奇异摄动系统鲁棒镇定问题

讨论了确定与不确定奇异摄动系统的稳定性问题。首先给出了确定系统稳定及不确定系统鲁棒稳定的条件,同时给出摄动参数的稳定上界,其次,对不稳定系统,给出了状态反馈可镇定的条件及控制器的求解。这些条件均可由MATLAB中的求解器求解。最后,数值实例验证了该方法的可行性和有效性。     

时滞奇异摄动系统的鲁棒控制

当不确定出现在滞后状态矩阵时,考虑了一类时滞的奇异摄动系统的二次稳定性,用线性矩阵不等式方法给出了上述系统二次稳定的充分条件,然后在此基础上用一种LMI迭代算法给出了控制器的设计,最后仿真算例表明了该方法的有效性.     

Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE

In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.     

Disturbance-observer-based LQR control of singularly perturbed systems via recursive decoupling methods

This paper addresses the disturbance-observer-based linear quadratic regulation (LQR) problem of singularly perturbed systems subject to harmonic disturbances. To reduce the computational burden and facilitate the on-board implementation, a recursive matrix decoupling method is proposed to decompose the stiff singularly perturbed model into the block-diagonal form. Then, a robust LQR controller is designed based on the equivalent decoupled system, which consists of a state feedback controller for performance optimisation and a robust controller for disturbance compensation. Moreover, the designed controller is integrated with a finite frequency disturbance observer to attenuate the effect of harmonic disturbances. Finally, a simulation example on a DC motor system is provided to verify the effectiveness of the proposed design method.     

Stability and stabilization for singularly perturbed systems with Markovian jumps

This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ?_i‐free but involving its bound are developed by constructing an ?_i‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.     

非线性离散奇异摄动系统的组合优化控制方法的合理性分析

分析一类非线性离散奇异摄动系统的降阶组合优化控制器的合理性, 即降阶组合控制器与原始高阶优化控制器之间的关系. 基于快、慢子系统的解耦, 分别对快、慢子系统设计子优化控制器, 并进一步提出作用于原高阶系统的组合优化控制器. 对原高阶系统设计传统高阶优化控制器, 提出组合优化控制器近似等于传统高阶优化控制器的充分条件. 最后通过仿真验证了所得到结论的正确性.

     

非线性奇摄动系统的小增益增长条件

给出小增益增长条件使得在此条件下快慢子系统的渐近稳定性能够保证其原奇摄动系统的相应稳定性,并给出估计摄动参数的稳定界的解析表示及其应用例子.     

Robustness analysis of nonlinear observers for the slow variables of singularly perturbed systems

Estimation of unmeasured variables is a crucial objective in a broad range of applications. However, the estimation process turns into a challenging problem when the underlying model is nonlinear and even more so when additionally it exhibits multiple time scales. The existing results on estimation for systems with two time scales apply to a limited class of nonlinear plants and observers. We focus on analyzing nonlinear observers designed for the slow state variables of nonlinear singularly perturbed systems. Moreover, we consider the presence of bounded measurement noise in the system. We generalize current results by considering broader classes of plants and estimators to cover reduced‐order, full‐order, and higher‐order observers. First, we show that the singularly perturbed system has bounded solutions under an appropriate set of assumptions on the corresponding boundary layer and reduced systems. We then exploit this property to prove that, under reasonable assumptions, the error dynamics of the observer designed for the reduced system are semiglobally input‐to‐state practically stable when the observer is implemented on the original plant. We also conclude stability results when the measurement noise belongs to . In the absence of measurement noise, we state results on semiglobal practical asymptotical stability for the error dynamics. We illustrate the generality of our main results through three classes of systems with corresponding observers and one numerical example.     

Anti-windup control for nonlinear singularly perturbed switched systems with actuator saturation

This paper considers the problem of anti-windup (AW) control for nonlinear singularly perturbed switched systems with actuator saturation. An AW controller consisting of a dynamic state feedback (DSF) controller and an AW compensator is firstly constructed. Then, two methods are proposed to determine the AW controller gain matrices by a common Lyapunov function. One of which assumes that the singular perturbation parameter ? is available and designs ?-dependent AW controller gains simultaneously. The other one, which considers the case that ? is unknown but sufficiently small, designs the ?-independent DSF controller gain matrices first and then designs the ?-independent AW compensator gain matrices. Both of the methods are reduced to solving convex optimisation problems and can achieve larger stability bound and basin of attraction than the existing results. Finally, examples are used to illustrate the feasibility and advantages of the proposed methods.     

一类非线性奇异摄动系统的近似最优控制

针对一类非线性奇异摄动系统,基于自适应动态规划算法提出了一种新型的近似最优控制设计方法.该方法基于奇异摄动系统的快、慢Hamilton-Jacobi-Bellman(HJB)方程,从初始性能指标开始,通过神经网络的近似和控制律与性能指标的逐步更新迭代,最终收敛到最优的性能指标,而不用直接求解复杂的HJB方程.同时给出了...