改进型BUTTERWORTH最优控制的逆问题

本文针对传统Butterworth传递函数在阶数越高,系统响应品质减弱的情况下,研究了改进型Butterworth的传递函数,并通过反向求出改进型butterworth传递函数最优控制的状态增益矩阵K,然后计算加权矩阵Q,不必经过复杂的Riccati方程求解,简单方便。加入干扰后,系统仍具有很好的鲁棒性,实用性强。     

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。     

正倒向随机微分方程与一类线性二次随机最优控制问题

讨论一类正倒向随机微分方程解的存在唯一性及其对应的一类线性二次随机最优控制问题,利用单调性方法证明了一类特殊的正倒向随机微分方程解的存在唯一性定理,利用该结果研究一类耦合了一个倒向随机微分方程的线性随机控制系统广义最优指标随机控制问题,得到由正倒向随机微分方程的解所表示的唯一最优控制的显式表达式,并得到精确的线性反馈及其对应的Riccati方程.     

采用状态反馈实现纯滞后系统的控制

本文提出了一种采用最优状态反馈来实现对纯滞后对象的控制方法。它将纯滞后环节进行非对称二阶伯德近似，然后按照Butterworth滤波器原理设计状态反馈系数，从而实现对纯滞后对象的近似最优控制。仿真实验表明该系统具有较强的鲁棒性和抗扰性能。     

基于Butterworth标准传递函数设计状态反馈系统

本文首先给出了Butterworth标准传递函数,然后提出了一种设计状态反馈系统的方法,该方法包括利用线性变换将能控系统化为能控标准形,使能控标准形系统的闭环传递函数等于Butterworth标准传递函数,通过比较法来求得能控标准形系统的状态反馈增益阵,再通过变换得到一般能控系统的状态反馈增益阵.设计示例表明该方法设计的状态反馈系统具有良好的阶跃响应特性.     

基于Butterworth标准传递函数设计状态反馈系统

本文首先给出了Butterworth标准传递函数,然后提出了一种设计状态反馈系统的方法,该方法包括:利用线性变换将能控系统化为能控标准形,使能控标准形系统的闭环传递函数等于Butterworth标准传递函数,通过比较法来求得能控标准形系统的状态反馈增益阵,再通过变换得到一般能控系统的状态反馈增益阵。设计示例表明该方法设计的状态反馈系统具有良好的阶跃响应特性。     

基于遗传算法的最优控制加权阵的设计

遗传算法作为一种全局优化算法在自动控制领域得到了广泛的应用，在线性二次型最优控制设计中加权阵的选择是一项既重要又困难的工作，提出一种根据系统瞬态响应这一具有直接工程意义的品质指标，通过遗传算法来确定线性二次型最优控制加权阵的设计方法。根据这样确定的加权阵设计的最优控制器可实现闭环系统具有所期望的响应特性，且满足最优性以保证闭环系统的渐近稳定性及具有较大的稳定裕量。通过一个单输入单输出三阶系统的仿真实例说明了此方法的可行性与有效性。     

带有随机丢包的最优控制中Riccati方程解存在的条件

讨论了带有随机丢包的最优控制. 在传感器网络中,控制器与被控对象通过不可靠无线网络通信,因此代数Riccati方程由于通信链路的随机丢包产生了新的参数. 证明了当丢包率大于一临界值时,此Riccati 方程的解不存在. 通过解线性矩阵不等式,得到了这一临界值.     

极大极小最优控制算法

提出坐标受限条件下无超调快速准确停车极大极小最优控制完整算法，给出基于一维寻查中权阵Ｑ优化方法加速减的最优算法转换曲线，开发受限ＤＤＣ在线实时算法，并给出自动位置最优控制实例。     

The effects of redundant control inputs in optimal control

For a stabilizable system, the extension of the control inputs has no use for stabilizability, but it is important for optimal control. In this paper, a necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions. A similar result is also provided for H ₂ optimal control problem. These results show an essential difference between single-input and multi-input control systems. Several examples are taken to illustrate related problems.     

Discrete time mean-field stochastic linear-quadratic optimal control problems

This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear operators, the problem is formulated as an operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the expectation operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained.     

Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.     

Data-driven policy iteration algorithm for continuous-time stochastic linear-quadratic optimal control problems

This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data-driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm.     

Numerical solutions for constrained time-delayed optimal control problems

In this paper, time-delayed optimal control problems governed by delayed differential equation are solved. Two different techniques based on integration and differentiation matrices are considered. The time-delayed term of the problem has been approximated by Chebyshev interpolating polynomials. On this basis, the optimal control problem can be solved as a mathematical programming problem. The example illustrates the robustness, accuracy and efficiency of the proposed numerical techniques.     

Nonlinear optimal control as quantum mechanical eigenvalue problems

A novel approach for approximating the nonlinear optimal feedback control of a system with a terminal cost is proposed. To lessen the difficulty due to nonlinearity, we try to treat the system in a framework of linear theories. For this, we assume a quantum mechanical linear wave associated with the system. Since the control system is constrained by state equations, we handle the system according to quantum mechanics of constrained dynamics. A Hamiltonian is represented as a linear operator acting on a function that describes behavior of waves. Subsequently, nonlinear feedback is calculated without any time integration in the backward direction. Using eigenvalues and eigenfunctions of the linear Hamiltonian operator, an optimal feedback law is given as a combination of analytic functions of time and state variables. We take as an example a system described by two scalar variables for state and control input. Simulation studies on the system by the eigenvalue analysis show that the proposed method reduces calculation time to nearly a tenth that of a numerical calculation of a Hamilton-Jacobi equation by a finite difference method.     

The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control

The purpose of this paper is to investigate the role that the so-called constrained generalized Riccati equation plays within the context of continuous-time singular linear–quadratic (LQ) optimal control. This equation has been defined following the analogy with the discrete-time setting. However, while in the discrete-time case the connections between this equation and the linear–quadratic optimal control problem has been thoroughly investigated, to date very little is known on these connections in the continuous-time setting. This note addresses this point. We show, in particular, that when the continuous-time constrained generalized Riccati equation admits a solution, the corresponding linear–quadratic problem admits an impulse-free optimal control. We also address the corresponding infinite-horizon LQ problem for which we establish a similar result under the additional constraint that there exists a control input for which the cost index is finite.     

Lagrangian manifolds and asymptotically optimal stabilizing feedback control

Approximations to nonlinear optimal control based on solving a Riccati equation which varies with the state have been put forward in the literature. It is known that such algorithms are asymptotically optimal given large scale asymptotic stability. This paper presents an analysis for estimating the size of the region on which large scale asymptotic stability holds. This analysis is based on a geometrical construction of a viscosity-type Lyapunov function from a stable Lagrangian manifold. This produces a less conservative estimate than existing approaches in the literature by considering regions of state space over which the stable manifold is multi-sheeted rather than just single sheeted.     

机器人机械臂的鲁棒最优控制

基于拉格朗日方程,把多关节机器人机械臂动力学模型转化成一线性状态方程。然后,针对此线性状态方程,通过解一线性二次型优化问题,得到鲁棒最优控制律,保证了关节变量全局渐近收敛。最后,以两关节机器人为例,仿真结果表明所设计的控制律的有效性和鲁棒性。     

A canonical structure for constrained optimal control problems

We consider a general class of optimal control problems with regional pole and controller structure constraints. Our goal is to show that for a fairly general class of regional pole and controller structure constraints, such constrained optimal control problems can be transformed to a new one with a canonical structure. A three-step transformation procedure is used to achieve our goal, which essentially amounts to repeated augmentations of plant dynamics and repeated reductions of the controller. The transformed problem is one of the standard optimal static output feedback with a decentralized and repeated structure.