基于奇异摄动理论的非仿射系统的输出调节问题

基于奇异摄动的时标分解理论和动态逆设计的方法,研究了一类非仿射非线性系统的输出调节问题.通过将控制律定义为一个快动态系统的解,得到了指数稳定的误差系统状态方程,从而实现了原系统的输出相对于外系统的参考信号具有零误差的跟踪效果.结果表明在满足标准假设和一组偏微分方程有解的前提下,该输出调节问题是可解的.仿真实例表明了该理论方法的有效性.     

Almost disturbance decoupling for single-input single-outputnonlinear systems

The almost disturbance decoupling problem for nonlinear single-input single-output systems is addressed by using singular perturbation methods and high-gain feedback. Sufficient conditions and the explicit high-gain nonlinear state feedback in solvable cases are given. They generalize both previous almost results for linear systems and exact ones for nonlinear systems. The necessity of the conditions is discussed; in particular, an example is given where the main structural condition is not satisfied and the high-gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system     

基于极值搜索算法的一类多输入多输出非仿射型非线性系统输出跟踪控制

针对一类状态不可测的多输入多输出非仿射型非线性系统, 提出了基于极值搜索算法的输出跟踪控制方法. 此方法无需设计系统状态观测器, 仅利用系统的输出量和极值搜索向量形成控制律. 应用平均化理论分析平均化系统的稳定性, 然后利用奇异值扰动方法, 证明了所提出的控制方法可以保证闭环系统的稳定性和输出跟踪误差的收敛性. 仿真结果验证了本文方法的有效性.     

基于奇异摄动理论的植物工厂温度控制

通过研究植物工厂与作物系统,结合非线性奇异摄动理论相关理论对植物工厂内部环境进行控制。首先阐述了基于能量角度对植物工厂与作物结合的动态模型描述各个系统状态变量之间的关系,然后建立了关于温度的最优控制模型,并将最优控制模型进行一般公式化。基于奇异摄动理论将非线性植物工厂与作物系统分解成快慢系统。利用系统中的双重时间尺度,分别设计出慢子系统和快子系统的成本函数。最后通过MATLAB软件进行仿真,得出最优控制曲线,结果表明得出的控制器能有效地控制植物工厂内部温度,并能保证对植物工厂加热时间最短,以实现植物工厂收益最高。     

离散时间奇异系统的可测扰动解耦

为离散时间广义非线性控制系统的可测扰动提供一种反演算法．运用一类正则动态补偿器解决了系统的解耦问题，并且证明系统既可利用动态反馈进行解耦，也可利用拟表态反馈进行解耦．     

挠性航天器的非线性PID和PI姿态控制器设计

针对存在模型不确性和常值干扰的挠性航天器, 提出一种不依赖于模型参数的非线性PID姿态控制器. 该控制器在小姿态偏差的情况下近似经典的线性PID控制器. 另外, 考虑到航天器上陀螺失效情况, 设计了一种仅需姿态测量信息的非线性PI控制器. 这两种控制器在局部均对常值干扰有抑制作用, 并能使无干扰作用的姿态控制系统半全局渐近稳定. 闭环系统的稳定性证明采用了奇异扰动理论, 以解决积分项的存在带来的稳定性分析问题. 文章最后用数学仿真验证了控制器的性能.     

Singular H∞ Suboptimal Control for a Class of Nonlinear Cascade Systems

In the present paper singular state feedback _∞ suboptimal control for a class of nonlinear cascade systems is addressed. Under the assumption that a regular state feedback _∞ suboptimal control problem is solvable for a particular subsystem of the cascade system, an auxiliary nonlinear system is defined. It is shown that a state feedback solution to the singular _∞ suboptimal control problem for the auxiliary system also applies to the original problem. The advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable. It is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input-output decoupled. The theory is applied to a problem of a rigid spacecraft with actuator dynamics. Application to the special case when a subsystem of the nonlinear cascade system is passive is also considered.     

Trajectory Tracking of Vertical Take-off and Landing Unmanned Aerial Vehicles Based on Disturbance Rejection Control

We investigate the trajectory tracking problem of vertical take-off and landing (VTOL) unmanned aerial vehicles (UAV), and propose a practical disturbance rejection control strategy. Firstly, the nonlinear error model is established completely by the modified Rodrigues parameters, while considering dynamics of the servo actuators. Then, a hierarchical control scheme is applied to design the translational and rotational controllers based on the time-scale property of each subsystem, respectively. And the linear extended state observer and auxiliary observer are used to deal with the uncertainties and saturation. At last, global stability of the closed-loop system is analyzed based on the singular perturbation theory. Simulation results show the effectiveness of the proposed control strategy.      

高超飞行器的再入非线性鲁棒控制

针对再入段高超飞行器非线性动力学模型存在不确定性和干扰,基于奇异摄动理论提出了鲁棒变结构+动态逆内外环解耦控制方法.为避免在线实时求逆,控制系统的外环基于简化的模型设计自适应滑模变结构控制律,通过反馈干扰观测器在线估计广义干扰量,实现角度的跟踪和闭环系统的稳定,抑止外来干扰.强耦合的姿态动力学内环采用动态逆跟踪角速度指...     

非线性系统的状态反馈大范围输出调节

本文首先定义了状态反馈大范围输出调节，然后用常微分方程的不变流形该问题进行了深入的探讨，指出非线性系统状态反馈大范围输出调节问题可解的充要条件是满足某个非线性时变偏微分方程。     

力矩输入有界的柔性关节机器人轨迹跟踪控制

为解决柔性关节机器人在关节驱动力矩输出受限情况下的轨迹跟踪控制问题,提出一种基于奇异摄动理论的有界控制器.首先,利用奇异摄动理论将柔性关节机器人动力学模型解耦成快、慢两个子系统.然后,引入一类平滑饱和函数和径向基函数神经网络非线性逼近手段,依据反步策略设计了针对慢子系统的有界控制器.在快子系统的有界控制器设计中,通过关节弹性力矩跟踪误差的滤波处理加速系统的收敛.同时,在快、慢子系统控制器中均采用模糊逻辑实现控制参数的在线动态自调整.此外,结合李雅普诺夫稳定理论给出了严格的系统稳定性证明.最后,通过仿真对比实验验证了所提出控制方法的有效性和优越性.     

交叉耦合非线性系统的输出调节

利用中心流形定理,给出交叉耦合非线性系统的输出调节问题可解的充要条件,定义了交 叉耦合非线性系统的零误差流形.利用幂级数展开的方法,给出该零误差流形存在的充要条 件,并讨论了该零误差流形的局部收敛性.     

Output regulation of nonlinear systems

The problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once a solution of this equation is available, a feedback law which solves the problem can easily be constructed. The theory developed incorporates previously published results established for linear systems     

Application of Vasileva's singular perturbation method to a problem in ecology

The simultaneous presence of fast and slow processes in ecological models leads to the formulation of model equations in a form amenable for the analysis by singular perturbation method. The method as originally proposed by Vasileva (1963) is applied to a specific species-resource logistic model and an algorithm useful for implementation on a digital computer is given. The solutions are obtained for zeroth, first and second order approximations. The accuracy of the solutions is examined by considering the integral-squared-error between the exact solutions and the perturbed solutions. The variation of this error with respect to the small parameter associated with the perturbation method is studied. An important result due to Tikhnov (1950) in the singular perturbation theory is illustrated. It is seen that Vasileva's singular perturbation method is a powerful analytical tool for investigations of various phenomena in the natural sciences.     

Optimal singular control for nonlinear semistabilisation

The singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton–Jacobi–Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.     

On performance recovery of robust dynamic surface control

Robust dynamic surface control (RDSC) is effective in alleviating the implementation difficulty of backstepping‐based multiple‐surface sliding control (MSSC) for a class of strict‐feedback nonlinear systems with mismatched uncertainties. However, the synthesis and analysis of the classical RDSC are conservative, which not only may lead to an impractical control law but also cannot fully reveal the technical nature of RDSC. This article provides a comprehensive study of a preferred RDSC law with an approximation of the signum function based on the singular perturbation theory. By formulating the control problem into a singular perturbation form, it is proven that the preferred RDSC recovers the performance of MSSC as the decrease of a filter parameter. The attractive features of the preferred RDSC revealed during the proposed synthesis and analysis include: (a) the control gain can be significantly reduced resulting in a sharp decrease of control energy and (b) the closed‐loop stability can be guaranteed by only decreasing the filter parameter. Simulation results have been shown to be consistent with the theoretical findings.     

Optimal control of a particular class of singularly perturbednonlinear discrete-time systems

This note studies a class of discrete-time nonlinear systems which depend on a small parameter. Using the singular perturbation theory in a systematic way, we give a trajectory approximation result based on the decomposition of the model into reduced and boundary layer models. This decomposition is used to analyze optimal control via maximum principle of such systems. As a result, significant order reduction of optimal control problems is achieved     

基于收缩理论的一类非线性系统自适应动态面控制

针对一类不确定非线性参数严反馈系统,提出基于收缩理论的自适应动态面控制方法.动态面控制器设计保证了各子系统关于状态误差部分收缩;对不确定参数构造收缩自适应律,并利用收缩下的奇异摄动分析降阶处理子系统,确保降阶前后状态误差间的偏差及滤波误差有界;通过分层子系统的收缩鲁棒性分析,证明了原闭环系统状态半全局收敛到以期望轨迹为中心的球域内,保证了跟踪误差及自适应估计有界.刚性机械臂系统仿真验证了所提出方法的有效性.     

Dynamic inversion control for a class of pure‐feedback systems

A dynamic inversion control method is proposed for a class of pure‐feedback nonlinear systems. By combing the back‐steeping control method with the singular perturbation theory, the virtual and the final actual control inputs are derived from the solutions of a series of fast dynamical equations. Stability analysis shows that the system output tracks the desired trajectory with bounded errors, which can be made arbitrarily small by choosing appropriate design parameters. Tracking performance is illustrated by simulation results. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

线性不确定奇异摄动系统的稳定控制鲁棒界

对于具有不确定量的奇异摄动系统，利用Lyapunov稳定性理论研究其稳定鲁棒控制问题。在一定条件下得到了任一理想奇异摄动系统的稳定鲁棒控制，也是不确定奇异摄动系统具有一定鲁棒界的稳定控制。给出了闭环奇异摄动系统渐近稳定的条件，讨论了鲁棒界及其变化范围。