共查询到20条相似文献，搜索用时 31 毫秒
1.
N. García-Chan L.J. Alvarez-Vázquez A. Martínez M.E. Vázquez-Méndez 《Journal of The Franklin Institute》2014
Within the framework of numerical modelling and multi-objective control of partial differential equations, in this work we deal with the problem of determining the optimal location of a new industrial plant. We take into account both economic and ecological objectives, and we look not only for the optimal location of the plant but also for the optimal management of its emissions rate. In order to do this, we introduce a mathematical model (a system of nonlinear parabolic partial differential equations) for the numerical simulation of air pollution. Based on this model, we formulate the problem in the field of multi-objective optimal control from a cooperative viewpoint, recalling the standard concept of Pareto-optimal solution, and pointing out the usefulness of Pareto-optimal frontier in the decision making process. Finally, a numerical algorithm – based on a characteristics/Galerkin discretization of the adjoint model – is proposed, and some numerical results for a hypothetical situation in the region of Galicia (NW Spain) are presented. 相似文献
2.
《Journal of The Franklin Institute》2022,359(5):1925-1970
The theory of optimal control plays an important role to solve several real-life problems. However, it is often seen that uncertainty is a major challenge in formulating the appropriate model corresponding to real world problems. To overcome this challenge, in this work, the theory of optimal control is developed in interval environment. Accordingly, the necessary and sufficient optimality conditions for the existence of maximizer of interval valued optimal control problem (IVOCP) are proposed. To validate the proposed theory, an imperfect production inventory model is developed in both crisp and interval environments in which customers’ demand is dependent on the selling price, specific absorption rate (SAR) of products and continuous time. In the proposed model, the production rate is considered as a function of time. In addition, manufacturer invests to reduce the carbon emission and to increase the environmental sustainability of the produced items. As the production rate is taken as a function of time, optimal control theory is used to study the optimal policy of the corresponding problem. To solve the optimal control problem for the proposed model in interval environment, sufficient optimality conditions of IVOCP are used. Thereafter, two numerical examples are considered and solved with the help of different meta-heuristic algorithms. Finally, to observe the impact of various system parameters to the optimal policy of the system, sensitivity analyses are carried out for the example in interval environment and impacts are shown graphically. 相似文献
3.
《Journal of The Franklin Institute》2002,339(4-5):479-498
In this paper, a numerical method to solve nonlinear optimal control problems with terminal state constraints, control inequality constraints and simple bounds on the state variables, is presented. The method converts the optimal control problem into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem with a sequence of constrained linear-quadratic optimal control problems, then each of the state variables is approximated by a finite length Chebyshev series with unknown parameters. The method gives the information of the quadratic programming problem explicitly (The Hessian, the gradient of the cost function and the Jacobian of the constraints). To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented. 相似文献
4.
In this work, a sampled-data control problem for neural-network-based systems with an optimal guaranteed cost is investigated. By constructing suitable time-dependent functionals and utilizing an improved free-matrix-based integral inequality, a sampled-data stability criterion for neural-network-based systems is derived. Based on a first result, a sampled-data controller design method for neural-network-based systems that meets the maximum sampling period and minimum guaranteed cost performance is proposed. The superiority and validity of the results will be verified by comparing with the existing results in a numerical example. 相似文献
5.
《Journal of The Franklin Institute》2022,359(8):3444-3465
This contribution is concerned with the application of optimal control theories and methods to an ecosystem. There are four major ingredients. The first ingredient is to present an optimal control problem for an ecosystem including infection and competition. The second ingredient is the existence results, which assert that in a given Hilbert space the controlled system admits a unique strong solution and the optimal control problem has at least one optimal pair. The third, which is the main new ingredient of this paper, is a maximum principle for the optimal control problem. The first-order necessary optimality condition for the optimal control is established by employing dual techniques. It provides a theoretical basis for the design of the optimal control strategy. The fourth ingredient is an example and its numerical simulation, which further confirm the results of this paper. 相似文献
6.
In this paper, we first develop an adaptive shifted Legendre–Gauss (ShLG) pseudospectral method for solving constrained linear time-delay optimal control problems. The delays in the problems are on the state and/or on the control input. By dividing the domain of the problem into a uniform mesh based on the delay terms, the constrained linear time-delay optimal control problem is reduced to a quadratic programming problem. Next, we extend the application of the adaptive ShLG pseudospectral method to nonlinear problems through quasilinearization. Using this scheme, the constrained nonlinear time-delay optimal control problem is replaced with a sequence of constrained linear-quadratic sub-problems whose solutions converge to the solution of the original nonlinear problem. The method is called the iterative-adaptive ShLG pseudospectral method. One of the most important advantages of the proposed method lies in the case with which nonsmooth optimal controls can be computed when inequality constraints and terminal constraints on the state vector are imposed. Moreover, a comparison is made with optimal solutions obtained analytically and/or other numerical methods in the literature to demonstrate the applicability and accuracy of the proposed methods. 相似文献
7.
This paper introduces an efficient direct approach for solving delay fractional optimal control problems. The concepts of the fractional integral and the fractional derivative are considered in the Riemann–Liouville sense and the Caputo sense, respectively. The suggested framework is based on a hybrid of block-pulse functions and orthonormal Taylor polynomials. The convergence of the proposed hybrid functions with respect to the L2-norm is demonstrated. The operational matrix of fractional integration associated with the hybrid functions is constructed by using the Laplace transform method. The problem under consideration is transformed into a mathematical programming one. The method of Lagrange multipliers is then implemented for solving the resulting optimization problem. The performance and computational efficiency of the developed numerical scheme are assessed through various types of delay fractional optimal control problems. Our numerical findings are compared with either exact solutions or the existing results in the literature. 相似文献
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9.
Kai Liu 《Journal of The Franklin Institute》2018,355(12):4839-4853
In this work, we consider an optimal control problem of a class of stochastic differential equations driven by additive noise with aftereffect appearing in control. We develop a semigroup theory of the driving deterministic neutral system and identify explicitly the adjoint operator of the corresponding infinitesimal generator. We formulate the time delay equation under consideration into an infinite dimensional stochastic control system without time lag by means of the adjoint theory established. Consequently, we can deal with the associated optimal control problem through the study of a Hamilton–Jacob–Bellman (HJB) equation. Last, we present an example whose optimal control can be explicitly determined to illustrate our theory. 相似文献
10.
利用变分法导出量子力学系统中一类最优控制问题的方程组，并使用具有最优搜索步长的开关变尺度法对最优控制问题进行数值迭代求解，最后在自旋1/2粒子上进行了系统仿真实验，验证了本文方法的有效性，同时对性能指标中参数的不同选择对整个最优控制效果影响的一般规律进行了分析。 相似文献
11.
The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control problem is investigated. A numerical solution method is developed to seek the optimal control strategy by the smoothing approximation method and the gradient of the cost functional together with that of the constraints. Numerical results show that the mass of target product per unit time at the terminal time is increased considerably. 相似文献
12.
Xing Tao Wang 《Journal of The Franklin Institute》2007,344(7):941-953
By applying hybrid functions of general block-pulse functions and Legendre polynomials, the linear-quadratic problem of linear time-varying systems with delays are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples illustrate that the algorithms are valid. 相似文献
13.
Said Abboudi 《Journal of The Franklin Institute》2011,348(7):1192-1207
A simultaneous estimation of two convective boundary conditions problem of a two-dimensional rectangular fin is proposed by numerical approach. The aim is to estimate the evolution of the distributions of the unknown heat transfer coefficients from the transient temperature histories taken with several sensors inside a two-dimensional fin. The estimation algorithm of this inverse heat conduction problem is based on the iterative regularization method and on the conjugate gradient method. An optimal choice of the vector of the descent parameters is used in this study and shows an increase in the convergence rate. The effects of some parameters (sensor number, position, measurement errors) on the inverse solutions are discussed. 相似文献
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I.S. Sadek 《Journal of The Franklin Institute》2011,348(7):1656-1667
The present paper deals with an optimal boundary control problem in which the process of systems under consideration is governed by a linear parabolic partial differential equation over an infinite time interval. The objective of the paper is to determine the optimal boundary control that minimize a given energy-based performance measure. The performance measure is specified as a quadratic functional of displacement and a suitable penalty term involving the boundary controls. In order to determine the optimal boundary controls, the problem with boundary controls are converted into a problem with distributed controls. The modal space technique is then used to reduce the system into the optimal control of time invariant lumped parameter system. The associated system of uncoupled first order initial value problems is solved in terms of controllers. Next step deals with the computation of the control and trajectory of the linear time-invariant lumped parameter. For this we approximate the controllers by a finite number of orthogonal exponential zero-interpolants over the interval [0,∞). The resultant performance index after using the optimality condition leads to a system of linear algebraic equations. The suggested technique is easy to implement on digital computer. We provide a numerical example to demonstrate the applicability and efficiency of the proposed approach. 相似文献
16.
A novel scheme is presented for solving the problem of optimal switching with nonlinear autonomous subsystems. This scheme determines the approximate global optimal solution for different initial conditions in a feedback form. Restrictions, including the need to enforce a mode sequence and/or a number of switching, do not exist for the developed method. Performance is evaluated in several examples with different complexities and the numerical simulation shows great promises for the controller. 相似文献
17.
《Journal of The Franklin Institute》2023,360(14):10433-10456
An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach. 相似文献
18.
The present paper proposes a numerical approach to a linear optimal control problem with a quadratic performance index. In this technique, the time interval is divided into a number of time segments and all of the unknown functions which appear in the performance index are either interpolated linearly with respect to time or assumed to be constant in each time segment. The augmented performance index is discretized within each time element through the ordinary finite element technique.The main advantage of the present method is as follows: all of the necessary conditions for the performance index to be stationary can be expressed in the form of algebraic equations and the performance sequence of the state variables can be eliminated. As a result, the optimal control problem is reduced to the simple one of finding the sequence of control variables alone, which minimizes the quadratic performance index.A general formulation of the method is given and simple numerical examples are shown to demonstrate the effectiveness of the technique. 相似文献
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20.
Abolhassan Razminia Mehdi Asadizadehshiraz Hamid Reza Shaker 《Journal of The Franklin Institute》2019,356(3):1590-1603
In this paper, a generalized trajectory tracking problem for a closed-loop control system is formulated in the optimal control context. A linear time varying plant is considered to track a closed-loop desired trajectory generated by a given mechanism. The theoretical results are obtained based on the Hamilton-Jacobi-Bellman theory in which some generalized semiquadratic value functions are employed as the Lagrangian. In addition, we employ a non-integer order integral of Riemann-Liouville type as the cost functional, so that the trajectory tracking process can be evaluated in an extended optimum manner wherein the fractionality plays the main role. By selecting a suitable fractional order of the integral, a satisfactory optimal control system can be deduced in which least concentration on selecting the weighting matrices is needed. To show the effectiveness of the results, some numerical examples illustrate the potentials. 相似文献