A Preliminary Analysis of Mesh Refinement for Optimal Control Using Discontinuity Detection via Jump Function Approximations

2018 ◽  
Author(s):  
Alexander T. Miller ◽  
William W. Hager ◽  
Anil V. Rao
Keyword(s):  
Optimal Control ◽  
Preliminary Analysis ◽  
Mesh Refinement ◽  
Discontinuity Detection ◽  
Jump Function ◽  
Function Approximations

A high-order Discontinuous Galerkin Method with mesh refinement for optimal control

Automatica ◽  
2017 ◽  
Vol 85 ◽  
pp. 70-82 ◽  
Author(s):  
João C.C. Henriques ◽  
João M. Lemos ◽  
Luís Eça ◽  
Luís M.C. Gato ◽  
António F.O. Falcão
Keyword(s):  
Optimal Control ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Mesh Refinement ◽  
High Order

scholarly journals A collocation method for optimal control of linear systems with inequality constraints

1998 ◽  
Vol 3 (6) ◽  
pp. 503-515 ◽  
Author(s):  
M. Razzaghi ◽  
J. Nazarzadeh ◽  
K. Y. Nikravesh
Keyword(s):  
Optimal Control ◽  
Operational Matrix ◽  
Inequality Constraints ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Block Pulse Functions ◽  
Quadratic Optimal Control ◽  
Operational Matrix Of Integration ◽  
Function Approximations ◽  
Control Of Linear Systems

A numerical method for solving linear quadratic optimal control problems with control inequality constraints is presented in this paper. The method is based upon hybrid function approximations. The properties of hybrid functions which are the combinations of block-pulse functions and Legendre polynomials are first presented. The operational matrix of integration is then utilized to reduce the optimal control problem to a set of simultaneous nonlinear equations. The inequality constraints are first converted to a system of algebraic equalities, these equalities are then collocated at Legendre–Gauss–Lobatto nodes. An illustrative example is included to demonstrate the validity and applicability of the technique.

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