共查询到20条相似文献，搜索用时 15 毫秒
1.
Geyang Xiao Huaguang Zhang Qiuxia Qu He Jiang 《Journal of The Franklin Institute》2018,355(5):2610-2630
In this paper, a novel iterative approximate dynamic programming scheme is proposed by introducing the learning mechanism of value iteration (VI) to solve the constrained optimal control problem for CT affine nonlinear systems with utilizing only one neural network. The idea is to show the feasibility of introducing the VI learning mechanism to solve for the constrained optimal control problem from a theoretical point of view, and thus the initial admissible control can be avoided compared with most existing works based on policy iteration (PI). Meanwhile, the initial condition of the proposed VI based method can be more general than the traditional VI method which requires the initial value function to be a zero function. A general analytical method is proposed to demonstrate the convergence property. To simplify the architecture, only one critic neural network is adopted to approximate the iterative value function while implementing the proposed method. At last, two simulation examples are proposed to validate the theoretical results. 相似文献
2.
Pa-Yee Tsai 《Journal of The Franklin Institute》2010,347(10):1850-1862
In this paper, a hybrid method which combines the Adomian decomposition method (ADM), the Laplace transform algorithm and the Padé approximant is introduced to solve the approximate analytic solutions of the nonlinear Riccati differential equations. This hybrid method demonstrates accurate and reliable results, and has a great improvement in the ADM truncated series solution which diverges rapidly as the applicable domain increases. Three examples herein are given to demonstrate good accuracy and fast convergence in comparison with the exact solution. 相似文献
3.
Our paper deals with an effective application of the pseudospectral method to solution of Hamiltonian boundary value problems in optimal control theory. The developed numerical methodology is based on the celebrated Gauss pseudospectral approach. The last one makes it possible to reduce the conventional Hamiltonian boundary value problem to an auxiliary algebraic system. The implementable algorithm we propose is computationally consistent and moreover, involves numerically tractable results for a relative small discretization grids. However, the solution of the obtained algebraic equations system may has a low convergence radius. We next use the differential continuation approach in order to weaken the necessity of the well-defined initial conditions for the above algebraic system. The presented solution procedure can be extremely useful when the generic shooting-type methods fail because of sensitivity or stiffness. We discuss some numerical results and establish the efficiency of the proposed methodology. 相似文献
4.
《Journal of The Franklin Institute》2023,360(12):8753-8771
In this paper, the optimal consensus control problem of nonlinear multi-agent systems(MASs) with completely unknown dynamics is considered. The problem is formulated in a differential graphical game approach which can be solved by Hamilton-Jacobi (HJ) equations. The main difficulty in solving the HJ equations lies in the nonlinear coupling between equations. Based on the Adaptive Dynamic Programming (ADP) technique, an VI-PI mixed HDP algorithm is proposed to solve the HJ equations distributedly. With the PI step, a suitable iterative initial value can be obtained according to the initial policies. Then, VI steps are run to get the optimal solution with exponential convergence rate. Neural networks (NNs) are applied to approximate the value functions, which makes the data-driven end-to-end learning possible. A numerical simulation is conducted to show the effectiveness of the proposed algorithm. 相似文献
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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
7.
A linear two-point boundary value problem is transformed into a Cauchy system in which a Green's function appears as an auxiliary dependent variable. It is then shown that the solution of the Cauchy system provides a solution of the original two-point boundary value problem. Some numerical aspects are discussed. 相似文献
8.
运用单调迭代法研究一类非线性三阶常微分方程三点边值问题,不仅获得其单调正解的存在性,还给出单调正解的两个迭代序列,并且迭代序列的初值是零函数或一次函数,这从计算的角度来说是非常有用和可行的。 相似文献
9.
In this paper, a numerical method based on polynomial approximation, using Hermite polynomial basis, to obtain the approximate solution of generalized pantograph equations with variable coefficients is presented. The technique we have used is an improved collocation method. Some numerical examples, which consist of initial conditions, are given to illustrate the reality and efficiency of the method. In addition, some numerical examples are presented to show the properties of the given method; the present method has been compared with other methods and the results are discussed. 相似文献
10.
Nonlinear two-point boundary value problems have always been difficult to solve. The difficulty is compounded if the problem tends to be inherently unstable. This paper describes an algorithm for solving such sensitive boundary value problems. The procedure is based on a computational method for finding the general solution of systems of ordinary differential equations used in conjunction with the multi-point quasilinearization method of Miele. The method is demonstrated by solving Troesch's problem and a singular perturbation problem. 相似文献
11.
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
12.
Xin Liu Xianqiang Yang Pengbo Zhu Weili Xiong 《Journal of The Franklin Institute》2019,356(16):9953-9971
This paper puts forward a robust identification solution for nonlinear time-delay state-space model (NDSSM) with contaminated measurements. To enhance the robustness of the developed method for outliers, the heavy-tailed Laplace distribution is employed to describe and protect the output measurement process. The undetermined time-delay is considered to be uniformly distributed and the boundary of it is known as a priori. In the developed solution, the uncertain time-delay is treated as a latent process variable and it is iteratively calculated with the expectation–maximization (EM) algorithm. The EM algorithm is actually an iterative optimization algorithm and it is effective for the hidden variable problems. The particle filter is introduced to numerically approximate the cost function (Q-function) in the EM algorithm since it is difficult to calculate directly. The efficacy of the developed solution is evaluated via a numerical test and a two-link robotic manipulator. 相似文献
13.
In the present paper, a new Legendre wavelet operational matrix of derivative is presented. Shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Then the scheme is tested for linear and nonlinear singular examples. The obtained results demonstrate efficiency and capability of the proposed method. 相似文献
14.
By use of the multiple Laplace transform a partial differential equation and its associated boundary conditions characterizing a boundary value problem in n independent real variables can be transferred directly into an algebraic equation in n independent complex variables. This algebraic equation can be solved for the multiple transform of the solution of the boundary value problem. Multiple inversion of this transform then gives the desired solution. The general theory underlying such solution of boundary value problems in two and three independent variables is advanced in detail. Use of this theory is illustrated by solution of two specific problems. 相似文献
15.
An initial value treatment is presented for a mixed boundary value problem of axisymmetric torsion of an elastic layer. The problem is expressed in terms of dual integral equations which are first reduced to a Fredholm integral equation of second kind with a continuous kernel. An initial value problem is derived for this Fredholm integral equation using invariant imbedding. This constitutes a new analytical approach to a large class of torsion problems. 相似文献
16.
This paper introduces an alternative method artificial neural networks (ANN) used to obtain numerical solutions of mathematical models of dynamic systems, represented by ordinary differential equations (ODEs) and partial differential equations (PDEs). The proposed trial solution of differential equations (DEs) consists of two parts: The initial and boundary conditions (BCs) should be satisfied by the first part. However, the second part is not affected from initial and BCs, but it only tries to satisfy DE. This part involves a feedforward ANN containing adjustable parameters (weight and bias). The proposed solution satisfying boundary and initial condition uses a feedforward ANN with one hidden layer varying the neuron number in the hidden layer according to complexity of the considered problem. The ANN having appropriate architecture has been trained with backpropagation algorithm using an adaptive learning rate to satisfy DE. Moreover, we have, first, developed the general formula for the numerical solutions of nth-order initial-value problems by using ANN.For numerical applications, the ODEs that are the mathematical models of linear and non-linear mass-damper-spring systems and the second- and fourth-order PDEs that are the mathematical models of the control of longitudinal vibrations of rods and lateral vibrations of beams have been considered. Finally, the responses of the controlled and non-controlled systems have been obtained. The obtained results have been graphically presented and some conclusion remarks are given. 相似文献
17.
《Journal of The Franklin Institute》1987,323(3):385-394
A method of using Laguerre functions is presented to obtain approximate solutions of a linear differential equation of the stretched type. The solution is essentially based on the development of two new operational matrices to manipulate, respectively, the differentiation and the stretch via Laguerre functions. It is shown that the proposed method is convenient for computer programming and appears comparable to the accuracy of other methods. Two examples are given for illustration. 相似文献
18.
By applying hybrid functions of general block-pulse functions and Legendre polynomials, linear Volterra integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of linear Volterra integrodifferential systems are derived. Using the results we obtain the optimal control and state as well as the optimal value of the objective functional. The numerical examples illustrate that the algorithms are valid. 相似文献
19.
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
20.
H.R. Marzban 《Journal of The Franklin Institute》2004,341(3):279-293
A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The operational matrices of integration, delay and product are utilized to reduce the solution of optimal control to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献