Successive Galerkin approximation algorithms for nonlinear optimal and robust control

DOI10.1080/002071798221542zbMath0945.49021OpenAlexW2068328804MaRDI QIDQ4955091

Timothy W. McLain, Randal W. Beard

Publication date: 12 June 2000

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2936&context=facpub

zbMATH Keywords

robust controlnonlinear optimal controlclosed-loop controlHamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equationssuccessive Galerkin approximation algorithms

Mathematics Subject Classification ID

Related Items (38)

Generalized nonlinear ℋ︁_∞ synthesis condition with its numerically efficient solution ⋮ Finite element methods for isotropic Isaacs equations with viscosity and strong Dirichlet boundary conditions ⋮ Robust optimal control of uncertain nonaffine MIMO nonlinear discrete-time systems with application to HCCI engines ⋮ Energy compensation-based approach for solving the HJI equation in the nonlinear H ∞ synthesis ⋮ Optimization of approximating networks for optimal fault diagnosis ⋮ A robust optimal control approach in the weighted Sobolev space for underactuated mechanical systems ⋮ Value-Gradient Based Formulation of Optimal Control Problem and Machine Learning Algorithm ⋮ SOS-based policy iteration for H_∞ control of polynomial systems with uncertain parameters ⋮ An iterative computational scheme for solving the coupled Hamilton-Jacobi-Isaacs equations in nonzero-sum differential games of affine nonlinear systems ⋮ Passivity‐based control design frameworks for hybrid nonlinear time‐varying dynamical systems ⋮ Unnamed Item ⋮ Robust Feedback Control of Nonlinear PDEs by Numerical Approximation of High-Dimensional Hamilton--Jacobi--Isaacs Equations ⋮ Neural network solution for finite-horizonH_∞state feedback control of nonlinear systems ⋮ Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems ⋮ Galerkin Method and Weighting Functions Applied to Nonlinear H∞ Control with Output Feedback ⋮ Online concurrent reinforcement learning algorithm to solve two‐player zero‐sum games for partially unknown nonlinear continuous‐time systems ⋮ Solutions of nonlinear optimal and robust control problems via a mixed collocation/DAE's based algorithm ⋮ Feedback control method using Haar wavelet operational matrices for solving optimal control problems ⋮ Variable structure disturbance rejection control for nonlinear uncertain systems with state and control delays via optimal sliding mode surface approach ⋮ An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm ⋮ Iterative computational approach to the solution of the Hamilton-Jacobi-Bellman-Isaacs equation in nonlinear optimal control ⋮ A neural network-based policy iteration algorithm with global \(H^2\)-superlinear convergence for stochastic games on domains ⋮ On the convergence of successive Galerkin approximation for nonlinear output feedback \(H_{\infty}\) control ⋮ Online solution of nonquadratic two-player zero-sum games arising in theH_∞control of constrained input systems ⋮ Approximating networks and extended Ritz method for the solution of functional optimization problems ⋮ Successive approximation procedure of optimal tracking control for nonlinear similar composite systems ⋮ A mixed PI/VI design method for nonlinear H_∞ Control ⋮ Nonlinear optimal approach to spacecraft formation flying using Lorentz and impulsive actuation ⋮ A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear \(H_\infty \) control ⋮ Feedback controller design for linear and a class of nonlinear optimal control problems ⋮ Approximate optimal adaptive control for weakly coupled nonlinear systems: A neuro-inspired approach ⋮ The design of suboptimal asymptotic stabilising controllers for nonlinear slowly varying systems ⋮ Non-equilibrium dynamic games and cyber-physical security: a cognitive hierarchy approach ⋮ Computationally efficient simultaneous policy update algorithm for nonlinearH_∞state feedback control with Galerkin's method ⋮ A numerical approach to hybrid nonlinear optimal control ⋮ When does stabilizability imply the existence of infinite horizon optimal control in nonlinear systems? ⋮ An improved iterative computational approach to the solution of the Hamilton–Jacobi equation in optimal control problems of affine nonlinear systems with application ⋮ Robust stabilization of non-linear systems by discontinuous dynamic state feedback

This page was built for publication: Successive Galerkin approximation algorithms for nonlinear optimal and robust control