Simultaneous Optimal Controls for Non-Stationary Stokes Systems

This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented.     

一类由抛物-双曲耦合组支配的边界最优控制问题

本文讨论了一类由抛物-双曲耦合组支配的第三边值最优控制问题.证明了该问题最优控制的存在性及其bang-bang性质.     

A numerical method for an optimal control problem with minimum sensitivity on coefficient variation

In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method.     

The Optimal Control of a Train

We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.     

A class of optimal state-delay control problems

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem–called an optimal state-delay control problem–that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control.     

带停时的奇异型随机控制问题研究

利用随机分析的知识及最优控制理论,推广了一类带停时的随机控制问题,针对不同参数,证明了最佳控制的存在性,分两种情况给出了最佳控制的存在区域,并给出了不同初始状态下,最佳控制的结构和最佳费用函数.由于将原模型中费用结构中的R-S积分的被积函数由1推广为满足某些条件的一般函数,所以推广后的模型更具一般性.     

Solving the optimal control problem of the parabolic PDEs in exploitation of oil

In this paper, the optimal control problem is governed by weak coupled parabolic PDEs and involves pointwise state and control constraints. We use measure theory method for solving this problem. In order to use the weak solution of problem, first problem has been transformed into measure form. This problem is reduced to a linear programming problem. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures. We find piecewise-constant optimal control functions which are an approximate control for the original optimal control problem.     

Risk-sensitive control of continuous time Markov chains

We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.     

非线性最优控制的反馈逼近

本文将在线性最优控制中经典的Ｋｌｅｉｎｍａｎ－Ｎｅｗｔｏｎ［１］方法推广到非线性的最优控制问题。我们证明,由一个稳定反馈控制生成的反馈控制序列在原点附近会一致逼近最优控制,并指出这一研究在Ｈ∞－非线性最优控制中的作用。     

Periodic optimal control for parabolic Volterra-Lotka type equations

This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L^∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.     

Optimal production control problem taking into account environmental pollution

We consider a simplified production control model taking into account environmental pollution. We obtain constructive conditions under which each optimal control is Lebesgue equivalent to an optimal bang-bang control.     

Relaxation methods for mixed-integer optimal control of partial differential equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments.     

On the existence of optimal controls for nonlinear infinite dimensional systems

We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.     

TACO: a toolkit for AMPL control optimization

We describe a set of extensions to the AMPL modeling language to conveniently model mixed-integer optimal control problems for ODE or DAE dynamic processes. These extensions are realized as AMPL user functions and suffixes and do not require intrusive changes to the AMPL language standard or implementation itself. We describe and provide TACO, a Toolkit for AMPL Control Optimization that reads AMPL stub.nl files and detects the structure of the optimal control problem. This toolkit is designed to facilitate the coupling of existing optimal control software packages to AMPL. We discuss requirements, capabilities, and the current implementation. Using the example of the multiple shooting code for optimal control MUSCOD-II, a direct and simultaneous method for DAE-constrained optimal control, we demonstrate how the problem information provided by the TACO toolkit is interfaced to the solver. In addition, we show how the MS-MINTOC algorithm for mixed-integer optimal control can be used to efficiently solve mixed-integer optimal control problems modeled in AMPL. We use the AMPL extensions to model three control problem examples and we discuss how those extensions affect the representation of optimal control problems. Solutions to these problems are obtained by using MUSCOD-II and MS-MINTOC inside the AMPL environment. A collection of further AMPL control models is provided on the web site http://mintoc.de. MUSCOD-II and MS-MINTOC have been made available on the NEOS Server for Optimization, using the TACO toolkit to enable input of AMPL models.     

Parametric identification problem with a regularizer in the form of the total variation of the control

We consider a linear dynamical system, for which we need to reconstruct the control input on the basis of a noisy output. We form the corresponding family of parametric optimal control problems in which the performance criterion contains terms corresponding to the problem regularization and clearing the output signal from speckle noises. The weight coefficient multiplying the term used for noise filtration plays the role of a parameter in the family of problems. We prove a theorem that describes the properties of solutions of parametric problems in a neighborhood of a regular point, analyze the differential properties of solutions of that problem, and derive formulas for the computation of derivatives of the optimal trajectory and the optimal control with respect to a parameter. We suggest a simple method for constructing approximate solutions of perturbed optimal control problems. These results permit one to control the performance of the reconstruction of the control in the original identification problem. An illustrative example is considered.     

Dynamic Network Inventory Control Model with Interval Nonstationary Demand Uncertainty

We consider a dynamic inventory control system described by a network model with an interval assigned nonstationary demand. We assume that unknown demand may take any value within the interval, which bounds depend on time. In terms of Kaucher interval arithmetic, we derive necessary and sufficient conditions for the existence of a feasible feedback control and sufficient conditions for the existence of an optimal feedback control strategy. We obtain an optimal feasible storage level and estimate the rate of the system convergence to this level. Then we develop the algorithm of finding the optimal control strategy. These results are applied to an example.     

Computational Control of an HIV Model

We consider a computational approach to solving an optimal control formulation of optimal drug scheduling in HIV infected individuals. The optimal control problem is transformed using the control parameterisation enhancing technique (CPET), which enables efficient computation of an optimal control using a relatively coarse discretisation. A number of numerical difficulties with the model are discussed, and for illustration, numerical examples are solved.     

Optimal Control Problems for a Class of Semilinear Multisolution Elliptic Equations

We study the optimal control problem for a class of elliptic problems that may possess multiple solutions. We obtain necessary conditions for optimal control by constructing a related parabolic problem and using known results for the parabolic problem.     

Optimal control of random evolutions

We consider a stochastic control problem for a random evolution. We study the Bellman equation of the problem and we prove the existence of an optimal stochastic control which is Markovian. This problem enables us to approximate the general problem of the optimal control of solutions of stochastic differential equations.