移动机器人速度加速度饱和约束下的时间最优控制

针对机器人运动系统中普遍存在的速度和加速度约束, 提出一种满足以上约束的机器人运动时间最优控制方法. 首先, 通过最优条件构造哈密尔顿函数, 根据极小值原理求解时间最优控制; 其次, 通过相轨迹分析, 证明了满足约束的时间最优控制律的形式; 再次, 通过求解最优时间, 将满足约束的时间最优控制律转换成末端时间为最优时间的燃料最优控制律; 最后, 在RoboCup 小型足球机器人上进行对比实验, 验证了该方法在规划与实际上的一致性.     

离散时间线性系统最优控制的遗传算法实现

本文提出了求解控制变量受区间约束情形的离散时间线性系统最优控制的遗传算法,在遗传算法框架下给出了离散时间线性系统最优控制问题可行解的编码及初始化方法,设计了选择、交叉、变异等遗传算子,并对初始化方法及各种遗传算子的可行性给出理论分析。     

基于改进遗传算法的时间最优控制问题求解

对原有遗传算法的不足进行分析 ,提出改进的遗传算法。对于高维、高精度问题 ,改进算法相对原算法可节省大量存储空间和解码时间。提出的选择算子仅与父代的大小顺序有关 ,既可避免原算法对适应值必须为正的限制 ,又可避免算法过早收敛到局部解。证明了新算法的全局收敛性 ,并对新的选择算子进行了性能分析。将改进的遗传算法引入受约束时间最优控制问题的求解 ,获得了令人满意的结果     

基于几何方法的约束线性系统控制快速算法

针对存在状态量和控制量约束的线性系统控制问题, 提出了新快速算法. 已有的处理上述约束系统控制问题的多面体方法和椭球方法在实际应用过程中分别存在计算繁琐和计算保守的问题. 在数学分析的基础上, 通过对上述算法的水平集计算过程的优化, 提出了一种计算简单的约束控制算法. 仿真结果表明, 这种算法计算简单, 且可以满足系统控制的要求.     

带状态约束的疏浚最优控制问题转化方法

疏浚作业系统追求疏浚产量最大化,同时需要保证横移土壤切削过程和泥浆管道输送过程稳定安全的运行,可归结为带状态不等式约束的线性二次型最优跟踪控制问题。针对该问题,提出一种系统状态空间增维的转化方法,引入辅助状态变量和控制变量,将状态不等式约束转化为等式约束,并构建具有控制安全性的等价疏浚系统。仿真结果表明,该方法能够较好地提高泥浆浓度,同时又可以限制系统中主要状态量长时间的过载运行,从而有效增强挖泥船疏浚施工的安全性与平稳性。     

通讯约束下的线性系统状态降维与估计

本文面向状态估计, 考察了通讯功率受限时线性动态系统状态的降维问题. 为了满足平行信道传输数据的维数限制和通讯功率约束, 采取降低状态维数的方法, 通过传输信号的新息, 提高传输效率, 利用有限的通信资源, 使得接收端的状态估计达到最优. 本文采用差分脉冲编码调制系统(DPCM), 基于最小误差熵估计准则和Kalman估计算法, 得出了最优的状态降维矩阵的设计方法, 并且对随机系统的可估计性以及对相应确定性系统的能观性进行了分析. 分析和仿真结果表明, 这种设计方法在传输信号满足通讯功率限制的条件下可以使接收端的状态估计性能达到最优.     

逐点线性化后退区间最优控制在飞机非线性控制中的应用

常规线性飞控系统针对推力矢量飞机这样的多控制冗余、非线性MIMO系统,无法实现非线性控制．本文针对推力矢量飞机非线性系统,阐述了一种逐点线性化后退区间最优控制算法满足飞行品质要求．首先将作动器,飞行品质和逐点线性化的飞机线性模型综合实现在线建模,然后以飞行状态与预测状态之间的误差、作动器的位置限制和速率限制作为最优指标,最后以此为基础,根据最优控制原理计算当前时刻飞机最优控制指令,实现飞机非线性控制．采用国内某型号飞机气动数据验证此算法的鲁棒性和稳定性．     

具有输出/全状态约束的固定时间滑模控制

本文主要解决具有约束的二阶系统的固定时间跟踪控制问题,分别讨论了具有输出约束与具有全状态约束的控制算法设计.首先,为解决输出约束下的固定时间控制问题,本文构建了具有输出约束的新型终端滑模变量,并设计了具有扰动抑制能力的固定时间滑模控制律,保证系统输出始终满足约束条件,同时跟踪误差在固定时间内收敛到原点的充分小的邻域内.进一步,为了处理具有全状态约束的控制问题,本文构建了具有全状态约束的终端滑模变量并设计了相应的固定时间滑模控制律.鉴于系统控制律的不连续性,文章采用非光滑分析及Lyapunov稳定性理论证明了闭环控制系统的稳定性.最后,在数值仿真中,将本文提出的方法与传统固定时间滑模方法进行对比,验证了所建立算法的有效性.     

最优控制理论在电力拖动系统中应用──电力拖动最优控制

本文介绍线性最优控制理论在电力拖动系统领域的应用，给出工程实用控制规律及实践的控制线路。     

基于强化学习的一类具有输入约束非线性系统最优控制

针对部分系统存在输入约束和不可测状态的最优控制问题,本文将强化学习中基于执行–评价结构的近似最优算法与反步法相结合,提出了一种最优跟踪控制策略.首先,利用神经网络构造非线性观测器估计系统的不可测状态.然后,设计一种非二次型效用函数解决系统的输入约束问题.相比现有的最优方法,本文提出的最优跟踪控制方法不仅具有反步法在处理...     

Stochastic linear quadratic optimal control problem with terminal state constraints

This paper addresses the stochastic linear quadratic (LQ) control problem with first- and second-order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative-noise stochastic system rather than an additive-noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two-point boundary-value problem (TPBVP). We provide the optimal closed-loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results.     

Necessary conditions for a class of optimal multiprocess with state constraints

In this article, we derive a maximum principle for a special class of free end time optimal control of multiprocesses involving a family of control systems acting in different regions defined by state constraints. We are mainly interested in problems with contiguous time intervals. The main feature of our maximum principle is that it covers the case where some of the regions considered may not be visited. This means that the intervals where the corresponding control systems are active may be reduced to a single point. The derivation of our maximum principle is done by reformulating the optimal multiprocess problem as an equivalent fixed time state constrained optimal control problem. This reformulated problem is also of interest since it provides the means to solve optimal multiprocess problems numerically via the direct method. We illustrate our findings with an example concerning the path planning of an autonomous underwater vehicle (AUV) using a simple kinematic model derived for simulations. We use simplified point‐mass model for the motion of an AUV in a horizontal plane and we assume that the ocean currents are known. We recast this problem as the multiprocess optimal control problem of interest and we study it via simulations presenting computational results partially validated by the maximum principle.     

Time/fuel optimal control of constrained linear discrete systems

A unified approach to solving three common optimal control problems is presented, for linear systems under general constraints. The problems are: (1) the time optimal control problem; (2) the fuel optimal control problem in fixed time; (3) the time optimal control problem with a fuel constraint. A special purpose linear programming algorithm is used. State variable constraints are efficiently handled by a cutting plane algorithm. An example of a sixth order system with two inputs and two state variable constraints illustrates the method as implemented on a personal computer.     

A control problem with pointwise state constraints

We consider a parabolic control problem in which the state is constrained pointwise. We obtain useful approximations by considering a regularized family of problems and show that the associated family of optimal controls converges strongly to the optimal control of the original problem.     

Fast model predictive control for linear periodic systems with state and control constraints

The design of stabilizing model predictive control laws for discrete‐time linear periodic systems with state and control constraints is considered. Two algorithms are presented. The first one is based on interpolation between several unconstrained periodic controllers. Among them, one controller is chosen for the performance while the rest are used to extend the domain of attraction. The second algorithm aims to improve the performance by combining model predictive control and interpolating control. The proposed approaches not only guarantee recursive feasibility and asymptotic stability but also are optimal for states near the origin. Copyright © 2017 John Wiley & Sons, Ltd.     

Multistage linear programming for discrete optimal control with distributed-lags

A multistage decomposition scheme is developed for optimizing discrete-time dynamic systems, which include distributed and/or multiple pure delays. The discrete optimal control problem in this paper consists of a system dynamics described by a multidimensional linear difference equation of high-order which is called the distributed-lag model, a linear objective function, and linear state and control constraints. This problem may be solved as a linear program by, for example, a revised simplex method. However, this leads to excessive storage requirement for large problems. Instead, by taking advantage of the staircase-structure of equality constraints (system equation), Dantzig-Wolfe decomposition principle is applied repeatedly in each stage, and an effective multistage decomposition algorithm for distributed-lag models is obtained. Significant advantage of the optimization technique in this paper is that it can handle any number of delay terms in the system without reducing the multidimensional high-order system equation to a conventional larger dimensional first-order system equation (state equation of normal form). Therefore, a substantial reduction of computational burden, the so called curse of dimensionality, in the existing discrete optimal control algorithms, is obtained. A numerical example of a congested urban road traffic control problem with many delays is included.     

Adaptive dynamic surface control of nonaffine nonlinear system with time‐varying state constraints

This paper investigates the problem of adaptive dynamic surface control for pure‐feedback time‐varying state constrained nonaffine nonlinear system. A continuous and semibounded condition is proposed of nonaffine function to ensure that the system can be controlled, and the invariant set is introduced for this mild condition. By employing the dynamic surface control technique, the “complexity explosion” problem caused by backstepping technique is averted in developed control method. Robust compensators are devised to weaken poor effect of disturbances and uncertainties. The time‐varying barrier Lyapunov functions are adopted to dispose the problem of time‐varying state constrains. Moreover, it is proved that the whole closed‐loop signals are bounded, the tracking error can converge to a small neighborhood of zero, and the system states are insured to maintain in the predefined compact sets. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.     

状态和输入受限的切换奇异布尔控制网络的最优控制

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

Optimal control for linear systems with state equality constraints

This paper deals with the optimal control problem for linear systems with linear state equality constraints. For deterministic linear systems, first we find various existence conditions for constraining state feedback control and determine all constraining feedback gains, from which the optimal feedback gain is derived by reducing the dimension of the control input space. For systems with stochastic noises, it is shown that the same gain used for constraining the deterministic system also optimally constrains the expectation of states inside the constraint subspace and minimizes the expectation of the squared constraint error. We compare and discuss performance differences between unconstrained (using penalty method), projected, and constrained controllers for both deterministic and stochastic systems. Finally, numerical examples are used to demonstrate the performance difference of the three controllers.