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.     

A priori error estimates of a meshless method for optimal control problems of stochastic elliptic PDEs

In this paper, we study the optimal control problems of stochastic elliptic equations with random field in its coefficients. The main contributions of this work are two aspects. Firstly, a meshless method coupled with the stochastic Galerkin method is investigated to approximate the control problems, which is competitive for high-dimensional random inputs. Secondly, a priori error estimates are derived for the solutions to the control problems. Some numerical tests are carried out to confirm the theoretical results and to demonstrate the efficiency of the proposed method.     

Optimal Control of an Elliptic-Parabolic System with Conjugation Conditions

New optimal control problems for distributed systems described by initial boundary-value problems are considered in the paper for an elliptic-parabolic equation with conjugation conditions and quadratic cost functions. Theorems of existence of a unique optimal control are proved for all the considered cases.     

A modified genetic algorithm for optimal control problems

This paper studies the application of a genetic algorithm to discrete-time optimal control problems. Numerical results obtained here are compared with ones yielded by GAMS, a system for construction and solution of large and complex mathematical programming models. While GAMS appears to work well only for linear quadratic optimal control problems or problems with short horizon, the genetic algorithm applies to more general problems equally well.     

Some Problems of Soil Media Ecology and Optimal Control Processes in Them

New multicomponent soil media ecology problems and respective optimal control problems are considered in the paper. Existence theorems for the unique optimal control are proved for all the cases considered. Computation algorithms of high-accuracy discretization are constructed for some new classes of problems with discontinuous solutions.     

Trigonometric approximation of optimal periodic control problems with variable delays

A trigonometric approximation scheme for optimal periodic control problems with state and control dependent delays is considered. The formulation of approximate problems is here adapted to a specific form of state equation with variable time delays. Sufficient conditions for the sequence of nearly optimal solutions of approximate problems to be a generalized minimizing sequence for the basic problem are given. The application of the method proposed to a periodic control of chemical reactors with recycles and controlled piping is pointed out.     

Motion control of a rotor with a cavity with a viscous fluid

A formulation and solution procedure of optimal control problems for perturbed relative uniform motion of a body with a cavity filled with a viscous incompressible fluid are proposed. In this paper, the case with a cylinder is considered; however, this approach is basically true for the a cavity of an arbitrary form. The formula for the angular velocity of perturbed motion depending on an external perturbing element is devised. After that, we have a possibility to set different optimal control problems and apply the formalism elaborated in the optimal control theory. Two illustrated problems are given.     

Injection engine as a control object. II. Problems of automatic control of the engine

Specific features of injection engine as a control object are discussed, strict formulations of problems of engine automatic control and principles of their solution are presented. Examples of solution of the problem of stabilization of air-fuel ratio and engine torque control problems are presented as illustrations for demonstration of application of modern methods of automatic control theory for solution of control problems of injection engines.     

A solution of nonlinear TPBVP's occuring in optimal control

A new method is presented to obtain feedback solution for nonsingular optimal control problems, which lead to polynomial type nonlinear two-point boundary-value problems. Examples of such problems treated in the paper are quadratic state regulators for nonlinear systems with an analytic generator including the special case of a bilinear problem, linear quadratic regulators with magnitude constraints on the control variables, and also linear problems with nonquadratic performance indices.The solution method is based on solving a related two-point boundary value problem by using an equivalent functional equation and the theory of the so-called polynomial operators. Considerations are made in discrete form and the resulting algorithms are readily applicable to direct computing and control. Due to computational burden the method is restricted to low dimensional problems. Demonstration of the use of the method is given by designing nonlinear regulators for two computer controlled pilot processes.     

Neural networks applied to optimal flight control

This paper presents a method for developing control laws for nonlinear systems based on an optimal control formulation. Due to the nonlinearities of the system, no analytical solution exists. The method proposed here uses the ‘black box’ structure of a neural network to model a feedback control law. The network is trained with the back-propagation learning method by using examples of optimal control produced with a differential dynamic programming technique. Two different optimal control problems from flight control are studied. The produced control laws are simulated and the results analyzed. Neural networks show promise for application to optimal control problems with nonlinear systems.     

基于保辛算法的绳系卫星系统闭环反馈控制问题求解

应用非线性系统滚动时域控制的保辛算法求解绳系卫星系统子星释放和回收过程的闭环反馈控制问题.通过第二类Lagrange方程推导出二体绳系卫星系统的动力学方程;通过拟线性化方法将绳系卫星系统闭环反馈控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代求解;通过保辛算法将线性非齐次Hamilton两端边值问题转化为线性方程组的求解;通过递进更新时间步的状态变量和控制变量,完成绳系卫星系统的闭环反馈控制.数值仿真表明:相对于Legendre伪谱方法,用保辛算法求解绳系卫星系统的闭环反馈控制问题的计算速度和收敛速度较快.绳系卫星系统的开环控制和闭环反馈控制问题数值仿真结果表明:在绳系卫星的初始状态存在偏差的情况下,使用开环控制会导致系统在终端无法达到稳定状态,而使用闭环反馈控制则能在一段时间内抵消初始状态向量偏差对系统产生的影响,最终达到稳定状态.     

有约束无模型控制

研究了有约束无模型控制问题,首先对一般的MISO无模型控制(NMC)给出了一个简单合理的收敛性条件.由于实际应用中完全无约束的控制系统并不存在,为此考虑输入输出有上下界约束的无模型控制问题(NMCC).通过无模型控制方法中的泛模型,将对输出的约束转化为对输入的约束,进一步分析了有约束无模型控制问题的可行条件,并在不可行时给出了对软约束的调整方法,进而得出求解这种约束问题的一般算法.最后给出了一个仿真算例说明了方法的有效性,并在一定条件下给出了约束问题的收敛性证明.     

On the application of minimum principle for solving partially observable risk-sensitive control problems

This paper is concerned with the application of a minimum principle derived for general nonlinear partially observable exponential-of-integral control problems, to solve linear-exponential-quadratic-Gaussian problems. This minimum principle is the stochastic analog of Pontryagin's minimum principle for deterministic systems. It consists of an information state equation, an adjoint process governed by a stochastic partial differential equation with terminal condition, and a Hamiltonian functional. Two methods are employed to obtain the optimal control law. The first method appeals to the well-known approach of completing the squares, by first determining the optimal control law that minimizes the Hamiltonian functional. The second method provides significant insight into relations with the HamiltoniJacobi approach associated with completely observable exponential-of-integral control problems. These methods of solution are particularly attractive because they do not assume a certainty equivalence principle, hence they can be used to solve nonlinear problems as well.     

无线传感器网络中覆盖控制技术综述

覆盖控制是无线传感器网络应用的一个基本问题,反映了网络所能提供的"感知"服务质量,可以使无线传感器网络的空间资源得到优化分配,进而更好地完成环境感知、信息获取和有效传输的任务;立足于无线传感器网络的覆盖控制问题,分析了网络覆盖技术在国内外研究的现状与发展,指出了传感器网络覆盖算法中需要解决的问题,并提出了将多目标进化算法与智能计算技术用于动态覆盖控制技术研究设想。     

A quasi-separation theorem for LQG optimal control with IQ constraints

We consider the deterministic, the full observation and the partial observation LQG optimal control problems with finitely many IQ (integral quadratic!) constraints, and show that Wohnam's famous Separation Theorem for stochastic control has a generalization to this case. Although the problems of filtering and control are not independent, we show that the interdependence of these two problems is so superficial that in effect, they are problems which can be treated separately. It is in this context that the label Quasi-Separation Theorem is to be understood. We conclude with a discussion of computation issues and show how gradient-type optimization algorithms can be used to solve these problems. In this way, a systematic computation algorithm is derived.     

网络控制系统的稳定性分析和研究

该文针对目前网络控制系统的研究现状,阐述了在网络控制系统的分析和设计中需要明确的几个基本问题。综述了具有时变传输周期、网络调度、数据丢包以及网络时滞时的网络控制系统的建模与各种控制策略问题。尤其是网络控制系统在这些情况下的稳定性研究问题,然后列举了一些具有代表性的网络控制系统稳定性分析的最新结果。在此基础上分析了网络控制系统稳定性分析研究中尚待解决的问题,以及新的研究方向。     

Optimal control problems treated with algorithms of linear and nonlinear programming

Algorithms solving optimal control problems for linear discrete systems and linear continuous systems (without discretization) are discussed. The algorithms are based on a new approach to solving linear programming problems worked out in Minsk (USSR). A new method for solving nonlinear programming problems is justified. It uses the network interpretation of nonlinear functions and special network operations. Results of numerical experiment (on geometric programming problems) are given. In conclusion an algorithm of solving optimal control problem for the system with nonlinear input is described.     

On overtaking optimal tracking for linear systems

Optimal tracking problems involving a time-varying linear plant and infinite-horizon quadratic performance index are considered. In general, such problems yield an unbounded performance index for every control and thus must be interpreted as so-called overtaking optimal control problems. A completing-the-square argument is used to derive the overtaking optimal control for a general problem formulation, and various properties are discussed.     

Optimal periodic control problem: a modified trigonometric approximation and quasi-stationarity conditions

The constrained optimal periodic control problem for a system described by differential equations and endowed with inertial controllers is considered, A sequence of discretized problems using trigonometric polynomials is proposed to approximate the problem. Instantaneous constraints for the state and control are handled by a new and more precise approach that imposes only a small number of non-linear but easily computable constraints. The convergence conditions for a sequence of optimal solutions of discretized problems are derived. The inclusion in the approximating scheme of various quasi-stationarity conditions for the control and state variables is analysed. Extension of a new approximating approach for inertialess and smooth problems is also discussed.     

Unified optimal projection equations for simultaneous reduced-order,robust modelling,estimation and control

An optimal design problem which unifies reduced-order modelling, estimation and control problems is stated. Necessary conditions for optimality are obtained in the form of a coupled system of modified Riccati and Lyapunov equations. The results permit treatment of several new problems, such as reduced-order dynamic compensation with partially known disturbances and unified reduced-order control and estimation. Upon appropriate specialization, results obtained previously for the individual problems of reduced-order modelling, estimation and control are recovered. An additional feature is the inclusion of parameter uncertainty bounds so that the necessary conditions for an auxiliary minimization problem serve as sufficient conditions for simultaneous robust, reduced-order modelling, estimation and control.