1,720,971 research outputs found
Optimizing semilinear representations for State-dependent Riccati Equation-based feedback control
Full text linkAn optimized variant of the State Dependent Riccati Equations (SDREs) approach for nonlinear optimal feedback stabilization is presented. The proposed method is based on the construction of equivalent semilinear representations associated to the dynamics and their affine combination. The optimal combination is chosen to minimize the discrepancy between the SDRE control and the optimal feedback law stemming from the solution of the corresponding Hamilton Jacobi Bellman (HJB) equation. Numerical experiments assess effectiveness of the method in terms of stability of the closed-loop with near-to-optimal performance.An optimized variant of the State Dependent Riccati Equations (SDREs) approach for nonlinear optimal feedback stabilization is presented. The proposed method is based on the construction of equivalent semilinear representations associated to the dynamics and their affine combination. The optimal combination is chosen to minimize the discrepancy between the SDRE control and the optimal feedback law stemming from the solution of the corresponding Hamilton Jacobi Bellman (HJB) equation. Numerical experiments assess effectiveness of the method in terms of stability of the closed-loop with near-to-optimal performance
An efficient policy iteration algorithm for dynamic programming equations
Full text linkWe present an accelerated algorithm for the solution of static Hamilton–Jacobi–Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear convergence in many relevant cases provided the initial guess is sufficiently close to the solution. This limitation often degenerates into a behavior similar to a value iteration method, with an increased computation time. The new scheme circumvents this problem by combining the advantages of both algorithms with an efficient coupling. The method starts with a coarse-mesh value iteration phase and then switches to a fine-mesh policy iteration procedure when a certain error threshold is reached. A delicate point is to determine this threshold in order to avoid cumbersome computations with the value iteration and at the same time to ensure the convergence of the policy iteration method to the optimal solution. We analyze the methods and efficient coupling in a number of examples in different dimensions, illustrating their properties
State-dependent Riccati equation feedback stabilization for nonlinear PDEs
Full text linkThe synthesis of suboptimal feedback laws for controlling nonlinear dynamics arising from semi-discretized PDEs is studied. An approach based on the State-dependent Riccati Equation (SDRE) is presented for 2 and ∞ control problems. Depending on the nonlinearity and the dimension of the resulting problem, offline, online, and hybrid offline-online alternatives to the SDRE synthesis are proposed. The hybrid offline-online SDRE method reduces to the sequential solution of Lyapunov equations, effectively enabling the computation of suboptimal feedback controls for two-dimensional PDEs. Numerical tests for the Sine-Gordon, degenerate Zeldovich, and viscous Burgers’ PDEs are presented, providing a thorough experimental assessment of the proposed methodology
A HJB-POD feedback synthesis approach for the wave equation
No full textWe propose a computational approach for the solution of an optimal control problem governed by the wave equation. We aim at obtaining approximate feedback laws by means of the application of the dynamic programming principle. Since this methodology is only applicable for low-dimensional dynamical systems, we first introduce a reduced-order model for the wave equation by means of Proper Orthogonal Decomposition. The coupling between the reduced-order model and the related dynamic programming equation allows to obtain the desired approximation of the feedback law. We discuss numerical aspects of the feedback synthesis and providenumerical tests illustrating this approach
An accelerated value/policy iteration scheme for optimal control problems and games
No full textWe present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems and differential games. The new scheme combines the advantages of value iteration and policy iteration methods by means of an efficient coupling. The method starts with a value iteration phase on a coarse mesh and then switches to a policy iteration procedure over a finer mesh when a fixed error threshold is reached.We present numerical tests assessing the performance of the scheme
Supervised learning for kinetic consensus control
Full text linkIn this paper, how to successfully and efficiently condition a target
population of agents towards consensus is discussed. To overcome the curse of
dimensionality, the mean field formulation of the consensus control problem is
considered. Although such formulation is designed to be independent of the
number of agents, it is feasible to solve only for moderate intrinsic
dimensions of the agents space. For this reason, the solution is approached by
means of a Boltzmann procedure, i.e. quasi-invariant limit of controlled binary
interactions as approximation of the mean field PDE. The need for an efficient
solver for the binary interaction control problem motivates the use of a
supervised learning approach to encode a binary feedback map to be sampled at a
very high rate. A gradient augmented feedforward neural network for the Value
function of the binary control problem is considered and compared with direct
approximation of the feedback law.Comment: 6 pages, 3 figure
Value iteration convergence of ε-monotone schemes for stationary Hamilton–Jacobi equations
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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