Approximated solutions to the nonlinear H2 and H∞ control approaches formulated in the Sobolev space

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dc.creatorDaniel N. Cardoso
dc.creatorGuilherme Vianna Raffo
dc.date.accessioned2025-04-10T14:56:06Z
dc.date.accessioned2025-09-09T00:28:31Z
dc.date.available2025-04-10T14:56:06Z
dc.date.issued2018
dc.identifier.doi10.23919/ECC.2018.8550612
dc.identifier.urihttps://hdl.handle.net/1843/81451
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.relation.ispartofEuropean Control Conference (ECC 2018)
dc.rightsAcesso Restrito
dc.subjectProgramação dinâmica
dc.subjectOtimização matemática
dc.subjectTeoria do controle
dc.subject.otherAerospace electronics , Method of moments , Optimal control , Transient analysis , Steady-state , Approximation algorithms
dc.subject.otherControl Approach , Sobolev Space , Cost Function , Numerical Experiments , Time Derivative , Control Theory , Variable Costs , Nonlinear Approach , Steady-state Performance , Transient Performance , Classical Estimation , Successive Approximation , Important Paradigm , Underactuated Systems , Optimal Control , Control Design , Mechanical Systems , Control Problem , Analytical Solutions , Optimal Control Law , Lebesgue Spaces , Nonlinear Control , Partial Differential Equations , Domain Of Interest , Gaussian Quadrature , Literary Works , External Disturbances , Nonlinear Problem , Stopping Criterion
dc.subject.otherwe proposed adapt the classical Successive Galerkin Approximation Algorithms to approximate solutions of the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isacs equations, that arises from the formulation of the nonlinear H2 and H∞ control approaches in the Sobolev space
dc.titleApproximated solutions to the nonlinear H2 and H∞ control approaches formulated in the Sobolev space
dc.typeArtigo de evento
local.citation.epage899
local.citation.spage1
local.description.resumoTwo important paradigms in control theory are the classical nonlinear H2 and H∞ control approaches. Their efficiency have already been demonstrated in several applications and the background theory is well developed. Despite their many advantages, they suffer from deficiencies such as minimum settling-time and minimum overshoot. An interesting approach to solve these lacks is the formulation of both controllers in the Sobolev space. Thanks to the nature of the W1,2- norm, the cost variable and its time derivative are taken into account in the cost functional, leading to improved transient and steady-state performance. Nevertheless, the HJB and HJBI equations that arises from the problem formulation in the Sobolev space are very hard to solve analytically. This work proposes an approach to approximate their solutions by adapting the classical Successive Galerkin Approximation Algorithms (SGAA). Numerical experiments are used to corroborate the proposed approach capacity to deal with underactuated systems when controlling the two-wheeled self-balanced vehicle.
local.publisher.countryBrasil
local.publisher.departmentENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
local.publisher.initialsUFMG
local.url.externahttps://ieeexplore.ieee.org/document/8550612

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