时滞系统的一种低阶l_1-控制

研究了离散时滞系统的一种低阶 l1-控制问题 .得到了系统可实现状态反馈及输出反馈 l1-控制的充分条件 ,并将其转化为线性矩阵不等式 (LMI)形式 ,给出了 l1-控制的显式表达形式 .文中的处理不是转化为无穷维受限优化问题 ,而是优化 l1-范数的一上界 .尽管得到的是次优 l1-控制律 ,但由于它具有确定的结构 ,故分析和设计过程十分简单     

差分有界干扰的最优抑制

提出了离散SISO系统中差分有界干扰的最优抗扰设计问题,讨论了控制对象含 (1-z)-1和不含(1-z)-1两种情况下问题的解法,并证明了上述两种情况都可以转化为 现有l1优化理论能够解决的问题.     

离散时间系统混合l1/H∞-控制问题

研究MIMO离散时间系统混合l1/H∞-控制问题.通过引入辅助优化问题,证明了目标优化值关于约束H∞指标的连续依赖性及其辅助问题最优化解的存在性,同时证明了辅助优化问题的截断序列问题解的收敛性,且其极限为混合l1/H∞-控制优化的辅助问题的最优化解.还给出了优化目标值的上下界逼近.     

l1鲁棒综合指标控制器的优化设计

本文讨论具有鲁棒稳定性和抗持续有界扰动的控制器设计问题.提出了一种新的综合 灵敏度指标函数,这种指标函数既可用于单变量系统也可用于多变量系统.通过选择权系数, 设计者可对鲁棒性和抗扰性灵活地进行加权,并给出了把这种l1综合指标优化设计问题转化 为一般l1优化问题求解的方法.     

基于l_∞范数和l_1范数最小化的二自由度最优鲁棒跟踪控制

研究了具有乘摄动模型不确定性并存在未知干扰系统的最优鲁棒跟踪控制问题 .采用二自由度控制器结构Youla参数化方法将最优鲁棒跟踪控制问题转化为两个相互独立的优化问题 :跟踪问题和鲁棒设计问题 .跟踪问题以l∞ 范数为性能指标通过极小化跟踪误差的最大幅值实现最优跟踪控制 ;鲁棒性设计问题中 ,将模型不确定性视为一种外界干扰 ,通过极小化干扰到误差的灵敏度函数的l1范数使得干扰对跟踪误差的影响最小 .通过截断处理 ,上述两种优化问题均可化为标准线性规划问题 .给出了截断阶数与逼近误差之间的关系 .仿真结果表明新方法的有效性 .     

一种基于Wiener模型的非线性预测控制算法

针对一类Wiener模型描述的非线性系统,提出了一种改进的非线性预测控制算法.该算法利用Laguerre函数描述Wiener模型动态线性部分的控制信号，将预测控制中在预测时域内优化求解未来控制输入序列转化为优化求解一组无记忆的Laguerre系数,以减少优化所需的计算量.利用静态模糊模型来逼近Wiener模型的非线性部分,将非线性预测控制优化问题转化为线性预测控制优化问题,克服了求控制输入时解非线性方程的困难,进而推导出了预测控制输入的解析式.CSTR过程的仿真结果表明了本文算法的有效性和可行性.     

MIMO离散时间系统混合l1/H2控制

研究了MIMO(多输入多输出)离散时间系统的混合l1/H2优化问题,该问题可描述为最优化一个传递函数矩阵的l1范数同时保证另一个传递函数矩阵的H2范数满足预定的指标.研究了最优目标函数值关于H2范数指标的连续性.证明了MIMO系统混合l1/H2控制问题最优解的存在性.由于基于标定-Q (scaled-Q)方法求解MIMO混合l1/H2问题,避免了进行零点插值运算的困难.通过求解有限维非线性规划问题可得到最优目标值的收敛的上下界.     

给定阶控制器■_1优化设计方法

研究了基于多输入多输出离散时间系统的给定阶控制器l1优化设计问题.基于You la参数化法,对自由参数Q分为多项式和有理多项式两种情况进行了讨论,并将有理式的情形转化为多项式的形式,最后将给定阶的控制器优化问题归结为求解标准的线性规划问题.在给定控制器阶次的条件下,得到使闭环系统内部稳定并使相应的l1范数最小的最优控制器.最后给出了算例来验证算法的有效性.*     

基于观测器的不确定广义时滞系统鲁棒预测控制

针对一类不确定广义时滞系统,讨论了其基于观测器的鲁棒预测控制问题,给出了系统观测器型预测控制器的设计方法.通过构造带有误差项的Lyapunov函数,应用线性矩阵不等式,将无穷时域二次性能指标"min-max"优化问题转化为凸优化问题,得到了鲁棒预测控制器存在的充分条件和显式表达式.证明了优化问题在初始时刻的可行解能保证广义闭环系统渐近稳定且正则无脉冲.仿真实例验证了所提出方法的有效性.     

Optimal control of the aeration system based on a simplified ASM1 model apply to Wastewater treatment plant

本文建立了基于ASM1模型的曝气系统简化数学模型,在此基础上提出了以曝气能量消耗最小为目标函数的曝气系统优化控制问题.采用联立配置法进行优化问题的求解,把非线性微分代数方程组的DAE系统转化为非线性代数方程组,将动态优化问题转化为非线性规划问题,最后调用IPOPT解法器求解.在动态入水的条件下进行曝气池的优化控制仿真,其结果显示比传统定值PID控制可节约近40％的能耗.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities (LMIs) involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

Stable and Quadratic Optimal Control for TS Fuzzy-Model-Based Time-Delay Control Systems

For the finite-horizon optimal control problem of the Takagi-Sugeno (TS) fuzzy-model-based time-delay control systems, by integrating the delay-dependent stabilizability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented to design the stable and quadratic optimal parallel distributed compensation (PDC) controllers. In this paper, the delay-dependent stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algebraic algorithm only involving the algebraic computation is derived in this paper for solving the TS fuzzy-model-based time-delay feedback dynamic equations. In addition, by using the SCSA, the stable and quadratic optimal PDC control problem for the TS fuzzy-model-based time-delay control systems is replaced by a static parameter optimization problem represented by the algebraic equations with constraint of the LMI-based stabilizability condition, thus greatly simplifying the stable and optimal PDC control design problem. The computational complexity for both differential and integral in the stable and optimal PDC control design of the original dynamic systems may therefore be reduced considerably. Then, for the static constrained optimization problem, the HTGA is employed to find the stable and quadratic optimal PDC controllers of the TS fuzzy-model-based time-delay control systems. A design example of the stable and quadratic optimal PDC controllers for the continuous-stirred-tank-reactor system is given to demonstrate the applicability of the proposed integrative approach.     

时滞广义区间系统的弹性保性能控制

研究了一类时滞广义区间系统的弹性保性能控制问题.利用线性矩阵不等式处理方法,导出了系统弹性保性能控制器存在的条件,证明了该条件等价于一个线性矩阵不等式的可行性问题,并用该线性矩阵不等式的可行解给出了弹性保性能控制器的一个参数化表示.进一步,通过求解一个凸优化问题,给出了系统的最优弹性保性能控制器的设计方法.最后的数值例子说明了所给方法的有效性.     

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.     

Sampled-data control of networked linear control systems

In this paper, the problem of synthesis and analysis for the networked control systems (NCSs) with time-driven digital controllers and event-driven holders is considered. The NCS is modelled as a sampled-data system with time-delay in its discrete-time subsystem. This model is able to capture many network-induced features, for example, time-delay and packet dropout. Moreover, the model allows different combinations of the time-driven or event-driven mode of the devices, including the samplers, the controllers and the holders. By transforming time-delay in the discrete-time subsystem into its continuous-time subsystem of the sampled-data system, we have also obtained a less conservative time-delay dependent stability result for the NCSs, using a new Lyapunov function and a relaxed condition. Some limitations of the existing literatures on network-induced time-delay and sampling period are removed in the proposed framework. Furthermore, a sampled-data control design procedure is developed for the NCSs. Linear matrix inequality approach has been employed to solve the stability and control design problems. Finally, numerical examples are included to demonstrate the effectiveness of the proposed stability result and the potential of the proposed techniques.     

一类多包传输网络控制系统的H∞鲁棒控制

研究了一类不确定时延多包传输网络控制系统的最优H∞控制问题. 针对传感器时钟驱动、控制器和执行器事件驱动的多包传输网络控制系统, 考虑不大于一个采样周期的不确定时延和有限能量的外部扰动, 提出一种基于模型的反馈控制策略, 利用Lyapunov理论推导了H∞控制律存在的充分条件, 通过求解矩阵不等式约束的优化问题得到最优H∞控制律. 数值仿真表明了所用方法的有效性.     

Singular linear-quadratic optimal control problem for a class of discrete singular systems with multiple time-delays

The singular linear-quadratic optimal control problem for a class of discrete-time linear singular systems with multiple time-delays is investigated. The equivalent relationship between this problem and the non-singular linear-quadratic problem for standard state-space discrete-time linear systems without time-delay is derived, and the necessary and sufficient condition guaranteeing this equivalent relationship is also given. The optimal control is synthesized as state feedback, and the closed-loop system is regular, impulse-free and without time-delay. An example is given to show the validity of the proposed method.     

带饱和执行器的不确定时滞系统的鲁棒控制

研究了一类具有饱和执行器约束的不确定时滞系统时滞依赖型无记忆鲁棒控制问 题.所考虑的时滞系统包括时变未知但有界的不确定参数以及状态和控制的时滞项.文中应 用了Lyapunov定理以及线性矩阵不等式(LMI)方法来研究该系统的分析和综合问题,导出 了一个新的鲁棒可镇定判据和相应的无记忆鲁棒镇定控制律设计方法.所得的基于一组 LMIs的结果是与时滞相关的.