The Bellman Equation
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Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
Author: Martino Bardi
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-05-21
The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games. The theory of viscosity solutions, initiated in the early 80's by the papers of M.G. Crandall and P.L. Lions [CL81, CL83], M.G. Crandall, L.C. Evans and P.L. Lions [CEL84] and P.L. Lions' influential monograph [L82], provides an - tremely convenient PDE framework for dealing with the lack of smoothness of the value functions arising in dynamic optimization problems. The leading theme of this book is a description of the implementation of the viscosity solutions approach to a number of significant model problems in op- real deterministic control and differential games. We have tried to emphasize the advantages offered by this approach in establishing the well-posedness of the c- responding Hamilton-Jacobi equations and to point out its role (when combined with various techniques from optimal control theory and nonsmooth analysis) in the important issue of feedback synthesis.
Hamilton-Jacobi-Bellman Equations
Author: Dante Kalise
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2018-08-06
Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
TensorFlow Reinforcement Learning Quick Start Guide
Author: Kaushik Balakrishnan
language: en
Publisher: Packt Publishing Ltd
Release Date: 2019-03-30
Leverage the power of Tensorflow to Create powerful software agents that can self-learn to perform real-world tasks Key FeaturesExplore efficient Reinforcement Learning algorithms and code them using TensorFlow and PythonTrain Reinforcement Learning agents for problems, ranging from computer games to autonomous driving.Formulate and devise selective algorithms and techniques in your applications in no time.Book Description Advances in reinforcement learning algorithms have made it possible to use them for optimal control in several different industrial applications. With this book, you will apply Reinforcement Learning to a range of problems, from computer games to autonomous driving. The book starts by introducing you to essential Reinforcement Learning concepts such as agents, environments, rewards, and advantage functions. You will also master the distinctions between on-policy and off-policy algorithms, as well as model-free and model-based algorithms. You will also learn about several Reinforcement Learning algorithms, such as SARSA, Deep Q-Networks (DQN), Deep Deterministic Policy Gradients (DDPG), Asynchronous Advantage Actor-Critic (A3C), Trust Region Policy Optimization (TRPO), and Proximal Policy Optimization (PPO). The book will also show you how to code these algorithms in TensorFlow and Python and apply them to solve computer games from OpenAI Gym. Finally, you will also learn how to train a car to drive autonomously in the Torcs racing car simulator. By the end of the book, you will be able to design, build, train, and evaluate feed-forward neural networks and convolutional neural networks. You will also have mastered coding state-of-the-art algorithms and also training agents for various control problems. What you will learnUnderstand the theory and concepts behind modern Reinforcement Learning algorithmsCode state-of-the-art Reinforcement Learning algorithms with discrete or continuous actionsDevelop Reinforcement Learning algorithms and apply them to training agents to play computer gamesExplore DQN, DDQN, and Dueling architectures to play Atari's Breakout using TensorFlowUse A3C to play CartPole and LunarLanderTrain an agent to drive a car autonomously in a simulatorWho this book is for Data scientists and AI developers who wish to quickly get started with training effective reinforcement learning models in TensorFlow will find this book very useful. Prior knowledge of machine learning and deep learning concepts (as well as exposure to Python programming) will be useful.