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...     

奇异摄动时滞系统次优控制的Chebyshev多项式级数方法

研究奇异摄动时滞系统次优控制的近似设计问题.基于奇异摄动的快慢分解理论,将系统的最优控制问题转化为无时滞快子问题和线性时滞慢子问题;利用Chebyshev多项式级数方法将时滞慢子问题的近似求解问题转化为线性代数方程组的求解问题,进而得到原系统的次优控制律,该控制律由Chebyshev多项式级数的基向量表示.仿真算例表明了该方法的有效性.     

Optimal disturbance rejection control for singularly perturbed composite systems with time‐delay

The optimal control problem for a class of singularly perturbed time‐delay composite systems affected by external disturbances is investigated. The system is decomposed into a fast linear subsystem and a slow time‐delay subsystem with disturbances. For the slow subsystem, the feedforward compensation technique is proposed to reject the disturbances, and the successive approximation approach (SAA) is applied to decompose it into decoupled subsystems and solve the two‐point boundary value (TPBV) problem. By combining with the optimal control law of the fast subsystem, the feedforward and feedback composite control (FFCC) law of the original composite system is obtained. The FFCC law consists of analytic state feedback and feedforward terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. Simulation results are employed to test the validity of the proposed design algorithm. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.

     

New results for near-optimal control of linear multiparameter singularly perturbed systems

In this paper, we consider the linear quadratic optimal control problem for multiparameter singularly perturbed systems in which N lower-level fast subsystems are interconnected through a higher-level slow subsystem. Different from the existing methods, a new method is developed to design a near-optimal controller which does not depend on the unknown small parameters. It is shown that the resulting controller in fact achieves an O(||μ||²) approximation to the optimal cost of the original optimal control problem.     

含正弦扰动奇异摄动时滞系统的最优减振控制

研究奇异摄动时滞系统在正弦扰动下的最优减振控制问题．基于奇异摄动的快慢分解理论,将原最优控制问题转化为无时滞快子问题和受扰线性时滞慢子问题,通过摄动法和前馈补偿技术求解时滞慢子系统的最优控制问题,得到了系统的前馈反馈组合控制(FFCC)律及其存在唯一性条件．FFCC律由线性解析项和共态向量无穷级数和表示的时滞补偿项组成,其中线性解析项可通过求解Riccati方程和Sylvester方程得到,时滞补偿项通过递推求解共态向量方程得到,仿真算例表明了方法的有效性．     

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.     

Robust state estimation for singularly perturbed systems

This paper deals with the design of interval observers for singularly perturbed linear systems. The full-order system is first decoupled into slow and fast subsystems. Then, using the cooperativity theory, an interval observer is designed for the slow and fast subsystems assuming that the measurement noise and the disturbances are bounded and the singular perturbed parameter is uncertain. This decoupling leads to two observers that estimate the lower and upper bounds for the feasible state domain. A numerical example shows the efficiency of the proposed technique.     

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.     

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。     

受扰奇异摄动时滞组合大系统的近似最优控制

研究一类受扰奇异摄动时滞组合大系统的近似最优控制问题．基于奇异摄动的快慢分解理论．将原组合大系统的最优控制问题分解为组合线性快优化子问题和降阶的受扰时滞组合慢优化子问题．通过采用前馈补偿方法抑制外部扰动,采用参数摄动法求解组合慢优化子问题,得到了系统的前馈反馈组合（FFCC）控制律．通过引入降维扰动观测器解决了FFCC律的物理可实现问题．仿真算例验证了所提出方法的有效性．     

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.     

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.     

奇异摄动控制系统:理论与应用

系统地回顾了近年来奇异摄动控制技术的发展,主要包括线性奇异摄动系统的稳定性分析与镇定、最优控制、H_∞控制,非线性奇异摄动系统的镇定、优化控制和基于积分流形的几何方法,以及奇异摄动技术在实际工业,例如机器人领域、航天技术领域和工程工业、制造业等中的成功应用.并指出了这一领域进一步研究的方向.     

奇异摄动系统的H∞控制: 基于奇异系统的方法

实际系统的奇异系统模型往往通过忽略系统的奇异摄动系统模型微分项系数矩阵中的小时间参数得到.然而, 传统的奇异系统控制器设计很少考虑微分项系数矩阵的摄动. 本文拓展了现有奇异系统输出动态反馈H_∞控制器的设计, 使得当实际闭环系统中存在小时间参数时, 仍然能保持稳定并且满足一定的H_∞性能指标. 仿真算例说明了本文提出方法的有效性.     

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.     

On the model-based networked control for singularly perturbed systems

In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.     

On the model-based networked control for singularly perturbed systems

In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.     

奇异摄动系统的H_∞控制:基于奇异系统的方法

实际系统的奇异系统模型往往通过忽略系统的奇异摄动系统模型微分项系数矩阵中的小时间参数得到.然而,传统的奇异系统控制器设计很少考虑微分项系数矩阵的摄动.本文拓展了现有奇异系统输出动态反馈H∞控制器的设计,使得当实际闭环系统中存在小时间参数时,仍然能保持稳定并且满足一定的H∞性能指标.仿真算例说明了本文提出方法的有效性.     

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.