On the Optimal Control Problem of a Nonlinear Elliptic Population System

The optimal control problem for a nonlinear elliptic population system is considered. First, under certain hypotheses, the existence and uniqueness of coexistence state solutions are shown. Then the existence of the optimal control is given and the optimality system is established.     

Wavelet based approximations in the optimal control of parabolic problems

We consider optimal control of a bilinear parabolic equation. The determination of such control requires to minimize a given energy performance measure. The performance measure of the system is taken as a combination of its modified total energy and the penalty term describing the approach used in the control process. Using an appropriate transformation modal expansion, the optimal control of a distributed parameter system (DPS) is simplified into the optimal control of a bilinear time-varying lumped parameter system (LPS). A computational efficient formulation to evaluate the optimal trajectory and control of the system is determined. It is based on the parametrization of the state and control variables by using finite wavelets. Numerical examples are provided to demonstrate the applicability and the efficiency of the proposed method and the results are quite satisfactory.     

Stability in Probability and Inverse Optimal Control of Evolution Systems Driven by Lévy Processes

This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson processes.This theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy processes.The inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and control.The approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.     

The stochastic sliding mode variable structure guidance laws based on optimal control theory

A stochastic sliding-mode variable structure guidance law involving optimal control theory is presented for the missile target intercept model, in which state noise, uncertain system parameters, target movement and measured noise are considered. This guidance law synthesizes the merits of optimal guidance law with line-of-sight rate convergence and sliding-mode guidance law with strong robustness. Through theoretic analysis, it is proved that the sliding mode hyperplane is sub-achievable in the closed loop system. The numerical results show the effectiveness of the proposed control algorithm.     

参数不确定离散广义大系统的保性能控制

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper. The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities (LMIs), and a desired state feedback controller is obtained via convex optimization. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

An adaptive control with optimal disturbances rejection

This paper provides a way to optimize the overall disturbances rejection performance of the adaptive control system in the presence of unknown external disturbances.Especially,the updatable non-empty admissible model set,which is consistent to the a priori knowledge of the plant parameter and the online measurements,is computed.With the overall system performance as the criteria,the nominal model is optimally chosen within the admissible model set.The optimal nominal model is subsequently used to synthesize the optimal closed-loop controller based on the 1 design methodology.Combining the above two aspects,an optimal adaptive control scheme is proposed.Because of the consistency of the identification criteria and control object,the adaptive control scheme proposed in this paper can achieve the overall optimal disturbances rejection performance,and the effect of the interplay between the identification and control of the adaptive system can be handled effectively.In addition,the computable optimal performance is also provided.     

广义快子系统的H∞最优模型降阶

In this paper, H∞ optimal model reduction for singular fast subsystems will be investigated. First, error system is established to measure the error magnitude between the original and reduced systems, and it is demonstrated that the new feature for model reduction of singular systems is to make H_ norm of the error system finite and minimal. The necessary and sufficient condition is derived for the existence of the H∞ suboptimal model reduction problem. Next, we give an exact and practicable algorithm to get the parameters of the reduced subsystems by applying the matrix theory. Meanwhile, the reduced system may be also impulsive. The advantages of the proposed algorithm are that it is more flexible in a straight-forward way without much extra computation, and the order of the reduced systems is as minimal as possible. Finally, one illustrative example is given to illustrate the effectiveness of the proposed model reduction approach.     

Scheduling and control of failure prone systems with demand uncertainty and job overlaps

Given that the overlapping of jobs is permitted, the paper studies the scheduling and control of failure prone production systems,i, e.so-called settings with demand uncertainty and job overlaps. Because a variable demand resource is revolved in the production and corrective maintenance control problems of the system, which switched randomly between zero and a maximum level, it is difficult to obtain the analytical solutions of the optimal single hedging point policy. An asymptotic optimal scheduling policy is presented and a double hedging point policy is offered to control simultaneously the production rate and the corrective maintenance rate of the system. The corresponding analytical solutions and approximate solutions are obtained. Considering the relationship of production, corrective maintenance and demand variable, an approximate optimal single hedging point control policy is proposed. Numerical results are presented.     

Parametric Transformation of Timed Weighted Marked Graphs: Applications in Optimal Resource Allocation

Timed weighted marked graphs are a subclass of timed Petri nets that have wide applications in the control and performance analysis of flexible manufacturing systems.Due to the existence of multiplicities(i.e.,weights)on edges,the performance analysis and resource optimization of such graphs represent a challenging problem.In this paper,we develop an approach to transform a timed weighted marked graph whose initial marking is not given,into an equivalent parametric timed marked graph where the edges have unitary weights.In order to explore an optimal resource allocation policy for a system,an analytical method is developed for the resource optimization of timed weighted marked graphs by studying an equivalent net.Finally,we apply the proposed method to a flexible manufacturing system and compare the results with a previous heuristic approach.Simulation analysis shows that the developed approach is superior to the heuristic approach.     

Adaptive dynamic programming for finite-horizon optimal control of linear time-varying discrete-time systems

This paper studies data-driven learning-based methods for the finite-horizon optimal control of linear time-varying discrete-time systems. First, a novel finite-horizon Policy Iteration (PI) method for linear time-varying discrete-time systems is presented. Its connections with existing infinite-horizon PI methods are discussed. Then, both data-driven off-policy PI and Value Iteration (VI) algorithms are derived to find approximate optimal controllers when the system dynamics is completely unknown. Under mild conditions, the proposed data-driven off-policy algorithms converge to the optimal solution. Finally, the effectiveness and feasibility of the developed methods are validated by a practical example of spacecraft attitude control.     

Existence of Solution for Generalized Coupled Differential Riccati Equation

By means of the recursive method, the existence of solution is obtained for the generalized coupled differential Riccati equation. As an application, we apply the existence results to consider the optimal control of Markovian jump linear singular system, and obtain the desired explicit representation of the optimal controller for the optimal control problem with the finite horizon.     

Preview control for a class of linear stochastic systems with multiplicative noise

ABSTRACT

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective.     

An optimal control model for a system of degenerate parabolic integro-differential equations

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 90–102, November–December 2007.     

A note on the existence and optimal control for mixed Volterra–Fredholm-type integrodifferential dispersion system of third order

The optimal control problem consists of a performance index subject to a set of differential equations that describes the path of the control and state variables. The main aim of this article is to prove the existence and uniqueness of a mild solution, optimal control, and time-optimal control of a mixed Volterra–Fredholm-type third-order dispersion system. By applying the strongly continuous semigroup theory and the Banach fixed-point theorem, we prove the existence and uniqueness of the considered system. The optimal control results are proved by using Mazur's lemma, Gronwall's inequality, and the minimizing sequence technique. The discussion on the time-optimal control of the third-order dispersion system is also presented.     

输入冗余在时间最优控制中的作用

随着冗余控制系统的不断出现, 本文主要研究了在可控线性系统中增加新的冗余控制通道所带来的优势. 对于时间最优控制问题, 这样的优势可以通过最优时间的缩短进行衡量. 本文证明了在最优控制存在且唯一的基础上, 如果增加的冗余控制通道中存在非空闲通道, 则对于任意的非零初始状态, 增加冗余控制通道后系统的最优时间将严格降低. 更进一步, 如果时间最优控制问题是正常的, 则最优时间也将严格下降. 另一方面, 如果忽略问题的正常性这个条件, 只要冗余控制通道中存在一个完全可控的通道, 最优时间同样也会严格下降. 最后, 我们通过两个数值例子印证了本文的理论结果.     

Optimal Strategies for a Semi-Markovian Inventory System

Control for a semi-Markovian inventory system is considered. Under general assumptions on system functioning, conditions for existence of an optimal nonrandomized Markovian strategy are found. It is shown that under some additional assumptions on storing conditions for the inventory, the optimal strategy has a threshold (s, S)-frame.     

控制系统l~1优化设计最优解的存在性和次优解

本文初步研究了控制对象有z平面单位圆上零极点时l~2优化设计问题解的存在性,指出在此种情况下l~1优化问题的最优解不一定总是存在。提出了解存在性的判别定理。在最优解不存在时给出了次优解的求取方法。     

控制系统ɭ1优化设计最优解的存在性和次优解*

本文初步研究了控制对象有z平面单位圆上零极点时?1优化设计问题解的存在性，指出在此种情况下?1优化问题的最优解不一定总是存在。提出了解存在性的判别定理。在最优解不存在时给出了次优解的求取方法。