Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation

From MaRDI portal
Publication:1388109

DOI10.1016/S0005-1098(97)00128-3zbMath0949.93022OpenAlexW2047090868MaRDI QIDQ1388109

Randal W. Beard, George N. Saridis, John Ting-Yung Wen

Publication date: 8 June 1998

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0005-1098(97)00128-3



Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).


Related Items (86)

Asymptotic stabilization of nonlinear systems with convex-polytope input constraints by continuous inputNeural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear systemsValue iteration and adaptive dynamic programming for data-driven adaptive optimal control designApproximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faultsAdaptive Optimal Control Without Weight TransportApproximation design of optimal controllers for nonlinear systems with sinusoidal disturbancesOptimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programmingObserver-based fault detection for uncertain nonlinear systemsRobust nonlinear \(H^{\infty}\) control design via stable manifold methodReinforcement learning solution for HJB equation arising in constrained optimal control problemOnline adaptive algorithm for optimal control with integral reinforcement learningPolicy iterations for reinforcement learning problems in continuous time and space -- fundamental theory and methodsNovel iterative neural dynamic programming for data-based approximate optimal control designSelf-learning robust optimal control for continuous-time nonlinear systems with mismatched disturbancesModel-free \(H_{\infty }\) control design for unknown linear discrete-time systems via Q-learning with LMIDerivatives pricing with market impact and limit order bookApproximately adaptive neural cooperative control for nonlinear multiagent systems with performance guaranteeRobust min-max optimal control design for systems with uncertain models: a neural dynamic programming approachOn the Cahn-Hilliard equation with no-flux and strong anchoring conditionsValue-Gradient Based Formulation of Optimal Control Problem and Machine Learning AlgorithmAdaptive dynamic programming for decentralized neuro‐control of nonlinear systems subject to mismatched interconnectionsA New Integral Critic Learning for Optimal Tracking Control with Applications to Boiler‐Turbine SystemsDynamic event-triggered controller design for nonlinear systems: reinforcement learning strategyOptimal polynomial feedback laws for finite horizon control problemsEvent‐driven adaptive near‐optimal tracking control of the robot in aircraft skin inspectionA transformation approach for solving the Hamilton-Jacobi-Bellman equation in \({\mathcal H}_2\) deterministic and stochastic optimal control of affine nonlinear systems.Optimal output tracking control of linear discrete-time systems with unknown dynamics by adaptive dynamic programming and output feedbackAn iterative computational scheme for solving the coupled Hamilton-Jacobi-Isaacs equations in nonzero-sum differential games of affine nonlinear systemsObserver‐based event triggered ADP approach for input‐constrained nonlinear systems with disturbancesData-driven optimal control via linear transfer operators: a convex approachRobust adaptive critic control design with network-based event-triggered formulationConvex quadratic equationOff-policy based adaptive dynamic programming method for nonzero-sum games on discrete-time systemReinforcement learning‐based optimal trajectory tracking control of surface vessels under input saturationsAdaptive optimal formation control for unmanned surface vehicles with guaranteed performance using actor‐critic learning architectureOptimized adaptive consensus tracking control for uncertain nonlinear multiagent systems using a new event-triggered communication mechanismPassivity‐based control design frameworks for hybrid nonlinear time‐varying dynamical systemsApproximate solutions to the Hamilton-Jacobi equations for generating functionsOutput feedback tracking control of a class of continuous-time nonlinear systems via adaptive dynamic programming approachPolynomial Approximation of High-Dimensional Hamilton--Jacobi--Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEsUnnamed ItemAdaptive dynamic programming and optimal control of nonlinear nonaffine systemsDistributed adaptive dynamic programming for data-driven optimal controlTwo-phase selective decentralization to improve reinforcement learning systems with MDPOptimal tracking control for large-scale interconnected systems with time-delaysModified value-function-approximation for synchronous policy iteration with single-critic configuration for nonlinear optimal controlStochastic optimal control via forward and backward stochastic differential equations and importance samplingGalerkin Method and Weighting Functions Applied to Nonlinear H∞ Control with Output FeedbackOn the infinite time solution to state-constrained stochastic optimal control problemsFeedback control methodologies for nonlinear systemsNumerical solutions to the Bellman equation of optimal controlOnline concurrent reinforcement learning algorithm to solve two‐player zero‐sum games for partially unknown nonlinear continuous‐time systemsSolutions of nonlinear optimal and robust control problems via a mixed collocation/DAE's based algorithmFeedback control method using Haar wavelet operational matrices for solving optimal control problemsSuccessive approximation approach of optimal control for nonlinear discrete-time systemsVariable structure disturbance rejection control for nonlinear uncertain systems with state and control delays via optimal sliding mode surface approachOnline actor-critic algorithm to solve the continuous-time infinite horizon optimal control problemOn infinite-time nonlinear quadratic optimal controlStochastic differential games: a sampling approach via FBSDEsIterative computational approach to the solution of the Hamilton-Jacobi-Bellman-Isaacs equation in nonlinear optimal controlA neural network-based policy iteration algorithm with global \(H^2\)-superlinear convergence for stochastic games on domainsOn the convergence of successive Galerkin approximation for nonlinear output feedback \(H_{\infty}\) controlSome numerical tests for an alternative approach to optimal feedback controlDecentralized adaptive optimal stabilization of nonlinear systems with matched interconnectionsOptimal control for nonlinear continuous systems by adaptive dynamic programming based on fuzzy basis functionsSuccessive approximation procedure of optimal tracking control for nonlinear similar composite systemsMulti-step heuristic dynamic programming for optimal control of nonlinear discrete-time systemsApproximate solutions to the time-invariant Hamilton-Jacobi-Bellman equationNonlinear optimal approach to spacecraft formation flying using Lorentz and impulsive actuationFeedback controller design for linear and a class of nonlinear optimal control problemsA new analytical method for solving a class of nonlinear optimal control problemsObserver-based approximate optimal tracking control for time-delay systems with external disturbancesGuaranteed cost spacecraft attitude stabilization under actuator misalignments using linear partial differential equationsStabilization of a class of nonlinear control systems via a neural network scheme with convergence analysisTensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman EquationsComputationally efficient simultaneous policy update algorithm for nonlinearHstate feedback control with Galerkin's methodNearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approachNonlinear optimal control as quantum mechanical eigenvalue problemsA numerical approach to hybrid nonlinear optimal controlData-based approximate policy iteration for affine nonlinear continuous-time optimal control designApproximate optimal trajectory tracking for continuous-time nonlinear systemsWhen does stabilizability imply the existence of infinite horizon optimal control in nonlinear systems?Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural NetworksReinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraintsAn improved iterative computational approach to the solution of the Hamilton–Jacobi equation in optimal control problems of affine nonlinear systems with applicationRobust stabilization of non-linear systems by discontinuous dynamic state feedback



Cites Work


This page was built for publication: Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation