Optimal decentralized control of dynamic systems

In this paper, several aspects of decentralized control theory applied to dynamic systems are studied. First of all, some classical definitions about matricial functions and new results on gradient calculations are presented. In the following we generalize to matricial problems the method of gradient projection of Rosen. Finally, some aspects of stability, initialization and initial condition independence are studied in detail, and two numerical examples are considered in order to emphasize the advantages of the given procedure: the decentralized Kalman filter and the optimal power-frequency control.     

Optimal control of dynamic systems with hysteresis

We formulate a model of hysteresis of Madelung type, and we study an optimal control problem associated with dynamical systems that include this type of hysteresis. We obtain and analyse a variant of dynamic programming equations for the solution of this optimal control problem.     

Optimal sensor selection for discrete-event systems with partial observation

For discrete-event systems under partial observation, we study the problem of selection of an optimal set of sensors that can provide sufficient yet minimal events observation information. The sufficiency of the observed information is captured as the fulfillment of a desired formal property. Selection of sensors can be viewed as a selection of an observation mask and also of an equivalence class of events. A sensor set is called optimal if any coarser selection of the corresponding equivalence class of events results in some significant loss of the events observation information. We study an optimal selection of sensors over the set of general "nonprojection" observation masks. We show that this problem is NP hard in general. For mask-monotonic properties, we present a "top-down" and a "bottom-up" algorithm each of polynomial complexity. We show that observerness is not mask-monotonic. We show that the computational complexity can be further improved if the property is preserved under the projection via an intermediary observation mask that is an observer. Our results are obtained in a general setting so that they can be adapted for an optimal selection of sensors for a variety of applications.     

Optimal pulse observation of one type of systems with delay

Consideration is given to a linear problem of optimal pulse observation of a non-stationary dynamic system with delay in an equation of its mathematical model. To compute estimates of an unknown vector parameter of the initial state of the system, fast direct and dual methods are proposed. The main role belongs to quasi-reduction of the fundamental matrix of solutions to systems with delay. As is shown, to perform iterations of the method, integration of auxiliary systems of ordinary differential equations on small time intervals is sufficient. An algorithm of the operation of an optimal estimator—device for computing estimates of current states—is described. The results are illustrated by the problem of optimal observation of the fourth-order system with delay.     

Optimal control of linear systems with time-delay and observation noise

The problem of controlling a linear system to minimize a quadratic cost criterion is investigated when the system output is a delayed linear combination of system states corrupted by additive observation noise. It is shown that the optimal control is generated by the cascade combination of a Kalman filter and a least mean-squared predictor. Expressions are derived for the minimum cost and for the state variances.     

基于动态补偿的线性系统最优干扰抑制

本文针对受外部干扰的线性时不变系统研究了基于动态补偿的最优干扰抑制问题,其中干扰信号为已知动态特性的扰动信号.首先,将原系统与扰动系统联立构成增广系统,进而转化为无扰动的标准线性二次最优问题.其次,给出了经具有适当动态阶的补偿器补偿后的闭环系统渐近稳定并且相关的Lyapunov方程正定对称解存在的条件,进一步给定的二次性能指标可写成一个与该解和闭环系统初值相关的表达式.为了得到系统的最优解,将该Lyapunov方程转化为一个双线性矩阵不等式形式,并给出了相应的路径跟踪算法以求得性能指标最小值以及补偿器参数.最后,通过数值算例说明应用本文方法可以不仅能够最小化线性二次指标,而且能够使得系统的干扰得到抑制.     

Optimal pulse control of dynamic systems in the shock phase

For minimization and maximization of the kinetic energy of a body hitting a fixed visco-elastic obstacle with the energy calculated at the instant of body detachment from the obstacle, the optimal control laws in the impact phase were obtained.     

Optimal observation strategies for model-based fault detection in distributed systems

In model oriented diagnostics of real-world systems, the problems of structural identification and parameter estimation are of crucial importance. They require a properly designed schedule of measurements in such a way as to obtain possibly the most informative observational data. The aim of this work is to develop a novel approach to fault detection in distributed systems based on the maximization of the power of parametric hypothesis test, which verifies the nominal state of the considered system. The optimal locations of sensors are determined using the performance index operating on the Fisher Information Matrix. A general scheme is then proposed and tested on a computer example regarding an advection-diffusion problem.     

Optimal filtering for linear systems with state and observation delays

In this paper, the optimal filtering problem for linear systems with state and observation delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate, error variance, and various error covariances. As a result, the optimal estimate equation similar to the traditional Kalman–Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman–Bucy filter. The resulting system of equations for determining the filter gain matrix consists, in the general case, of an infinite set of equations. It is however demonstrated that a finite set of the filtering equations, whose number is specified by the ratio between the current filtering horizon and the delay values, can be obtained in the particular case of equal or commensurable (τ=qh, q is natural) delays in the observation and state equations. In the example, performance of the designed optimal filter for linear systems with state and observation delays is verified against the best Kalman–Bucy filter available for linear systems without delays and two versions of the extended Kalman–Bucy filter for time delay systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal smoothing of non-linear dynamic systems via Monte Carlo Markov chains

We consider the smoothing problem of estimating a sequence of state vectors given a nonlinear state space model with additive white Gaussian noise, and measurements of the system output. The system output may also be nonlinearly related to the system state. Often, obtaining the minimum variance state estimates conditioned on output data is not analytically intractable. To tackle this difficulty, a Markov chain Monte Carlo technique is presented. The proposal density for this method efficiently draws samples from the Laplace approximation of the posterior distribution of the state sequence given the measurement sequence. This proposal density is combined with the Metropolis-Hastings algorithm to generate realizations of the state sequence that converges to the proper posterior distribution. The minimum variance estimate and confidence intervals are approximated using these realizations. Simulations of a fed-batch bioreactor model are used to demonstrate that the proposed method can obtain significantly better estimates than the iterated Kalman-Bucy smoother.     

Optimal filtering for linear systems with state and multiple observation delays

This article solves the optimal filtering problem for linear systems with state and multiple observation delays. The optimal estimate equation similar to the traditional Kalman–Bucy one is derived, and the system of equations for determining the filter gain matrix consists of an infinite set of equations. It is then demonstrated that a finite set of the filtering equations can be obtained in case of commensurable delays. In the example, the designed optimal filter is compared to the traditional Kalman–Bucy filter.     

Optimal linear estimation for continuous stochastic systems with random observation delays

This paper is concerned with the linear minimum mean square error estimation for Itô‐type differential equation systems with random delays, where the delay process is modeled as a finite‐state Markov chain. By first introducing a set of equivalent delay‐free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay‐free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady‐state optimal estimator are studied for time‐invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time‐invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

控制系统中实时任务的动态优化调度算法

提出一种新的调度算法——带有非周期服务器的EDF调度算法.分析了所有任务的可调度性,给出了可调度条件,并给出一种新的周期性任务模型以及主优先级和辅助优先级的概念.它们在保证任务可调度的前提下,对周期性任务的采样频率和控制延时进行优化.仿真结果表明,该算法可以提高周期性任务的采样频率,并降低控制延时,即能优化系统的性能.     

Optimal control of stochastic dynamic systems with past history and poison switchings

An optimal control problem for systems of stochastic differential-functional linear equations with past history and Poisson switchings is formulated. The Bellman equation is solved for this problem.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 112–118, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

动态区间系统的最优保性能控制--LMI方法

针对动态区间系统和一个给定的二次型性能指标,研究了其保性能控制问题,基于线性矩阵不等式(LMI)提出了最优保性能控制器设计方法,并将相关结果推广到参数不确定系统.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于设计动态区间系统与秩-1型参数不确定系统的最优保性能控制器,非常有效.     

一类非线性动态系统基于强化学习的最优控制制

提出一类非线性不确定动态系统基于强化学习的最优控制方法. 该方法利用欧拉强化学习算法估计对象的未知非线性函数, 给出了强化学习中回报函数和策略函数迭代的在线学习规则. 通过采用向前欧拉差分迭代公式对学习过程中的时序误差进行离散化, 实现了对值函数的估计和控制策略的改进. 基于值函数的梯度值和时序误差指标值, 给出了该算法的步骤和误差估计定理. 小车爬山问题的仿真结果表明了所提出方法的有效性.

     

Optimal assignment of dynamic priorities in queuing systems with two types of customers

We consider queuing systems with two types of customers. For such systems, we develop numerical procedures for computation of optimal dynamic priorities in the case of multiplicative priority functions. The optimality criterion is based on the total queue length for customers of both types. Our technique allows one to take into account waiting-time bounds. The optimization problem is formulated in the language of linear-fractional programming. To illustrate our technique, we present some numerical results at the end of the paper.     

Optimal design of controlled multibody dynamic systems for performance,robustness and tolerancing

The multidisciplinary design approach has gained increasing popularity in recent years due to its ability to deal with conflicting design requirements imposed by discipline-specific objectives. The traditional design process involving multiple disciplines is typically a sequential process where the design objectives are met one at a time in a sequence of designs. However, in doing so, unnecessary limitations are imposed on the design parameters and the final design is far from being optimal. The effectiveness of integrated design methodology has been proven and such designs are being obtained in many applications. However, most of the work in this area has been problem and/or system specific and does not address important manufacturing considerations, such as tolerance allocation, robustness with respect to machining tolerances, etc. The results presented in this paper are intended to contribution towards filling these gaps. In particular, the new approach will help designers avoid a common known pitfall of performance optimization, i.e. the fact that designs that are optimized for performance alone are notoriously sensitive to deviations from the nominal design. Thus, optimizing for performance alone leads to designs that fall below acceptable standards of robustness; they are also expensive to manufacture because the tolerances must be kept very tight to ensure acceptable performance. The approach presented here will allow the user to systematically tradeoff performance versus robustness and tolerancing concerns. A proof-of-concept example that was solved to evaluate this methodology is also presented in this paper. This example provides a convincing demonstration of the fact that small sacrifices in performance can yield huge benefits in the other areas, provided a methodology is available for making these tradeoffs in a systematic way. This especially can be used by designers in various fields such as automotive, aerospace, deployable structures, machine tools (including hexapods), robotic systems, precision machinery, etc.     

Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming

An intelligent-optimal control scheme for unknown nonaffine nonlinear discrete-time systems with discount factor in the cost function is developed in this paper. The iterative adaptive dynamic programming algorithm is introduced to solve the optimal control problem with convergence analysis. Then, the implementation of the iterative algorithm via globalized dual heuristic programming technique is presented by using three neural networks, which will approximate at each iteration the cost function, the control law, and the unknown nonlinear system, respectively. In addition, two simulation examples are provided to verify the effectiveness of the developed optimal control approach.     

Optimal control of processing times in single-stage discrete event dynamic systems with blocking

This note concerns an optimal control problem in single-stage discrete event dynamic systems with finite buffers and blocking. The system is modeled as a deterministic queue, slated to process a finite sequence of jobs. Each job is characterized by its arrival time, service time, and due date, and has associated with it a cost function that penalizes short service times, buffer times, and lateness of completion times with respect to the due date. The sequencing (order) of the jobs at the server is given, and the variable parameter consists of the jobs' service times. Even though the cost function associated with each job is assumed to be convex, the aggregated cost functional is not convex. Therefore, much of the analysis focuses on a decomposition of the problem into a finite sequence of reduced-order convex programming problems which can be solved one at a time. This approach has been investigated in the past, but the present note provides an analysis under the most general and realistic assumptions considered to date.