Trigonometric approximation of optimal periodic control problemsfor systems with inertial controllers

A constrained optimal periodic control (OPC) problem for nonlinear systems with inertial controllers is considered. A sequence of approximate problems containing trigonometric polynomials for approximation of the state, control, and functions in the state equations and in the optimality criterion is formulated. Sufficient conditions for a sequence of nearly optimal solutions of approximate problems to be norm-convergent to the basic problem optimal solution are derived. It is pointed out that the direct approximation approach in the space of state and control combined with the finite-dimensional optimization methods such as the space covering and gradient-type methods makes probable the finding of the global optimum for OPC problems     

Optimal control problem via neural networks

This paper attempts to propose a new method based on capabilities of artificial neural networks, in function approximation, to attain the solution of optimal control problems. To do so, we try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. In the proposed error function, we used trial solutions for the trajectory function, control function and the Lagrange multipliers. These trial solutions are constructed by using neurons. Then, we minimize the error function that contains just the weights of the trial solutions. Substituting the optimal values of the weights in the trial solutions, we obtain the optimal trajectory function, optimal control function and the optimal Lagrange multipliers.     

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.     

Difference approximation of optimal periodic control problems

The constrained optimal periodic control problem is approximated by a sequence of discretized problems in which the system of differential equations of the basic continuous problem is replaced by a system of one–step difference equations. Two kinds of approximate optimal controls are derived from the optimal solutions of discretized problems: the first in the form of a step function and the second in the form of a special trigonometric polynomial generated by a positive kernel. Sufficient conditions for approximate solutions to be weakly convergent to the optimal solution of the basic problem are given. Certain improvements in the difference approximation considered are discussed and potential applications given.     

The singular control problem and approximate solutions

A method is presented which permits the solution of singular control problems by approximating the nonnormal system with a normal system. It is shown that the approximation can be made arbitrarily accurate. The optimal control of the approximate system is then determined and applied to the actual system. Bounds are obtained on the errors in boundary conditions and the degree of suboptimality brought about by the technique. The method is valid for minimum time and minimum fuel problems with linear constant plants. Examples are presented.     

Error analysis of solutions of second-order boundary value problems obtained with residual correction method

Based on the maximum principle of differential equations and with the aid of asymptotic iteration technique, this paper tries to establish monotonic relation of second-order obstacle boundary value problems with their approximate solutions to eventually obtain the upper and lower approximate solutions of the exact solution. To obtain numerical solutions, the cubic spline approximation method is applied to discretize equations, and then according to the ‘residual correction method’ proposed in this paper, residual correction values are added into discretized grid points to translate once complex inequalities’ constraint mathematical programming problems into simple equational iteration problems. The numerical results also show that such method has the characteristic of correcting residual values to symmetrical values for such problems, as a result, the mean approximate solutions obtained even with a considerably small quantity of grid points still quite approximate the exact solution. Furthermore, the error range of approximate solutions can be identified very easily by using the obtained upper and lower approximate solutions, even if the exact solution is unknown.     

A framework for evolutionary optimization with approximate fitnessfunctions

It is not unusual that an approximate model is needed for fitness evaluation in evolutionary computation. In this case, the convergence properties of the evolutionary algorithm are unclear due to the approximation error of the model. In this paper, extensive empirical studies are carried out to investigate the convergence properties of an evolution strategy using an approximate fitness function on two benchmark problems. It is found that incorrect convergence will occur if the approximate model has false optima. To address this problem, individual- and generation-based evolution control are introduced and the resulting effects on the convergence properties are presented. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization, which is able to guarantee the correct convergence of the evolutionary algorithm, as well as to reduce the computation cost as much as possible. Control of the evolution and updating of the approximate models are based on the estimated fidelity of the approximate model. Numerical results are presented for three test problems and for an aerodynamic design example     

面向LonWorks网络的OPC Server设计与实现

OPC是工业控制领域中应用程序互操作规范。针对自主研制的LonWorks网络，实现了其OPC server，使得OPC client软件能方便地从本地或远程访问这种网络。在讨论了应用程序的实时数据库、图形用户接口、OPC对象、I/O读写等实现原理的基础上，研究了该OPC server的写命令处理和多线程同步等关键技术。     

Optimal worst case estimation for LPV–FIR models with bounded errors

This work presents an approximate solution method for the infinite-time nonlinear quadratic optimal control problem. The method is applicable to a large class of nonlinear systems and involves solving a Riccati equation and a series of algebraic equations. The conditions for uniqueness and stability of the resulting feedback policy are established. It is shown that the proposed approximation method is useful in determining the region in which the constrained and unconstrained optimal control problems are identical. A reactor control problem is used to illustrate the method.     

Optimal controls of multidimensional modified Swift–Hohenberg equation

In this paper, we deal with the optimal control problem governed by multidimensional modified Swift–Hohenberg equation. After showing the relationship between the control problem and its approximation, we derive the optimality conditions for an optimal control of our original problem by using one of the approximate problems.     

基于OPC和Profibus-DP总线的远程控制

针对远程控制系统难以实现和控制效果不理想的问题,提出了一种基于OPC(OLEfor Process Control)和Profibus-DP总线的远程控制实现方法。建立了以太网和Profibus-DP现场总线两层网络的双水箱液位控制装置实验平台,给出了基于OPC和Profibus-DP总线的远程控制系统框图和控制原理。系统通过Profibus-DP总线实现现场设备的数据实时采集,并传递给SI-MATIC NETOPC服务器,客户端MCGS获取OPC服务器的实时数据,利用Matlab实现BP神经网络优化PID控制参数,优化后的参数通过SIMATIC NET OPC服务器传递给Profibus-DP总线控制系统,实现远程控制。实验结果表明,提出的远程控制方法有效,具有较好的控制效果。     

Optimal scanning measurement problem for a stochastic distributed-parameter system

This paper deals with the problem of determining the optimal measurement scheduling for a stochastic distributed-parameter system (DPS) based on spatially continuous and discrete-scanning observations. These two types of measurement are realized by the optimal motion of spatially-movable sensors and the optimal selection of measurement data from spatially-fixed sensors, respectively. For the continuous scanning case, the existence of optimal solutions for the problem is proved and the N-modal approximation problem is established. For the discrete case, however, it is impossible to derive the existence conditions. Therefore, it is shown that there exist optimal relaxed solutions by introducing the relaxed control theory. A practical method for constructing an approximate solution for the relaxed problem is proposed. Necessary conditions for approximate-optimality are represented in the form of a matrix minimum principle, and a feasible algorithm is developed to determine the approximate solution. A numerical example is considered and the present two types of optimal measurement trajectory are compared.     

Analysis of the machine repair problem: a diffusion process approach

An approximate method based on the diffusion equation is presented for analyzing a non-Markovian machine repair problem. The basic argument used in this approximation is that in the repair stage, the number of failed machines at time t, N(t), is almost always non-empty under heavy-traffic conditions. When time t becomes large, [N(t), t #62; 0] will tend to become a normally distributed random process with appropriate means and variances. With the assumption of normality the estimation of the diffusion parameters becomes tractable, and the method can be used to solve machine repair problems.The objective of this study is to obtain the formulas for the steady state utilization factor of the system repair stage based on the diffusion approximation methodology. For selected systems, the approximate values of the utilization factor of the repair stage are compared with the true values obtained through simulation to show the accuracy of this approximation.     

General SISO Takagi-Sugeno fuzzy systems with linear ruleconsequent are universal approximators

Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, “Are TS fuzzy systems with linear rule consequent universal approximators?” If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided     

A streamlined approximation and duality scheme for structural optimization

An efficient and commonly used approach to structural optimization is to solve a sequence of approximate design problems that are constructed iteratively. As is well-known, a major part of the computational burden of this scheme lies in the sensitivity analysis needed to state the approximate problems. We propose a possibility for reducing this burden by streamlining the calculations in a combined approximation and duality scheme for structural optimization. The difference between this scheme and the traditional one is that, instead of calculating all the constraint gradients to state an approximate design problem explicitly, linear combinations of these gradients are generated as they are needed during the solution of the approximate problem by the dual method. We show, by analysing some typical scenarios of problem characteristics, that this rearrangement of the calculations may be a computationally viable alternative to the traditional scheme. An advantage of streamlining the calculations is that there is no need to incorporate an active set strategy in the scheme, as is usually done, since all the design constraints may be taken into consideration without any loss of computational efficiency. This may, clearly, enhance the practical rate of convergence of the overall approximation scheme. Moreover, the proposed rearrangement of the calculations may make it computationally viable to apply iterative equation solvers to the structural analysis problem. Numerical results with direct as well as iterative equation solvers show that the streamlined scheme is a feasible and promising approach to structural optimization.     

Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation

In this paper we study the convergence of the Galerkin approximation method applied to the generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman equation. We state sufficient conditions that guarantee that the Galerkin approximation converges to the solution of the GHJB equation and that the resulting approximate control is stabilizing on the same region as the initial control. The method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the LQR design method.     

Error bound on the solution of a linear differential equation in Chebyshev series

A bound is derived for the norm of the difference between the solution of a linear differential equation with known input, and an approximate solution obtained by expansion in a Chebyshev series. The approach is to derive a bound on the difference between two approximate solutions of different order. This bound is obtained in terms of the order of the approximation of lowest degree, the difference in the orders of approximation, and certain matrix norms. Extending this expression so that it is valid for arbitrarily large differences in order yields a norm bound on the difference between the approximate solution and the exact solution. The basic approach can be extended to other orthogonal function sets.     

.Net平台的OPC DA客户端开发

针对基于COM的OPC服务器信息的复杂性和不透明性,调用OPC基金会发布的程序集,快速实现了.Net平台的客户端程序。通过对平台互操作原理、COM组件对象与.Net类对象差异的比较,解析了程序集中对服务器接口数据进行重新封送、重组的必要性,并结合OPC规范,程序集结构逐步实现了对数据服务器的访问。试验结果表明,基于程序集的客户端开发对系统集成及信息共享起到了极大的作用。     

A new solution to optimization-satisfaction problems by a penalty method

This paper is concerned with an optimization-satisfaction problem to determine an optimal solution such that a certain objective function is minimized, subject to satisfaction conditions against uncertainties of any disturbances or opponents' decisions. Such satisfaction conditions require that plural performance criteria are always less than specified values against any disturbances or opponents' decisions. Therefore, this problem is formulated as a minimization problem with the constraints which include max operations with respect to the disturbances or the opponents' decision variables. A new computational method is proposed in which a series of approximate problems transformed by applying a penalty function method to the max operations within the satisfaction conditions are solved by usual nonlinear programming. It is proved that a sequence of approximated solutions converges to a true optimal solution. The proposed algorithm may be useful for systems design under unknown parameters, process control under uncertainties, general approximation theory, and strategic weapons allocation problems.     

OPC技术在分布异构环境下的数据通信

随着计算机和网络等技术的发展,自动化领域发生着深刻的变化,在分布式异构环境下的数据通信已经成为研究的一个热点。文中详细分析了OPC(OLE for process control)技术的原理,对OPC的核心技术COM/DCOM作了深入的阐述。论述了OPC的体系结构,并以高速公路监控系统为例,说明了OPC技术在分布异构环境下数据通信的实现。