Auto Generation of Implicit Integrators for Embedded NMPC with Microsecond Sampling Times

Quirynen, Rien; Vukov, Milan; Diehl, Moritz

doi:10.3182/20120823-5-nl-3013.00013

Cited by 29 publications

(39 citation statements)

References 11 publications

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“…This section compactly describes the general implementation of auto generated IRK methods, presented earlier in [8] and [9]. Their formulation is handled in Subsection III-A, for ODE as well as DAE systems of index 1.…”

Section: Auto Generated Irk Methodsmentioning

confidence: 99%

“…This direct approach provides very accurate sensitivities, which is important for optimization. The Jacobian evaluation in (10) and its factorization can be reused in (8) for the next integration step [8]. Algorithm 1 compactly describes the resulting implementation.…”

Section: Sensitivity Generationmentioning

confidence: 99%

“…The assumption in this paper is therefore that the step size and order of the integration method are fixed. It has been shown that code generation for Implicit Runge-Kutta (IRK) methods with a tailored approach for computing the sensitivities can be very efficient [8]. This is important because of the attractive properties of A-stable IRK methods and their natural extension from systems of Ordinary Differential Equations (ODE) to Differential Algebraic Equations (DAE) of index 1.…”

Section: Introductionmentioning

confidence: 99%

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Efficient NMPC for nonlinear models with linear subsystems

Quirynen

Gros

Diehl

2013

52nd IEEE Conference on Decision and Control

Self Cite

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Real-time optimal control algorithms for fast, mechatronic systems need to be run on embedded hardware and they need to respect tight timing constraints. When using nonlinear models, the simulation and generation of sensitivities forms a computationally demanding part of any algorithm. Automatic code generation of Implicit Runge-Kutta (IRK) methods has been shown to reduce its CPU time significantly. However, a typical model also shows a lot of structure that can be exploited in a rather elegant and efficient way. The focus of this paper is on nonlinear models with linear subsystems. With the proposed model formulation, the new auto generated integrators can be considered a powerful generalization of other solvers, e.g. those that support quadrature variables. A speedup of up to 5 − 10 is shown in the integration time for two examples from the literature.

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Section: Auto Generated Irk Methodsmentioning

confidence: 99%

Section: Sensitivity Generationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient NMPC for nonlinear models with linear subsystems

Quirynen

Gros

Diehl

2013

52nd IEEE Conference on Decision and Control

Self Cite

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“…Recent extensions of the ACADO Code Generation tool include support for implicit integrators for ODEs and differential algebraic equations (DAEs) [24,25]. One of the inherent properties of the multiple shooting algorithm is that model simulation and sensitivity generation can be performed on each shooting interval independently.…”

Section: Fast Solvers Based On Automatic Code Generationmentioning

confidence: 99%

“…Both schemes are based on a piecewise constant control parametrization and the system dynamics f(x, u) are discretized over the shooting intervals using an implicit Runge-Kutta method of order 2 [25].…”

Section: Control Of Autonomous Vehiclesmentioning

confidence: 99%

Model Predictive Control of Autonomous Vehicles

Zanon¹,

Frasch

Vukov³

et al. 2014

Lecture Notes in Control and Information Sciences

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The control of autonomous vehicles is a challenging task that requires advanced control schemes. Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) are optimization-based control and estimation techniques that are able to deal with highly nonlinear, constrained, unstable and fast dynamic systems. In this chapter, these techniques are detailed, a descriptive nonlinear model is derived and the performance of the proposed control scheme is demonstrated in simulations of an obstacle avoidance scenario on a low-fricion icy road. IntroductionDue to the well known vehicle-road dynamics, Model Predictive Control (MPC) is an excellent tool for precise trajectory planning in autonomous vehicle guidance, which can be of great importance in dangerous driving situations. High sampling rates (i.e., in the range of tenths of Hertz) and long prediction horizons however, which are required for a safe operation, pose a computational challenge, particularly in combination with the involved nonlinear vehicle dynamics. Many recent chapter chose a two-level MPC approach to overcome this computational challenge, being composed of a coarse path planning algorithm with a long prediction horizon, and a higher-fidelity path following algorithm on a shorter horizon, cf.

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Optimal experiment design for nonlinear dynamic (bio)chemical systems using sequential semidefinite programming

et al. 2014

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Optimal experiment design (OED) for parameter estimation in nonlinear dynamic (bio)chemical processes is studied in this work. To reduce the uncertainty in an experiment, a suitable measure of the Fisher information matrix or variance–covariance matrix has to be optimized. In this work, novel optimization algorithms based on sequential semidefinite programming (SDP) are proposed. The sequential SDP approach has specific advantages over sequential quadratic programming in the context of OED. First of all, it guarantees on a matrix level a decrease of the uncertainty in the parameter estimation procedure by introducing a linear matrix inequality. Second, it allows an easy formulation of E‐optimal designs in a direct optimal control optimization scheme. Finally, a third advantage of SDP is that problems involving the inverse of a matrix can be easily reformulated. The proposed techniques are illustrated in the design of experiments for a fed‐batch bioreactor and a microbial kinetics case study. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1728–1739, 2014

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Auto Generation of Implicit Integrators for Embedded NMPC with Microsecond Sampling Times

Cited by 29 publications

References 11 publications

Efficient NMPC for nonlinear models with linear subsystems

Efficient NMPC for nonlinear models with linear subsystems

Model Predictive Control of Autonomous Vehicles

Optimal experiment design for nonlinear dynamic (bio)chemical systems using sequential semidefinite programming

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