跟踪问题转化为一般非线性时不变系统的最优控制问题,并基于近似动态规划算法(ADP)获得近似最优值函数与最优控制策略.为有效地实现该算法,本文利用评价网与执行网来估计值函数及相应的控制策略,并且在线更新二者.为了消除神经网络近似过程中产生的误差,本文在设计控制器时增加一个鲁棒项;并且通过Lyapunov稳定性定理来证明本文提出的控制策略可保证系统跟踪误差渐近收敛到零,同时也验证在较小的误差范围内,该控制策略能够接近于最优控制策略.最后给出两个时变跟踪轨迹实例来证明该方法的可行性与有效性.     

An optimal scheme for fast rate fault detection based on multirate sampled data

Multirate systems are abundant in industry. In this paper, the problem studied is designing a residual generator for fault detection based on multirate sampled data. The key new feature of such a residual generator is that it operates at a fast rate for prompt fault detection. The design is based on optimizing a performance index to obtain an optimal parity space based residual generator. The lifting technique is used to convert the time-varying multirate design problem into a time-invariant one with a causality constraint for implementability. A procedure for computing an explicit optimal, causal solution is proposed. The advantages of this design are shown through an example.     

Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria

Optimal control of general nonlinear nonaffine controlled systems with nonquadratic performance criteria (that permit state- and control-dependent time-varying weighting parameters), is solved classically using a sequence of linear- quadratic and time-varying problems. The proposed method introduces an “approximating sequence of Riccati equations” (ASRE) to explicitly construct nonlinear time-varying optimal state-feedback controllers for such nonlinear systems. Under very mild conditions of local Lipschitz continuity, the sequences converge (globally) to nonlinear optimal stabilizing feedback controls. The computational simplicity and effectiveness of the ASRE algorithm is an appealing alternative to the tedious and laborious task of solving the Hamilton–Jacobi–Bellman partial differential equation. So the optimality of the ASRE control is studied by considering the original nonlinear-nonquadratic optimization problem and the corresponding necessary conditions for optimality, derived from Pontryagin's maximum principle. Global optimal stabilizing state-feedback control laws are then constructed. This is compared with the optimality of the ASRE control by considering a nonlinear fighter aircraft control system, which is nonaffine in the control. Numerical simulations are used to illustrate the application of the ASRE methodology, which demonstrate its superior performance and optimality.     

Linear periodically time-varying discrete-time systems: Aliasing and LTI approximations

Linear periodically time-varying (LPTV) systems are abundant in control and signal processing; examples include multirate sampled-data control systems and multirate filter-bank systems. In this paper, several ways are proposed to quantify aliasing effect in discrete-time LPTV systems; these are associated with optimal time-invariant approximations of LPTV systems using operator norms.     

Adaptive control allocation

In this work we address the control allocation problem for a nonlinear over-actuated time-varying system where parameters affine in the effector model may be assumed unknown. Instead of optimizing the control allocation at each time instant, a dynamic approach is considered by constructing update-laws that represent asymptotically optimal allocation search and adaptation. Using Lyapunov analysis for cascaded set-stable systems, uniform global/local asymptotic stability is guaranteed for the sets described by the system, the optimal allocation update-law and the adaptive update-law.     

Applications of non-uniform in time robust global asymptotic output stability to robust partial state feedback stabilization

The problem of adding an integrator is considered for time-varying control systems. Sufficient conditions for the solution of this problem are given, which are weaker than the corresponding conditions given in the literature. To this end, the notion of non-uniform in time robust global asymptotic output stability (RGAOS) is used. Applications to problems of partial state feedback global stabilization are considered.