数字式预见控制的计算机算法研究

分析了计算机实现数字式预见控制的主要问题,给出了一种Riccati方程式的数字解法,提出了用计算机实现数字式预见控制的可行性和算法。研究表明这种算法的精度较高,易于计算机实现。     

人机系统最优预见补偿跟踪控制研究

1　引　言预见控制理论是最优跟踪控制问题的新的出发点 ,其有效性在机器人、数字机床等路径控制中得到证实[1 ] .本文将预见控制应用到人机控制系统 .人具有“先前看”的能力 ,尤其是训练有素的驾驶员具有积极利用未来目标信号提高跟踪品质的预见操纵行为 .以驾驶员 -飞机目标跟踪控制系统为例 ,在人的最优控制模型( OCM)基础上 ,通过目标信息的预见显示 ,建立人的最优预见控制模型 ( OPCM) .应用数字最优预见控制理论 [2 ] ,对信号发生器产生的目标信号进行预见跟踪控制 .2　驾驶员最优预见控制模型 ( OPCM)2 .1　数字最优预见控制最…     

一类具有输入时滞的时变离散系统的预见控制

针对一类具有输入时滞的时变离散系统,研究其预见控制问题.利用差分算子的性质,对系统的输入时滞项和目标信号进行差分处理,构造包含目标信号但不含时滞的扩大误差系统.基于最优控制和预见控制的相关理论,得到了扩大误差系统带有预见前馈补偿的控制器.进一步,利用矩阵分解方法,将高阶Riccati方程进行降阶处理,从而得到原时滞系统的预见控制器.最后通过仿真实例验证了所提出方法的有效性.     

线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.     

非线性离散系统的信息融合最优预见控制

将信息融合思想引入非线性离散系统的预见控制,提出了信息融合最优预见控制,将对控制系统的所有性能要求和系统动力学转化为可融合信息;然后从信息融合估计的角度,使原问题转化为求控制量的"融合估计"问题.推导了基于卡尔曼滤波器的最优预见控制算法,讨论了预见步数的选取问题,并通过对机械手的转移控制仿真研究说明了信息融合最优预见控制算法的有效性.     

基于误差系统的信息融合最优预见跟踪控制

针对期望轨迹和干扰可预见的最优跟踪问题, 提出了一种基于误差系统的信息融合最优控制方法. 将线性伺服系统转化为误差系统; 利用信息融合估计方法, 通过融合期望轨迹、干扰输入、误差系统状态等信息, 获得误差系统协状态以及控制增量的最优估计. 构建了由积分项、状态反馈控制项和预见前馈补偿项组成的最优预见控制系统. 线性直流电机系统的控制仿真结果表明, 信息融合最优预见控制下的位置跟踪精度比传统最优预见控制下的要高.     

一般型最优有限预见控制及其在地形跟踪中的应用研究

提出一种新的预见控制方法－－一般最优有限预见控制方法，并将其应用于巡航导弹地形跟踪控制设计。将参考信号和干扰信号考虑成更一般的形式，在其自相关函数数值已知的条件下，得到了一般型有限预见伺服系统设计问题的最优解。通过仿真证实，采用该方法设计地形跟踪系统，可以明显地改善巡航导弹的地形跟踪性能。     

最优预见伺服系统与最优预见FF补偿系统的统一处理

最优预见伺服系统一般与基本最优伺服系统共用同一个二次型性能指标函数设计预见前馈补偿项,其设计的着眼点是进一步减小性能指标函数.当控制系统的基本反馈部分不是采用最优控制方法设计时,历史上采用另一个性能指标函数设计预见前馈补偿,并把所得系统称为预见FF(前馈)补偿系统.这里把两种设计方法统一起来处理后,不仅最优预见伺服系统与最优预见FF补偿系统都仅仅是特例,而且给设计者扩大了选择的余地.最后给出了数值仿真,把这种设计方法与最优伺服系统、最优预见伺服系统进行了比较.     

一类线性离散广义系统最优预见控制器设计

提出一类广义线性离散系统的预见控制问题.首先,利用差分算子构造扩大误差系统,然后通过引入一些恒等式,把可预见的目标信号的差分也包含在扩大误差系统的状态向量中,把所考虑的广义系统的预见控制问题转化为一个形式上的普通广义系统的控制问题.由熟知的广义系统最优控制理论的结论,得到广义系统的带有预见作用的控制器.对扩大误差系统的R-能稳性和能检测性进行了详细讨论.     

一般型最优有限预见控制及其在地形跟踪中的应用研究

提出一种新的预见控制方法——一般型最优有限预见控制方法,并将其应用于巡航导弹地形跟踪控制系统的设计.将参考信号和干扰信号考虑成更一般的形式,在其自相关函数值已知的条件下,得到了一般型有限预见伺服系统设计问题的最优解.通过仿真证实,采用该方法设计地形跟踪系统,可以明显地改善巡航导弹的地形跟踪性能.     

Iterative learning control design based on composite energy function with input saturation

In this work, an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation. The analysis of convergence in the iteration domain is based on composite energy function, which consists of both input and state information along the time and iteration axes. Through rigorous analysis, the learning convergence in the iteration domain can be guaranteed under the input saturation, provided the desired trajectory is realizable within the saturation bound.     

基于目标的动态加权模糊控制

针对单输入、多目标控制系统，提出一种基于目标的动态加权模糊控制模型。该模型根据控制目标设计子模糊控制器，通过模糊推理得到的加权系数动态连接各个子目标模糊控制器，使多个子目标模糊控制器在控制过程中既相互竞争又相互协调。该模型用于吊车控制的仿真结果证明了其有效性。     

Analysis and control of parabolic PDE systems with input constraints

This paper develops a general framework for the analysis and control of parabolic partial differential equations (PDE) systems with input constraints. Initially, Galerkin's method is used for the derivation of ordinary differential equation (ODE) system that capture the dominant dynamics of the PDE system. This ODE systems are then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed-loop stability in the presence of constraints. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator. The theoretical results are used to stabilize an unstable steady-state of a diffusion-reaction process using constrained control action.     

On the weighting factors of the quadratic criterion in optimal control

By the introduction of the time integral of the output variable of a second-order system, the optimal feedback control law with respect to the quadratic performance criterion gives the conventional proportional-integral-derivative (PID) control. Some comparisons between the weighting factors of the quadratic criterion and the parameters of the PID controller are given. The values of the weighting factors corresponding to the classical methods of Cohen-Coon and Ziegler-Nichols are calculated ; negative values of the weighting factors are obtained.     

一种约束输入的广义预测控制新算法

提出一种约束输入的广义预测控制新算法（GPCIC），该算法不必求逆矩阵，占用内存小，计算速度快，仿真结果表明，该算法具有良好的控制性能。     

Global stable tracking control of underactuated ships with input saturation

In this paper, tracking control of underactuated ship in the presence of input saturation is addressed. By dividing the tracking error dynamic system into a cascade of two subsystems, the torques in surge and yaw axes are designed separately using the backstepping technique. More specifically, we design the yaw axis torque in such a way that its corresponding subsystem is finite time stable, which makes it to be de-coupled from the second subsystem after a finite time. This enables us to design the torque in the surge axis independently. It is shown that the closed-loop system is stable and the mean-square tracking errors can be made arbitrarily small by choosing design parameters. Simulation results also verify the effectiveness of the proposed scheme.     

Nonlinear dynamic allocator for optimal input/output performance trade-off: Application to the JET tokamak shape controller

In this paper, we revisit the dynamic allocation scheme for input redundant plants proposed in Zaccarian (2009). within a set-point regulation setting and propose generalizations that apply to cases where the plant under consideration is not input redundant but the control specifications allow us to modify the set-point regulation within certain bounds. In this case, the input allocator is extended to the nonredundant case by allowing it to improve the input allocation selection at the price of some output regulation error. We also establish here desirable convergence properties of the allocator, which were only addressed for the linear case in Zaccarian (2009). In particular, we design the allocator dynamics as the gradient of a cost function and establish its convergence to the minimum of the cost function under some mild conditions. The allocation scheme is applied to the JET tokamak shape controller by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom.     

Robust and optimal predictive control of the COVID-19 outbreak

We investigate adaptive strategies to robustly and optimally control the COVID-19 pandemic via social distancing measures based on the example of Germany. Our goal is to minimize the number of fatalities over the course of two years without inducing excessive social costs. We consider a tailored model of the German COVID-19 outbreak with different parameter sets to design and validate our approach. Our analysis reveals that an open-loop optimal control policy can significantly decrease the number of fatalities when compared to simpler policies under the assumption of exact model knowledge. In a more realistic scenario with uncertain data and model mismatch, a feedback strategy that updates the policy weekly using model predictive control (MPC) leads to a reliable performance, even when applied to a validation model with deviant parameters. On top of that, we propose a robust MPC-based feedback policy using interval arithmetic that adapts the social distancing measures cautiously and safely, thus leading to a minimum number of fatalities even if measurements are inaccurate and the infection rates cannot be precisely specified by social distancing. Our theoretical findings support various recent studies by showing that (1) adaptive feedback strategies are required to reliably contain the COVID-19 outbreak, (2) well-designed policies can significantly reduce the number of fatalities compared to simpler ones while keeping the amount of social distancing measures on the same level, and (3) imposing stronger social distancing measures early on is more effective and cheaper in the long run than opening up too soon and restoring stricter measures at a later time.     

A gap metric based weighting method for multimodel predictive control of MIMO nonlinear systems

A novel weighting method is proposed for multimodel predictive control of nonlinear systems with multiple scheduling variables (MIMO nonlinear systems), in which the gap metric is employed to formulate weighting functions for local controller combination. Compared to existent weighting functions, the proposed weighting method has two major advantages: firstly, there is only one tuning parameter, which makes it simpler. Secondly, the weights depend only on the scheduling vector and can be calculated off-line and stored in a look-up table. Therefore, the computational load can be reduced, especially for nonlinear systems with multiple scheduling variables. A MIMO CSTR system is studied to demonstrate the effectiveness of the proposed weighting method.     

Backstepping control integrated with Lyapunov-based model predictive control

In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.