Decentralized optimal control of a group of dynamical objects

The problem of optimal control of a group of coupled dynamical objects is considered. The cases are examined in which the centralized control of a group of objects is impossible. Fast real-time optimal control algorithms of each of the dynamical systems are described that use information exchanged between group members in the course of control. The proposed methods supplement the earlier developed real-time optimal control methods for an individual dynamical system. The results are illustrated using optimal control of two coupled mathematical pendulums as an example.     

分数阶抛物方程控制系统最优控制的稳定性

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.     

Feedback control for a class of pest management problems modeled by a noninteractively distributed system

A class of distributed-parameter optimal control problems whose system dynamics are more akin to those of systems of ordinary differential equations is presented together with a set of necessary conditions for optimality. It is shown that certain insect pest management problems fall within the ambit of this theory, which is then used to investigate the properties of the optimal pesticide application schedule and to synthesize a part-feedback control strategy. This latter strategy is presented in a way which makes it applicable to devising strategies for the application of pesticides in agricultural systems that are too complex to be easily modeled, but for which correlations are available between pest levels at certain points during the growing season and yield losses.     

一般目标信号和干扰信号下多采样率系统的最优预见控制器设计

针对目标信号和干扰信号为多项式的情形,研究了多采样率离散时间控制系统的最优预见控制问题.首先利用离散时间系统提升技术,把所研究的系统转化成单采样率的扩大系统.然后构造扩大误差系统,把问题转化为包含预见信号的最优调节问题.最后利用最优预见控制理论的结果得到系统的最优预见控制输入,其中包含积分器和预见前馈补偿.本文还对扩大误差系统的能控性和能观测性和相应的代数Riccati方程的可解性进行了讨论.     

Linear-quadratic optimal control under non-Markovian switching

We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an underlying independent marked point process, so that our model is general enough to include controlled switching systems where the switching mechanism is not required to be Markovian. The problem is solved by means of a Riccati equation, which turned out to be a backward stochastic differential equation driven by the Brownian motion and by the random measure associated with the marked point process.     

Sufficient Conditions for Robust Stability of LQG Optimal Control Systems Including Delayed Perturbations

Linear-quadratic Gaussian (LQG) optimal control systems subject to time-varying delay and nonlinear state perturbations are considered. Some robust stability conditions are derived which result in several bounds on the delayed state perturbations so that the uncertain linear-quadratic Gaussian optimal control systems with time-varying delay can remain stable in the sense of uniform ultimate boundedness. The modified Lyapunov equation and the improved Razumikhin-type theorem are employed to investigate such robust stability conditions. Finally, a numerical example is given to demonstrate the validity of the results.     

Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay

Nonlinear optimal control of dynamic systems with endogenous time delays is analyzed. Such systems have important applications and are described by Volterra integral equations with unknowns in the integration limits. The paper focuses on the structure and asymptotic behavior of solutions to several optimization problems with endogenous delay. It is shown that, in certain cases, a special delay trajectory exists and attracts the optimal solution. In economics, such behavior corresponds to the turnpike properties of the optimal lifetime of capital in vintage capital models. The authors thank Professor F. Chernousko for his kind assistance and Professor W. Trotti for a supporting grant from Prairie View A&M University.     

Controlled networks and their applications

A new kind of networks is considered in which the flow is controlled by reconfiguring the network. Flow control models in the network are considered, and optimal flow control problems in the network are stated.     

An optimal control approach to the design of periodic orbits for mechanical systems with impacts

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control. Specifically, we design an optimal control based strategy that combines trajectory optimization, dynamics embedding, optimal control relaxation and root finding techniques. The proposed strategy allows us to design, in a numerically stable manner, trajectories that optimize a desired cost and satisfy boundary state constraints consistent with a periodic orbit. To show the effectiveness of the proposed strategy, we perform numerical computations on a compass biped model with torso.     

Numerical methods for controls for nonlinear stochastic systems with delays and jumps: applications to admission control

We consider numerical methods of the Markov chain approximation type for computing optimal controls and value functions for systems governed by nonlinear stochastic delay equations. Earlier work did not allow Poisson random measure driving processes or delays that are concentrated on points with positive probability. In addition, the Poisson measures can be controlled. Previous proofs are not adequate for the present case. The algorithms are developed and convergence proved as the approximating parameters go to their limits. One motivating example concerns admissions control to a network, where the file arrival process is governed by a Poisson process, and arrivals might be admitted or not, according to the control, which leads to a controlled Poisson process. Numerical data for such an example are presented. The original problem is recast in terms of a transportation equation, which allows the development of practical algorithms. For the problems of interest, alternative methods can entail prohibitive memory and computational requirements.     

随机递归最优控制和混合最优控制问题

对随机递归最优控制问题即代价函数由特定倒向随机微分方程解来描述和递归混合最优控制问题即控制者还需 决定最优停止时刻, 得到了最优控制的存在性结果. 在一类等价概率测度集中,还给出了递归最优值函数的最小和最大数学期望.     

在常规故障和临界人为错误条件下具有易损坏存储部件并联可修系统稳态解中p_0的最优控制

讨论了两个部件并联和一个储备部件,并且具有临界认为错误和故障的可修系统稳态解中p_0的最优控制问题.     

An inverse optimal problem in discrete-time stochastic control

In this paper, we study an inverse optimal problem in discrete-time stochastic control. We give necessary and sufficient conditions for a solution to a system of stochastic difference equations to be the solution of a certain optimal control problem. Our results extend to the stochastic case the work of Dechert. In particular, we present a stochastic version of an important principle in welfare economics.     

Optimal Control of Non-stationary Differential Linear Repetitive Processes

Differential repetitive processes are a distinct class of continuous-discrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics.     

OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED PARAMETER DELAY SYSTEMS

In this paper we consider the optimal control problem for a class of infinite dimensional delay evolution systems whose principal operator is the infinitesimal generator of an analytic semigroup. We give an existence result of α - solutions of the controlled systems and prove the existence of solutions for an extremal problem subject to such systems. In particular, the necessary conditions of optimality for the same problem are presented.     

Optimal control in a macroeconomic problem

The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived.     

具有内部构造安全保障体系的冗余机器系统稳态解的最优控制

讨论了两不同部件并联的具有内部构造安全保障体系的冗余机器系统稳态解的最优控制.     

Extensions of the generalized moment theorem and applications to distributed-parameter control systems

In this paper, we present extensions to the generalized moment theorem and apply it to optimal control problems for a certain class of distributed-parameter systems. We also apply it to the time-optimal control problem and extend the results of Ref. 1 pertaining to the largest controllable set, so that we can discuss the problem of recoverability for some distributed-parameter systems.The author wishes to express his gratitude to Professor P. K. C. Wang for his guidance and suggestions.     

Numerical solution of the optimal boundary control of transverse vibrations of a beam

Boundary control is an effective means for suppressing excessive structural vibrations. By introducing a quadratic index of performance in terms of displacement and velocity, as well as the control force, and an adjoint problem, it is possible to determine the optimal control. This optimal control is expressed in terms of the adjoint variable by utilizing a maximum principle. With the optimal control applied, the determination of the corresponding displacement and velocity is reduced to solving a set of partial differential equations involving the state variable, as well as the adjoint variable, subject to boundary, initial, and terminal conditions. The set of equations may not be separable and analytical solutions may only be found in special cases. Furthermore, the computational effort to determine an analytic solution may also be excessive. Herein a numerical algorithm is presented, which easily solves the optimal boundary control problem in the space‐time domain. An example of a continuous system is analyzed. This is the case of the vibrating cantilever beam. Using a finite element recurrence scheme, numerical solutions are obtained, which compare the behavior of the controlled and uncontrolled systems. Also, the analytic solution to the problem is compared with the results obtained using the numerical scheme presented. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 558–568, 1999