The Experts below are selected from a list of 32325 Experts worldwide ranked by ideXlab platform

Derong Liu - One of the best experts on this subject based on the ideXlab platform.

  • improved value iteration for neural network based stochastic optimal control design
    Neural Networks, 2020
    Co-Authors: Mingming Liang, Ding Wang, Derong Liu
    Abstract:

    Abstract In this paper, a novel value iteration adaptive dynamic programming (ADP) algorithm is presented, which is called an improved value iteration ADP algorithm, to obtain the optimal policy for discrete stochastic processes. In the improved value iteration ADP algorithm, for the first time we propose a new criteria to verify whether the obtained policy is stable or not for stochastic processes. By analyzing the convergence properties of the proposed algorithm, it is shown that the iterative value Functions can converge to the optimum. In addition, our algorithm allows the initial value Function to be an arbitrary positive semi-Definite Function. Finally, two simulation examples are presented to validate the effectiveness of the developed method.

  • discrete time two player zero sum games for nonlinear systems using iterative adaptive dynamic programming
    International Symposium on Neural Networks, 2016
    Co-Authors: Qinglai Wei, Derong Liu
    Abstract:

    This paper is concerned with a discrete-time two-player zero-sum game of nonlinear systems, which is solved by a new iterative adaptive dynamic programming (ADP) method. In the present iterative ADP algorithm, two iteration procedures, which are upper and lower iterations, are implemented to obtain the upper and lower performance index Functions, respectively. Initialized by an arbitrary positive semi-Definite Function, it is shown that the iterative value Functions converge to the optimal performance index Function if the optimal performance index Function of the two-player zero-sum game exists. Finally, simulation results are given to illustrate the performance of the developed method.

  • optimal self learning control scheme for discrete time nonlinear systems using local value iteration
    International Joint Conference on Neural Network, 2016
    Co-Authors: Qinglai Wei, Derong Liu
    Abstract:

    In this paper, an optimal self-learning control scheme for discrete-time nonlinear systems is developed using a new local value iteration based adaptive dynamic programming (ADP) algorithm. The developed local value iteration algorithm permits an arbitrary positive semi-Definite Function to initialize the algorithm. In the developed local value iteration algorithm, the iterative value Function and iterative control law are updated by a subset of the state space. A new analysis method of the convergence property is presented to show that the iterative value Functions will converge to the optimum. The convergence criterion for the local value iteration algorithm is presented. A simulation example is given to demonstrate the validity of the present optimal control scheme.

  • value iteration adaptive dynamic programming for optimal control of discrete time nonlinear systems
    IEEE Transactions on Systems Man and Cybernetics, 2016
    Co-Authors: Qinglai Wei, Derong Liu, Hanquan Lin
    Abstract:

    In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-Definite Function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value Function converges to the optimal performance index Function. Initialized by different initial Functions, it is proven that the iterative value Function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value Function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

  • Nearly optimal control scheme for discrete-time nonlinear systems with finite approximation errors using generalized value iteration algorithm
    IFAC Proceedings Volumes, 2014
    Co-Authors: Qinglai Wei, Derong Liu
    Abstract:

    Abstract In this paper, a new generalized value iteration algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The idea is to use iterative adaptive dynamic programming (ADP) to obtain the iterative control law which makes the iterative performance index Function reach the optimum. The generalized value iteration algorithm permits an arbitrary positive semi-Definite Function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index Function in each iteration cannot be accurately obtained, a new design method of the convergence criterion for the generalized value iteration algorithm with finite approximation errors is established to make the iterative performance index Functions converge to a finite neighborhood of the lowest bound of all performance index Functions. Simulation results are given to illustrate the performance of the developed algorithm.

H G Georgiadis - One of the best experts on this subject based on the ideXlab platform.

  • plane strain crack problems in microstructured solids governed by dipolar gradient elasticity
    Journal of The Mechanics and Physics of Solids, 2009
    Co-Authors: P A Gourgiotis, H G Georgiadis
    Abstract:

    Abstract The present study aims at determining the elastic stress and displacement fields around the tips of a finite-length crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin–Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-Definite Function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lame constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein–Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the crack tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur. Also, in the vicinity of the crack tip, the crack-face displacement closes more smoothly as compared to the standard result and the strain field is bounded. Finally, the J-integral (energy release rate) in gradient elasticity was evaluated. A decrease of its value is noticed in comparison with the classical theory. This shows that the gradient theory predicts a strengthening effect since a reduction of crack driving force takes place as the material microstructure becomes more pronounced.

  • balance laws and energy release rates for cracks in dipolar gradient elasticity
    International Journal of Solids and Structures, 2008
    Co-Authors: C G Grentzelou, H G Georgiadis
    Abstract:

    Abstract It is the purpose of this work to derive the balance laws (in the Gunther–Knowles–Sternberg sense) pertaining to dipolar gradient elasticity. The theory of dipolar gradient (or grade 2) elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Microstructure in linear elasticity. Arch. Rational Mech. Anal. 16, 51–78] and is appropriate to model materials with periodic structure. According to this theory, the strain–energy density assumes the form of a positive-Definite Function of the strain (as in classical elasticity) and the gradient of both strain and rotation (additional terms). The balance laws are derived here through a more straightforward procedure than the one usually employed in classical elasticity (i.e. Noether’s theorem). Indeed, the pertinent balance laws are obtained through the action of the standard operators of vector calculus (grad, curl and div) on appropriate forms of the Hamiltonian of the system under consideration. These laws are directly related to the energy release rates in the processes of crack translation, rotation and self-similar expansion. Under certain conditions, they are identified with conservation laws and path-independent integrals are obtained.

  • energy theorems and the j integral in dipolar gradient elasticity
    International Journal of Solids and Structures, 2006
    Co-Authors: H G Georgiadis, C G Grentzelou
    Abstract:

    Within the framework of Mindlins dipolar gradient elasticity, general energy theorems are proved in this work. These are the theorem of minimum potential energy, the theorem of minimum complementary potential energy, a variational principle analogous to that of the Hellinger–Reissner principle in classical theory, two theorems analogous to those of Castigliano and Engesser in classical theory, a uniqueness theorem of the Kirchhoff–Neumann type, and a reciprocal theorem. These results can be of importance to computational methods for analyzing practical problems. In addition, the J-integral of fracture mechanics is derived within the same framework. The new form of the J-integral is identified with the energy release rate at the tip of a growing crack and its path-independence is proved. The theory of dipolar gradient elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Microstructure in linear elasticity. Arch. Rational Mech. Anal. 16, 51–78] and is appropriate to model materials with periodic structure. According to this theory, the strain-energy density assumes the form of a positive-Definite Function of the strain (as in classical elasticity) and the second gradient of the displacement (additional term). Specific cases of the general theory considered here are the well-known theory of couple-stress elasticity and the recently popularized theory of strain-gradient elasticity. The latter case is also treated in the present study. 2005 Elsevier Ltd. All rights reserved.

Xiong Yang - One of the best experts on this subject based on the ideXlab platform.

  • Finite-Approximation-Error-Based Discrete-Time Iterative Adaptive Dynamic Programming
    IEEE Transactions on Cybernetics, 2014
    Co-Authors: Fei-yue Wang, Xiong Yang
    Abstract:

    In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index Function converge to the solution of the Hamilton-Jacobi-Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-Definite Function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index Function in each iteration cannot accurately be obtained, for the first time a new “design method of the convergence criteria” for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index Function converge to a finite neighborhood of the optimal performance index Function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method.

C G Grentzelou - One of the best experts on this subject based on the ideXlab platform.

  • balance laws and energy release rates for cracks in dipolar gradient elasticity
    International Journal of Solids and Structures, 2008
    Co-Authors: C G Grentzelou, H G Georgiadis
    Abstract:

    Abstract It is the purpose of this work to derive the balance laws (in the Gunther–Knowles–Sternberg sense) pertaining to dipolar gradient elasticity. The theory of dipolar gradient (or grade 2) elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Microstructure in linear elasticity. Arch. Rational Mech. Anal. 16, 51–78] and is appropriate to model materials with periodic structure. According to this theory, the strain–energy density assumes the form of a positive-Definite Function of the strain (as in classical elasticity) and the gradient of both strain and rotation (additional terms). The balance laws are derived here through a more straightforward procedure than the one usually employed in classical elasticity (i.e. Noether’s theorem). Indeed, the pertinent balance laws are obtained through the action of the standard operators of vector calculus (grad, curl and div) on appropriate forms of the Hamiltonian of the system under consideration. These laws are directly related to the energy release rates in the processes of crack translation, rotation and self-similar expansion. Under certain conditions, they are identified with conservation laws and path-independent integrals are obtained.

  • energy theorems and the j integral in dipolar gradient elasticity
    International Journal of Solids and Structures, 2006
    Co-Authors: H G Georgiadis, C G Grentzelou
    Abstract:

    Within the framework of Mindlins dipolar gradient elasticity, general energy theorems are proved in this work. These are the theorem of minimum potential energy, the theorem of minimum complementary potential energy, a variational principle analogous to that of the Hellinger–Reissner principle in classical theory, two theorems analogous to those of Castigliano and Engesser in classical theory, a uniqueness theorem of the Kirchhoff–Neumann type, and a reciprocal theorem. These results can be of importance to computational methods for analyzing practical problems. In addition, the J-integral of fracture mechanics is derived within the same framework. The new form of the J-integral is identified with the energy release rate at the tip of a growing crack and its path-independence is proved. The theory of dipolar gradient elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Microstructure in linear elasticity. Arch. Rational Mech. Anal. 16, 51–78] and is appropriate to model materials with periodic structure. According to this theory, the strain-energy density assumes the form of a positive-Definite Function of the strain (as in classical elasticity) and the second gradient of the displacement (additional term). Specific cases of the general theory considered here are the well-known theory of couple-stress elasticity and the recently popularized theory of strain-gradient elasticity. The latter case is also treated in the present study. 2005 Elsevier Ltd. All rights reserved.

Demni Nizar - One of the best experts on this subject based on the ideXlab platform.

  • Markov semi-groups associated with the complex unimodular group $Sl(2,\mathbb{C})$
    2019
    Co-Authors: Demni Nizar
    Abstract:

    In this paper, we derive the explicit expressions of two Markov semi-groups constructed by P. Biane in \cite{Bia1} from the restriction of a particular positive Definite Function on the complex unimodular group $Sl(2,\mathbb{C})$ to two commutative subalgebras of its universal $C^{\star}$-algebra. Our computations use Euclidean Fourier analysis together with the generating Function of Laguerre polynomials with index $-1$, and yield absolutely-convergent double series representations of the semi-group densities. In the last part of the paper, we discuss the coincidence, noticed by Biane as well, occurring between the heat kernel on the Heisenberg group and the semi-group corresponding to the intersection of the principal and the complementary series. To this end, we appeal to the metaplectic representation $Mp(4,\mathbb{R})$ and to the Landau operator in the complex plane.Comment: The intertwining operator is derived in the case of principal serie

  • Markov semi-groups associated with the complex unimodular group $Sl(2,\mathbb{C})$
    Springer Verlag, 2019
    Co-Authors: Demni Nizar
    Abstract:

    The intertwining operator is derived in the case of principal seriesInternational audienceIn this paper, we derive the explicit expressions of two Markov semi-groups constructed by P. Biane in \cite{Bia1} from the restriction of a particular positive Definite Function on the complex unimodular group $Sl(2,\mathbb{C})$ to two commutative subalgebras of its universal $C^{\star}$-algebra. Our computations use Euclidean Fourier analysis together with the generating Function of Laguerre polynomials with index $-1$, and yield absolutely-convergent double series representations of the semi-group densities. In the last part of the paper, we discuss the coincidence, noticed by Biane as well, occurring between the heat kernel on the Heisenberg group and the semi-group corresponding to the intersection of the principal and the complementary series. To this end, we appeal to the metaplectic representation $Mp(4,\mathbb{R})$ and to the Landau operator in the complex plane