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Relevant bibliographies by topics / Hamilton-Jacobi equation. Optimal control. Euler method

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Journal articles
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Academic literature on the topic 'Hamilton-Jacobi equation. Optimal control. Euler method'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Hamilton-Jacobi equation. Optimal control. Euler method"

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Abe, Yoshiki, Gou Nishida, Noboru Sakamoto, and Yutaka Yamamoto. "Robust NonlinearH∞Control Design via Stable Manifold Method." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/198380.

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This paper proposes a systematic numerical method for designing robust nonlinearH∞controllers without a priori lower-dimensional approximation with respect to solutions of the Hamilton-Jacobi equations. The method ensures the solutions are globally calculated with arbitrary accuracy in terms of the stable manifold method that is a solver of Hamilton-Jacobi equations in nonlinear optimal control problems. In this realization, the existence of stabilizing solutions of the Hamilton-Jacobi equations can be derived from some properties of the linearized system and the equivalent Hamiltonian system

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NOCHETTO, RICARDO H., and GIUSEPPE SAVARÉ. "NONLINEAR EVOLUTION GOVERNED BY ACCRETIVE OPERATORS IN BANACH SPACES: ERROR CONTROL AND APPLICATIONS." Mathematical Models and Methods in Applied Sciences 16, no. 03 (2006): 439–77. http://dx.doi.org/10.1142/s0218202506001224.

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Nonlinear evolution equations governed by m-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order [Formula: see text]. Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in L1, as well as to Hamilton–Jacobi equations in C0are given. The error analysis relies on a comparison principle, for the novel notion of relaxed solutions, which combines

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Mohan, Manil T. "Dynamic programming and feedback analysis of the two dimensional tidal dynamics system." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 109. http://dx.doi.org/10.1051/cocv/2020025.

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In this work, we consider the controlled two dimensional tidal dynamics equations in bounded domains. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled 2D tidal dynamics equations. The existence of an optimal control is shown and the dynamic programming method for the optimal control of 2D tidal dynamics system is also described. We show that the feedback control can be obtained from the solution of an infinite dimensional Hamilton-Jacobi equation. The non-differentiability and lack of smoothness of the value functio

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Sweilam, N. H., S. M. AL-Mekhlafi, and D. Baleanu. "Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model." International Journal of Biomathematics 11, no. 08 (2018): 1850115. http://dx.doi.org/10.1142/s1793524518501152.

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In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo’s definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton’s iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functio

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ALZIARY, B., and P. L. LIONS. "A GRID REFINEMENT METHOD FOR DETERMINISTIC CONTROL AND DIFFERENTIAL GAMES." Mathematical Models and Methods in Applied Sciences 04, no. 06 (1994): 899–910. http://dx.doi.org/10.1142/s0218202594000492.

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We develop here a simple method for the computation of value functions of deterministic optimal control or differential games problems which allows to refine locally a grid and reduce memory space. Given an approximation of optimal trajectories, one can solve the associated Hamilton-Jacobi equation in a tubular neighborhood with state-constraints boundary conditions. We study here the validity of such an approach and we illustrate it on various examples.

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Rakhshan, Seyed Ali, Sohrab Effati, and Ali Vahidian Kamyad. "Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation." Journal of Vibration and Control 24, no. 9 (2016): 1741–56. http://dx.doi.org/10.1177/1077546316668467.

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The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional deri

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Swaidan, Waleeda, and Amran Hussin. "Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/240352.

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Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlin

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Rubio, José de Jesús, and Adrian Gustavo Bravo. "Optimal Control of a PEM Fuel Cell for the Inputs Minimization." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/698250.

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The trajectory tracking problem of a proton exchange membrane (PEM) fuel cell is considered. To solve this problem, an optimal controller is proposed. The optimal technique has the objective that the system states should reach the desired trajectories while the inputs are minimized. The proposed controller uses the Hamilton-Jacobi-Bellman method where its Riccati equation is considered as an adaptive function. The effectiveness of the proposed technique is verified by two simulations.

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Matinfar, M., and M. Dosti. "Solving Linear Optimal Control Problems Using Cubic B-spline Quasi-interpolation." MATEMATIKA 34, no. 2 (2018): 313–24. http://dx.doi.org/10.11113/matematika.v34.n2.817.

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In this article, we apply an impressive method for solving linear optimal control problem based on cubic B-spline quasi-interpolation. Hamilton-Jacobi equation are applied to linear optimal control problem convert to systems of first-order equations. The main idea of our scheme is approximation derivative with cubic B-spline quasi-interpolation. This method is straightforward, without restrictive assumptions.The results of scheme are made in pleasant agreement with analytic solutions. The accuracy of the proposed method is demonstrated by absolute error. Our scheme is simple to implement becau

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Dao, Phuong Nam, Hong Quang Nguyen, Minh-Duc Ngo, and Seon-Ju Ahn. "On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning." Energies 13, no. 19 (2020): 5069. http://dx.doi.org/10.3390/en13195069.

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In this paper, a tracking control approach is developed based on an adaptive reinforcement learning algorithm with a bounded cost function for perturbed nonlinear switched systems, which represent a useful framework for modelling these converters, such as DC–DC converter, multi-level converter, etc. An optimal control method is derived for nominal systems to solve the tracking control problem, which results in solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal controller obtained by solving the HJB equation can stabilize the perturbed nonlinear switched systems. To

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Dissertations / Theses on the topic "Hamilton-Jacobi equation. Optimal control. Euler method"

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Helin, Mikael. "Inverse Parameter Estimation using Hamilton-Jacobi Equations." Thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123092.

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Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possibl

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Qu, Zheng. "Nonlinear Perron-Frobenius theory and max-plus numerical methods for Hamilton-Jacobi equations." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/92/71/22/PDF/thesis.pdf.

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Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur

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Iourtchenko, Daniil V. "Optimal bounded control and relevant response analysis for random vibrations." Link to electronic thesis, 2001. http://www.wpi.edu/Pubs/ETD/Available/etd-0525101-111407.

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Thesis (Ph. D.)--Worcester Polytechnic Institute.<br>Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration. Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration; energy balance method. Includes bibliographical references (p. 86-89).

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Chen, Zhuliang. "Numerical Methods for Optimal Stochastic Control in Finance." Thesis, 2008. http://hdl.handle.net/10012/3794.

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In this thesis, we develop partial differential equation (PDE) based numerical methods to solve certain optimal stochastic control problems in finance. The value of a stochastic control problem is normally identical to the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation or an HJB variational inequality. The HJB equation corresponds to the case when the controls are bounded while the HJB variational inequality corresponds to the unbounded control case. As a result, the solution to the stochastic control problem can be computed by solving the corresponding HJB equation/variational

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Conference papers on the topic "Hamilton-Jacobi equation. Optimal control. Euler method"

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Nusawardhana, Antonius, and Stanislaw H. Zak. "Optimality of Synergetic Controllers." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14839.

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Optimality properties of synergetic controllers are analyzed using the Euler-Lagrange conditions and the Hamilton-Jacobi-Bellman equation. First, a synergetic control strategy is compared with the variable structure sliding mode control. The synergetic control design methodology turns out to be closely related to the methods of variable structure sliding mode control. In fact, the method of sliding surface design from the sliding mode control are essential for designing similar manifolds in the synergetic control approach. It is shown that the synergetic control strategy can be derived using t

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Rafikov, Marat, and Jose´ Manoel Balthazar. "Optimal Linear and Nonlinear Control Design for Chaotic Systems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84998.

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In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulation

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Ghosh, Bijoy K., Takafumi Oki, Sanath D. Kahagalage, and Indika Wijayasinghe. "Asymptotically Stabilizing Potential Control for the Eye Movement Dynamics." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-5864.

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In this paper, we analyze the problem of stabilizing a rotating eye movement control system satisfying the Listing’s constraint. The control system is described using a suitably defined Lagrangian and written in the corresponding Hamiltonian form. We introduce a damping control and show that this choice of control asymptotically stabilizes the equilibrium point of the dynamics, while driving the state to a point of minimum total energy. The equilibrium point can be placed by appropriately locating the minimum of a potential function. The damping controller has been shown to be optimal with res

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