加权多步预报控制

本文提出了一类加权多步预报控制(WLPC)算法.这种算法是由极小化一个很一般的 加权二次型性能指标得到的.由于权因子可以根据闭环极点配置、前馈零点增补和动态性能 要求任意选取,所以可保证闭环系统的稳定性和对建模误差的鲁棒性.文中给出了这方面结 果的理论证明和仿真实例.     

加权多步预报控制——鲁棒性的频域分析

本文给出了加权多步预报控制（ＷＬＰＣ）^[1]算法的鲁棒性分析，其中包括WLPC算法允许的建模误差的界域和鲁棒性的频性分析结果。分析表明，只要适当选取权因子且配置好闭环极点，ＷＬＰＣ算法是一鲁棒性能良好的控制算法。     

多变量双线性广义预测极点配置自校正解耦控制器（续）

对一类多变量双线性系统提出了一种基于预测状态空间实现的GPP自校正控制算法,建立了预测状态与模型结构参数和输入输出信息之间的直接关系,给出了含有多个加权矩阵的多变量二次型性能指标。增加了系统设计的自由度。由于加权因子可以根据闭环系统稳定性要求以及系统动态特性、前馈零点增补、输出滤波和跟踪要求分别加以选取,可以保证闭环系统稳定并改善了系统动态特性增强了鲁棒性,仿真结果表明了该算法具有GPP的诸多优点。     

多变量双线性广义预测极点配置自校正解耦控制器

对一类多变量双线性系统提出了一种基于预测状态空间实现的GPP自校正控制算法,建立了预测状态与模型结构参数和输入输出信息之间的直接关系。给出了含有多个加权矩阵的多变量二次型性能指标,增加了系统设计的自由度。由于加权因子可以根据闭环系统稳定性要求以及系统动态特性、前馈零点增补、输出滤波和中上要求分别加以选取,可以保证闭环系统-稳定并改善了系统动态特性增强了鲁棒性。仿真结果表明了该算法具有GPP的诸多优点。     

多变量发酵过程的神经网络在线解耦控制

为提高多变量系统解耦控制的性能,提出了一种基于参考模型的神经网络在线解耦控制方法.构造神经网络实现前馈解耦,通过参考模型的输出与被控系统输出估计耦合作用对被控量的影响,由此设计神经网络权值参数学习算法,在线调整网络参数使多变量耦合系统实现解耦;对解耦后的子系统分别设计闭环控制器,以达到优良的控制性能.仿真实验结果表明,提出的解耦控制方法是简单有效的.     

多变量动态矩阵控制系统的闭环稳定性

定量分析了无约束多输入多输出（MIMO）动态矩阵控制系统的闭环稳定条件,首先基于脉冲响应模型重新描述了动态矩阵控制（DMC）算法;在此基础上,推导得到了MIMODMC系统的闭环稳定条件,以便于预测控制系统的分析与设计。     

多输入/多输出系统动态矩阵控制鲁棒稳定性

研究了基于脉冲响应模型的动态矩阵预测控制(DMC)算法,针对多输入、多输出(MIMO)系统脉冲响应模型的特点,利用脉冲响应系数误差矩阵范数平方和定义预测模型的模型误差,以线性矩阵不等式(LMI)的形式提出了DMC闭环鲁棒稳定充要条件,将DMC算法闭环稳定问题转换为一类线性矩阵不等式的可解问题.并且研究了模型误差与闭环系统稳定性之间的关系,给出了保证系统稳定条件下模型误差界的求取方法,通过求解一个线性矩阵不等式约束的凸优化问题得到保证闭环系统稳定的误差界.最后,利用算例对本文方法的有效性进行了验证.     

梯格形自适应控制

本文讨论并解决了具有d步时延的多变量系统的梯格形自适应控制问题.为此,把自适 应控制下的闭环系统嵌入到ARMA模型中,采用梯格算法进行预报;用简捷方法推导了d步 梯格预报公式,并给出了控制量的确定方法.采用梯格自适应控制可方便地调节模型阶次,从 而可以克服对象阶次不准引起的自适应控制失效问题.     

基于Kp=S1D1U1分解的多变量鲁棒模型参考自适应控制

针对具有噪声的多变量系统,利用高频增益矩阵K。_p=S_1D_1U_1分解,提出了一种多变量鲁棒直接型模型参考自适应控制．通过重新证明一些同单变量系统鲁棒自适应控制理论相似的性质,及重新定义规范化信号,找出了闭环系统的所有信号与规范化信号之间的关系,严格地分析了闭环系统的稳定性和鲁棒性．     

基于状态反馈精确线性化的三相四桥臂逆变器的控制

根据三相四桥臂逆变器的工作原理,应用开关函数建立了控制系统数学模型,引入开关周期平均算子将离散的系统转化为连续系统.根据系统的主要控制目标选取状态变量、输入变量和输出变量,得到适合于微分几何方法的3输入3输出的仿射非线性系统模型.根据非线性微分几何理论,从理论上证明了该模型满足多输入、多输出系统精确线性化的条件,推导出非线性状态反馈控制律.对非线性坐标变换后得到的线性系统,利用二次型最优控制策略时,根据无源性控制方法的思想,提出一种闭环系统能量函数,并推导出权矩阵的参数形式.将最优化得到的控制律进行逆变换来实现原系统的优化控制设计.仿真结果验证了该方法的有效性和正确性.     

一种多变量广义最小方差自校正控制器

本文对一类多变量系统给出了一种广义最小方差自校正控制器,并讨论了系统加入这种 控制器后的闭环特性,将二次型性能指标的加权阵与系统闭环极-零点联系起来,从而就可根 据系统的期望闭环极点的位置在线选取加权阵.仿真结果表明这种控制器性能良好,工作可 靠.     

LQ最优控制之逆问题的研究

本文通过适当地选取LQ性能指标函数中的加权矩阵R,给出了该二次型性能指标函数中的另一个加权矩阵Q与系统的开环特征多项式、闭环特征多项式的系数以及系数的系数矩阵A、B之间的对应关系。如果给定一个系统以及该系统的一组最优闭环极点,就可以求得矩阵Q。同时,用本文的研究结果,还可以直接确定系统的最优状态反馈系数矩阵。     

关于确定加权矩阵的两个定理

给定一线性连续或离散时间系统以及与其对应的二次型性能指标函数,文中证明了在系统的开、闭环特征多项式,系统的系数矩阵以及二次型性能指标函数中的加权矩阵之间存在一组确定的显式关系.根据这组关系,满足期望闭环特征值要求的加权矩阵的确定问题变为求解一组具有二次变量的非线性方程组.对于高阶系统,用数值方法求解该方程组也是十分方便的.     

Constrained optimal control

The explicit form of the optimal control law of a given linear, discrete-time, time-invariant process subject to a quadratic cost criterion is well known. In some applications it is desirable that the state of a controlled dynamic process be nonnegative, given a certain class of initial disturbances. Using the controllable block companion transformation, sufficient conditions on the weighting matrices of the cost criterion are derived to ensure that the closed-loop response of the original process with the standard, unconstrained optimal feedback law will be nonnegative. It is shown that the nondiagonal elements of the transformed weighting matrices can be chosen to ensure nonnegativity     

Stabilizing receding horizon H ∞ control for linear discrete time-varying systems

In this paper, we simply derive matrix inequality conditions on the terminal weighting matrices for linear discrete time-varying systems that guarantee non-increasing and non-decreasing monotonicities of the saddle-point value of a dynamic game. We show that the derived terminal inequality conditions ensure the closed-loop stability of the receding horizon H X control (RHHC). The stabilizing RHHC guarantees the H X norm bound of the closed-loop system. The derived terminal inequality conditions include most well-known existing terminal conditions for the closed-loop stability as special cases. The condition on the state weighting matrix is weakened so as to include even the zero matrix. The results for time-invariant systems are obtained correspondingly from those in the time-varying case.     

Implementation of stabilizing receding horizon controls for time-varying systems

In this paper, a new stabilizing receding horizon control (RHC) scheme is proposed for linear discrete time-varying systems, which can be easily implemented by using linear matrix inequality (LMI) optimization. The control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix. The resulting stabilizing RHC scheme leads to time-varying finite terminal weighting matrices even for time-invariant systems, which is more general than in the case of using constant matrices. Based on the proposed scheme, another implementation method is also discussed for easy computation and numerical feasibility consideration of LMI optimization, although the second method does not guarantee the closed-loop stability theoretically. Through a simulation example, the effectiveness of the proposed schemes is illustrated.     

连续系统线性二次型期望极点配置问题的研究

本文以线性二次型性能指标中的加权矩阵和最 优闭环系统在频域内的解析关系为基础,提出了一种新的期望极点配置方法．该方法的主要 优点是不必求解复杂的矩阵Riccati方程也可很容易地确定满足指定闭环极点配置要求的状 态反馈矩阵．本文还讨论了指定闭环极点的选择方法,并用例子说明这种极点配置方法的有 效性和简便性．     

Disturbance attenuation for constrained discrete-time systems via receding horizon controls

In this note, we propose new receding horizon H/sub /spl infin// control (RHHC) schemes for linear input-constrained discrete time-invariant systems with disturbances. The proposed control schemes are based on the dynamic game problem of a finite-horizon cost function with a fixed finite terminal weighting matrix and a one-horizon cost function with time-varying finite terminal weighting matrices, respectively. We show that the resulting RHHCs guarantee closed-loop stability in the absence of disturbances and H/sub /spl infin// norm bound for 2-norm bounded disturbances. We also show that the proposed schemes can easily be implemented via linear matrix inequality optimization. We illustrate the effectiveness of the proposed schemes through simulations.     

A note on the solution of the algebraic Riccati equation

In this note, we consider the problem of solving the algebraic Riccati equation (ARE) arising in the optimal control theory, Several cases are studied. The solution here is, unlike the usual ones, related directly to the controllability and the observability matrices, the weighting matrices and the resulting closed-loop eigenvalues. As a result, it only requires few matrix operations to obtain the solution.     

General receding horizon control for linear time-delay systems

A general receding horizon control (RHC), or model predictive control (MPC), for time-delay systems is proposed. The proposed RHC is obtained by minimizing a new cost function that includes two terminal weighting terms, which are closely related to the closed-loop stability. The general solution of the proposed RHC is derived using the generalized Riccati method. Furthermore, an explicit solution is obtained for the case where the horizon length is less than or equal to the delay size. A linear matrix inequality (LMI) condition on the terminal weighting matrices is proposed, under which the optimal cost is guaranteed to be monotonically non-increasing. It is shown that the monotonic condition of the optimal cost guarantees closed-loop stability of the RHC. Simulations demonstrate that the proposed RHC effectively stabilizes time-delay systems.