Fast NMPC of a chain of masses connected by springs

Wirsching, Leonard; Bock, Hans H.; Diehl, Moritz

doi:10.1109/cca.2006.285936

Cited by 20 publications

(15 citation statements)

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“…In order to efficiently solve the inequality constrained OCP in (3), let us consider the adjoint-based SQP algorithm with Gauss-Newton type Hessian approximation and inexact Jacobian information as introduced originally in [7,39] for fast nonlinear MPC. Each SQP iteration solves a convex QP subproblem…”

Section: Sqp Algorithm With Inexact Jacobiansmentioning

confidence: 99%

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

Hespanhol

Quirynen

2019

Optimization Methods and Software

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Nonlinear model predictive control (NMPC) generally requires the solution of a non-convex 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 twosided 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 nonlinear MPC.

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Section: Sqp Algorithm With Inexact Jacobiansmentioning

confidence: 99%

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

Hespanhol

Quirynen

2019

Optimization Methods and Software

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“…We consider the chain mass control problem, presented in (Wirsching et al, 2006). The task of the controller is to return a chain of masses connected with springs to its steady state, starting from a perturbed initial configuration.…”

Section: Nmpc Case Study: Chain Of Massesmentioning

confidence: 99%

Hardware Tailored Linear Algebra for Implicit Integrators in Embedded NMPC

et al. 2017

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Nonlinear Model Predictive Control (NMPC) requires the efficient treatment of the dynamic model in the form of a system of continuous-time differential equations. Newtontype optimization relies on a numerical simulation method in addition to the propagation of first or higher order derivatives. In the case of stiff or implicitly defined dynamics, implicit integration schemes are typically preferred. This paper proposes a tailored implementation of the necessary linear algebra routines (LU factorization and triangular solutions), in order to allow for a considerable computational speedup of such integrators. In particular, the opensource BLASFEO framework is presented as a library of efficient linear algebra routines for small to medium-scale embedded optimization applications. Its performance is illustrated on the nonlinear optimal control example of a chain of masses. The proposed library allows for considerable speedups and it is found to be overall competitive with both a code-generated solver and a high-performance BLAS implementation.

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“…The control problem in this benchmark example is to stabilize a chain of masses that operate under state and input constraints using the MPC approach . The optimization problem is formulated and converted to a dense form that consists of n = 240 variables and involves m = 1898 linear inequality constraints.…”

Section: Dominant Speed Factorsmentioning

confidence: 99%

Dominant speed factors of active set methods for fast MPC

Herceg

Jones

Morari

2014

Optim Control Appl Methods

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The paper presents a review of active set (AS) algorithms that have been deployed for implementation of fast model predictive control (MPC). The main purpose of the survey is to identify the dominant features of the algorithms that contribute to fast execution of online MPC and to study their influence on the speed. The simulation study is conducted on two benchmark examples where the algorithms are analyzed in the number of iterations and in the workload per iteration. The obtained results suggest directions for potential improvement in the speed of existing AS algorithms.

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Fast NMPC of a chain of masses connected by springs

Cited by 20 publications

References 0 publications

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

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

Hardware Tailored Linear Algebra for Implicit Integrators in Embedded NMPC

Dominant speed factors of active set methods for fast MPC

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