Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control

Nonlinear model predictive control (NMPC) generally requires the solution of a non-convex dynamic optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or that may include implicit algebraic equations. This...

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Bibliographic Details
Published in:Optimization methods & software Vol. 36; no. 5; pp. 1030 - 1058
Main Authors: Hespanhol, Pedro, Quirynen, Rien
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.09.2021
Taylor & Francis Ltd
Subjects:
Algorithms
Convergence
convergence analysis
Differential equations
direct collocation
Jacobi matrix method
Jacobian matrix
multiple shooting
Nonlinear control
Nonlinear model predictive control
Optimal control
Optimization
Predictive control
Quadratic programming
quasi-Newton updates
sequential quadratic programming
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:Nonlinear model predictive control (NMPC) generally requires the solution of a non-convex dynamic optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or that may include implicit algebraic equations. This paper provides a local convergence analysis for the recently proposed adjoint-based sequential quadratic programming (SQP) algorithm that is based on a block-structured variant of the two-sided rank-one (TR1) quasi-Newton update formula to efficiently compute Jacobian matrix approximations in a sparsity preserving fashion. A particularly efficient algorithm implementation is proposed in case an implicit integration scheme is used for discretization of the optimal control problem, in which matrix factorization and matrix-matrix operations can be avoided entirely. The convergence analysis results as well as the computational performance of the proposed optimization algorithm are illustrated for two simulation case studies of NMPC.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2019.1653869