带有持续扰动的时滞非线性大系统的最优跟踪控制

研究具有外界持续扰动的时滞非线性大系统的无静差最优跟踪控制问题.将时滞非线性大系统分解为带有互联项的N个时滞非线性子系统,基于内模原理对子系统构造扰动补偿器,将带有外部持续扰动的子系统化为无扰动的增广系统.通过灵敏度法求解不含时滞的两点边值问题,得到子系统的最优跟踪控制律,截取最优跟踪控制律的前N项作为次优控制律来近似系统的最优控制律.仿真实例表明了该设计方法的有效性.     

带有持续扰动非线性系统的前馈-反馈最优控制

研究具有外界持续扰动作用下非线性系统的最优控制问题,提出了一种设计前馈一反馈最优控制器的逐次逼近算法．利用该算法可将在扰动作用下的非线性系统的最优控制问题转化为求解线性非齐次两点边值序列的问题．得到的最优控制律由解析的线性前馈-反馈项和伴随向量序列极限形式的非线性补偿项组成．通过截取非线性补偿序列的有限项,可得到前馈-反馈次优控制律．仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制．     

具有持续扰动的时滞系统前馈2反馈最优控制

针对外部持续扰动下的线性时滞系统，提出一种前馈-反馈最优控制的逐次逼近算法．利用逐次逼近算法，将既含有时滞项又含有超前项的两点边值问题转化为不合时滞项和超前项的线性两点边值问题族，并证明了线性两点边值问题族的解序列一致收敛于原系统最优控制律．得到的最优控制律由解析的无时滞前馈-反馈控制部分和伴随向量序列极限形式的时滞补偿控制部分组成．通过截取时滞补偿序列的有限项，得到系统的前馈-反馈次优控制律．仿真示例表明，该方法对外部持续扰动具有良好的鲁棒性．     

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     

受扰非线性离散系统的前馈反馈最优控制

利用逐次逼近法研究含外部扰动的非线性离散系统的线性二次型前馈反馈最优控制问题.首先将系统的最优控制问题转化为非线性两点边值问题族.其次,构造了该问题族的由精确线性项和非线性补偿项组成的解序列,并证明了解序列一致收敛到系统的最优解.最后,通过截取最优控制序列解中非线性补偿项的有限项,得到系统的前馈反馈次优控制(FFSOC)律及设计算法.仿真算例表明,该算法容易实现,且对抑制外部扰动的鲁棒性优于经典的反馈次优控制(FSOC).     

非线性相似组合大系统最优控制的逐次逼近过程

研究一类仿射非线性相似组合大系统关于二次型性能指标的最优控制问题．首先通过模型简化,将非线性相似组合大系统化为若干个准解耦的子系统;然后利用非线性系统最优控制的逐次逼近设计方法,将求解高阶强耦合的非线性两点边值问题简化为求解一族解耦的线性两点边值问题序列．该线性两点边值问题序列的解一致收敛于非线性相似组合大系统的最优控制,得到的最优控制律由线性最优控制的解析项与非线性补偿序列的极限项组成．通过截取最优控制非线性补偿序列的有限次逼近值．得到了非线性组合大系统的次优控制律．     

具有控制时滞系统的最优无静差正弦扰动抑制

研究在外部正弦扰动作用下，控制含时滞的线性系统的最优无静差调节器设计问题．首先利用Artstein变换将控制变量含时滞的系统转化为不舍时滞的系统；然后利用内模原理构造扰动补偿器，将带扰动的系统转化为无扰动的增广系统，从而将无静差扰动抑制问题转化为无扰动增广系统的最优调节器设计问题；最后利用最优控制理论求得最优无静差反馈控制律．仿真结果表明了所提出方法的有效性．     

控制时滞系统基于观测器的最优扰动抑制

研究在持续外界扰动作用下含有控制时滞线性系统的最优扰动抑制问题. 首先利用模型转换将控制时滞系统转化为无时滞系统. 然后证明最优控制律的存在唯一性, 并通过求解Riccati方程和Sylvester方程设计含前馈补偿器和控制记忆项的最优控制律, 其中的前馈控制项和控制记忆项分别补偿了扰动和控制时滞对系统的影响. 通过构造扰动状态观测器, 解决了前馈补偿器的物理不可实现问题. 仿真实例验证了所设计的最优控制律的有效性.     

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．     

非线性互联大系统的最优控制:逐次逼近法

The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.     

事件触发双模分布式预测控制

本文针对有界扰动作用下的线性离散大系统,提出了事件触发双模分布式预测控制设计方法.利用输入状态稳定性(input-to-state stability,ISS)理论建立了仅与子系统自身信息相关的事件触发条件.只有子系统满足相应的事件触发条件,才进行状态信息的传输和分布式预测控制优化问题的求解,并与邻域子系统交互最优解作用下的关联信息.当子系统进入不变集时,采用状态反馈控制律进行镇定,并与进入不变集的邻域子系统不再交互信息.分析了算法的递推可行性和系统的闭环稳定性,给出了扰动的上界.最后,通过车辆控制系统对算法进行仿真验证,结果表明,本文提出的方法能够有效降低优化问题的求解次数和关联信息的交互次数,节约计算资源和通信资源.     

Robust tracking control for a class of MIMO nonlinear systems with measurable output feedback

This paper proposes a robust output feedback controller for a class of nonlinear systems to track a desired trajectory. Our main goal is to ensure the global input-to-state stability (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. Our approach consists of constructing a nonlinear observer to reconstruct the unavailable states, and then designing a discontinuous controller using a back-stepping like design procedure to ensure the ISS property. The observer design is realized through state transformation and there is only one parameter to be determined. Through solving a Hamilton–Jacoby inequality, the nonlinear control law for the first subsystem specifies a nonlinear switching surface. By virtue of nonlinear control for the first subsystem, the resulting sliding manifold in the sliding phase possesses the desired ISS property and to certain extent the optimality. Associated with the new switching surface, the sliding mode control is applied to the second subsystem to accomplish the tracking task. As a result, the tracking error is bounded and the ISS property of the whole system can be ensured while the internal stability is also achieved. Finally, an example is presented to show the effectiveness of the proposed scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

离散时滞系统的近似最优扰动抑制

研究了状态变量合有时滞的离散系统在外部扰动下的最优控制问题．通过引入一个灵敏度参数，将原系统的最优扰动抑制问题转化为一族不含超前项和时滞项的两点边值问题，并由此导出了最优扰动抑制控制器的这代近似设计方法．得到的最优扰动抑制控制律由解析的前馈一反馈项和伴随向量级数和形式的补偿项组成，截取伴随向量级数的有限和得到原系统的次优扰动抑制控制律．数值仿真表明该近似最优控制器对外部持续扰动具有良好的鲁棒性。     

OPTIMAL TRACKING CONTROL FOR DISCRETE TIME‐DELAY SYSTEMS WITH PERSISTENT DISTURBANCES

Optimal tracking control (OTC) for discrete time‐delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time‐advance on time‐delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

基于观测器的受扰非线性系统近似最优跟踪控制

研究一类受扰非线性系统的最优输出跟踪控制问题.给出了有限时域最优输出跟踪控制律的近似设计算法.首先将求解受扰非线性系统最优跟踪控制问题转换为求解状态向量与伴随向量耦合的非线性两点边值问题,然后利用逐次逼近方法构造序列将其转化为求解两个解耦的线性微分方程序列问题.通过迭代求解伴随向量的序列,可得到由解析的线性前馈-反馈控制部分和伴随向量的极限形式的非线性补偿部分组成的最优输出跟踪控制律.利用参考输入降维观测器和扰动降维观测器,解决了前馈控制的物理可实现问题.最后仿真结果表明了该方法的有效性.     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

时滞离散系统最优输出跟踪控制的灵敏度法

针对具有有限时间二次型性能指标的时滞离散系统,研究了最优输出跟踪控制问题.通过引入一个灵敏度参数,将原最优输出跟踪控制问题转化为不含超前项和时滞项的一族两点边值问题.得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成,其解析函数由一次性求解R iccati矩阵差分方程和矩阵差分方程得到,补偿项由求解伴随向量差分方程的递推公式得到.仿真结果表明了该方法的有效性.     

Adaptive dynamic surface-based differential games for a class of pure-feedback nonlinear systems with output constraints

ABSTRACT

This paper investigates the zero-sum differential game problem for a class of uncertain nonlinear pure-feedback systems with output constraints and unknown external disturbances. A barrier Lyapunov function is introduced to tackle the output constraints. By constructing an affine variable at each dynamic surface control design step rather than utilising the mean-value theorem, the tracking control problem for pure-feedback systems can be transformed into an equivalent zero-sum differential game problem for affine systems. Then, the solution of associated Hamilton–Jacobi–Isaacs equation can be obtained online by using the adaptive dynamic programming technique. Finally, the whole control scheme that is composed of a feedforward dynamic surface controller and a feedback differential game control strategy guarantees the stability of the closed-loop system, and the tracking error is remained in a bounded compact set. The simulation results demonstrate the effectiveness of the proposed control scheme.