半车非线性悬架的非平稳随机振动及控制

研究了1/2车非线性悬架模型在路面随机激励下的非平稳振动响应,并基于随机最优控制理论对其进行主动控制.首先利用等效线性化方法将具有非线性阻尼及迟滞刚度的非线性悬架模型线性化,然后将主动、被动悬架非平稳随机响应进行比较,结果表明非线性主动悬架的性能要优于被动悬架.最后,通过Monte-Carlo数值模拟验证了理论结果.     

Parametrized guaranteed cost method with prescribed performance via critic-only ADP for uncertain nonlinear systems and disturbances

In this paper, a novel parametrized guaranteed cost control (PGCC) method with prescribed performance control (PPC) is proposed for nonlinear systems with unknown bounded uncertainties and external disturbances described by Euler-Lagrange (EL) equations. The proposed method is capable of ensuring a robust optimal performance in the presence of dynamics constraints without the specific information of nonlinear perturbation. As a consequence, the conditions in the form of disturbances and uncertainties are also relaxed. The augmented model is converted by transforming the uncertainties and disturbances in the original system to a mismatched term using asymmetric PPC. By designing and modifying the novel guaranteed cost function to account for the maximum value of the nonlinear perturbation, an infinite-horizon PGCC problem is proposed by the unconstrained stationary optimal control problem. The relevant proposed linear parametrized Hamilton-Jacobian-Bellman (PHJB) equation is approximated to solve by a critic-only neural network (NN) with efficient computationally. Uniformly ultimately bounded stability is guaranteed via a Lyapunov-based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme.     

Lagrangian duality between constrained estimation and control

We show that the Lagrangian dual of a constrained linear estimation problem is a particular nonlinear optimal control problem. The result has an elegant symmetry, which is revealed when the constrained estimation problem is expressed as an equivalent nonlinear optimisation problem. The results extend and enhance known connections between the linear quadratic regulator and linear quadratic state estimation problems.     

A polynomial approach for optimal control of switched nonlinear systems

Optimal control problems for switched nonlinear systems are investigated. We propose an alternative approach for solving the optimal control problem for a nonlinear switched system based on the theory of moments. The essence of this method is the transformation of a nonlinear, nonconvex optimal control problem, that is, the switched system, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high‐performance numerical computing. Consequently, we propose to convexify the control variables by means of the method of moments obtaining semidefinite programs. Copyright © 2013 John Wiley & Sons, Ltd.     

Threads Yield Continuations

Just as a traditional continuation represents the rest of acomputation from a given point in the computation, a subcontinuationrepresents the rest of a subcomputation from agiven point in the subcomputation. Subcontinuationsare more expressive than traditional continuations and have been shown to beuseful for controlling tree-structured concurrency, yet they havepreviously been implemented only on uniprocessors. This article describes aconcurrent implementation of one-shot subcontinuations. Like one-shotcontinuations, one-shot subcontinuations are first-class but may be invokedat most once, a restriction obeyed by nearly all programs that usecontinuations. The techniques used to implement one-shot subcontinuationsmay be applied directly to other one-shot continuation mechanisms and may begeneralized to support multi-shot continuations as well. A novel feature ofthe implementation is that continuations are implemented in terms ofthreads. Because the implementation model does not rely upon any speciallanguage features or compilation techniques, the model is applicable toany language or language implementation that supports a small set of threadprimitives.     

聚合物驱最优控制问题求解算法的设计与实现

为了获得聚合物驱油的最大利润,通过最优控制来确定聚合物的最佳注入策略是一种有效的方法。该最优控制问题的数值解涉及到油藏数值模拟、伴随方程和非线性规划问题。给出了基于面向对象的算法设计方案及其实现细节。利用全隐式差分格式离散化聚合物驱模型,并采用Newton-Raphson求解所得到非线性方程组,在求解前向模型的同时构造了伴随方程。对一个三维聚合物驱注入问题进行了实例求解,表明了所实现算法的实用性和有效性。     

船舶航向非线性H∞逆优化输出反馈控制

为抑制船舶航向非线性优化控制中模型参数摄动和由状态观测器引入的不确定观测误差,提出了一种非线性H∞逆优化控制算法.首先,基于无源理论设计观测器以实现海浪滤波,该观测器无需海浪扰动的方差信息从而减少了观测器参数数量.然后,考虑模型参数摄动对观测误差的影响,给出了描述系统局部(全局)性态的局部(全局)H∞优化性能指标.在以广义黎卡提方程(GARE)对局部优化问题的求解的基础上,应用逆优化方法将全局H∞优化问题转化为构造闭环系统的Lyapunov函数问题,得到同时满足两种指标的优化控制器,并证明了稳定性.仿真结果证明了该算法的有效性.     

Dynamic routing and admission control for virtual circuit networks

The dynamic joint routing and admission control problem in multiple class multiple source-destination virtual circuit networks is considered. A nonlinear dynamic queueing model for virtual circuit networks that considers the dynamic interaction among the virtual circuit and packet processes is introduced. Then a multi-objective cost function of rejecting and maintaining virtual circuits, as well as of delaying and servicing packets is defined. The combined problem is formulated as an optimal control problem. Necessary optimality conditions are provided by Pontryagin's maximum principle. Sufficient optimality conditions based on the convexity of the Hamiltonian function are also given. For the finite horizon, the optimal controls can be found after numerically solving a Two-Point Boundary-Value Problem. For the longrun stationary equilibrium, the state-dependent routing and admission controls are derived.This work was supported by the National Science Foundation under Grant DMC-8452002 together with matching funds from AT&T Information Systems.     

An iterative method for suboptimal control of a class of nonlinear time-delayed systems

This work presents an approximate solution method for the infinite-horizon nonlinear time-delay optimal control problem. A variational iteration method (VIM) is applied to design feedforward and feedback optimal controllers. By using the VIM, the original optimal control is transformed into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The existence and uniqueness of the optimal control law are proved. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation results demonstrate the validity and applicability of the VIM.     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

桥式吊车系统的伪谱最优控制设计

对于桥式吊车系统的最优控制问题,根据实际的工况要求,性能指标有时不一定是标准的二次形式.同时,在实际的控制问题中,状态和控制输入往往会受到一些边界条件和路径过程中的约束.针对这一问题,本文应用Chebyshev伪谱优化算法来处理,它可以处理状态和控制约束的非线性最优化问题以及一个非标准的目标函数.首先对桥式吊车系统模型进行一系列的坐标变换,将其转变为上三角系统形式的误差模型.然后将桥式吊车最优控制问题转化成具有一系列代数约束的参数优化问题,即非线性规划问题.通过求解离散化后的参数优化问题,得到桥式吊车的最优控制律.本文还给出了Chebyshev伪谱最优解的可行性和一致性分析.最后,在仿真研究中验证该控制器的有效性.     

Realization of a bounded feedback in a nonlinear control problem

We substantiate a method for design of a limited feedback to control a system whose mathematical model includes a nonlinear state function. Designing such a feedback is based on a positional solution of auxiliary optimal control problems which provides the transition from the vicinity of one equilibrium state to the vicinity of a new equilibrium state and stabilization of the system in the new state. Preassigned additional constrains on the trajectory of the control system are satisfied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 108–116, January–February 2009.     

Stabilization with discounted optimal control

We provide a condition under which infinite horizon discounted optimal control problems can be used in order to obtain stabilizing controls for nonlinear systems. The paper gives a mathematical analysis of the problem as well as an illustration by a numerical example.     

一类混杂系统建模和优化控制的研究

为解决混杂系统优化控制的计算复杂性问题,针对结合逻辑规则的工业过程混杂模型,采用结合约束程序的混合整数非线性规划算法,求解这种混杂模型的优化控制。计算实例表明,通过混杂建模方法,可以充分利用工业对象的机理模型以及操作工经验或专家经验,建立系统的更精确模型;结合约束程序混合整数非线性规划算法可以较迅速地求解混杂模型优化控制问题,从而使该方法可以用于工业过程实时控制中。     

多输入非线性系统控制的分步变换与设计

研究多输入非线性系统基于分步变换及设计思想的非线性控制器设计问题。针对一般多输入非线性系统，首先利用非线性状态变换的方法进行非线性变换，得到一中间非线性系统模型，然后引入状态反馈，使得闭环系统为线性能控标准模型；从而利用分步设计的思想，实现非线性系统的最优控制。最后以－液位－温度控制系统为例，通过仿真说明该方法的有效性和可行性。     

Numerical solution of some initial optimal control problems using the reproducing kernel Hilbert space technique

ABSTRACT

In this paper, we present a general technique for solving a class of linear/nonlinear optimal control problems. In fact, an analytical solution of the state variable is represented in the form of a series in a reproducing kernel Hilbert space. Sometimes with the aid of this series form, we can also present the optimal control variable in a series form. An iterative method is given to obtain the approximate optimal control and state variables and the cost functional is numerically obtained. Convergence analysis of the method is also provided. Several numerical examples are tested to demonstrate the applicability and efficiency of the method.     

Controllability Problems for Differential Gompertzian Dynamic Equations

Control problems are considered in the class of differential Gompertzian dynamics equations. Controllability conditions in the nonstationary case are formulated. A general form of a controller for a stationary system and of a scalar controller are obtained in generalized functions. Criteria for different cases of convex closed control sets are presented.     

非线性系统自适应最优切换控制方法

针对具有未知动态和M个平衡点的连续时间非线性系统, 将线性自适应最优切换控制器和未建模动态补偿器相结合, 基于嵌入转换技术和近似动态规划思想, 提出一种自适应最优切换控制方法. 首先在非线性系统的M个平衡点建立M个线性化模型, 当模型参数已知时, 提出由线性最优切换控制器、切换准则、未建模动态补偿器以及非线性系统组成的控制系统结构; 当模型参数未知时, 在每个平衡点附近采集输入和状态数据, 利用黎卡提方程的迭代求解公式、最小二乘方法、极小值原理以及二次规划技术得到非线性系统的自适应最优切换控制器和最优切换序列; 最后进行仿真实验, 实验结果验证了所提方法的有效性、优越性和实际可应用性.     

基于拟线性化和Haar 函数的最优控制问题的直接求解方法

针对有约束条件的非线性最优控制问题,提出一种基于拟线性化和Haar函数的数值求解方法.首先将最优控制问题转化为一系列的二次规划问题,并使用系数未知的Haar函数对问题中的状态变量进行近似;然后应用拟线性化法将原非线性最优控制问题转化为相应的一系列受限的二次最优控制问题进行求解;最后基于所提出的方法对2个受限非线性最优控制问题进行求解,并通过仿真结果表明了采用所提出的算法求解最优控制问题的有效性.