Fast Nonlinear Model Predictive Control with an Application in Automotive Engineering

Albersmeyer, Jan; Beigel, Dörte; Kirches, Christian; Wirsching, Leonard; Bock, Hans Georg; Schlöder, Johannes P.

doi:10.1007/978-3-642-01094-1_37

Cited by 13 publications

(7 citation statements)

References 8 publications

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“…∇A and B(w). Therefore, problem (3) with currently available but inexact sensitivities is solved at a faster rate [23], [24]. To account for the inexact Jacobian, a so-called optimality improvement step is employed by solving a slightly modified QP problem as…”

Section: B Inexact Sensitivity Schemesmentioning

confidence: 99%

“…The value of γ i cannot be computed on-line by using (23) for real time applications. However, an estimate of it can be obtained by relying on the following theorem.…”

Section: Practical Implementationmentioning

confidence: 99%

“…According to Theorem 2, if the singular values of M −1 (p i ) are all equal, (23) holds for γ i = 1. For general matrices whose singular values are not identical, (23) holds for γ i > 1. Hence, γ i is estimated by…”

Section: Practical Implementationmentioning

confidence: 99%

See 2 more Smart Citations

An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control

Chen

Bruschetta

Cuccato

et al. 2019

IEEE Trans. Automat. Contr.

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In recent years, efficient optimization algorithms for Nonlinear Model Predictive Control (NMPC) have been proposed, that significantly reduce the on-line computational time. In particular, direct multiple shooting and Sequential Quadratic Programming (SQP) are used to efficiently solve Nonlinear Programming (NLP) problems arising from continuoustime NMPC applications. One of the computationally demanding steps for on-line optimization is the computation of sensitivities of the nonlinear dynamics at every sampling instant, especially for systems of large dimensions, strong stiffness, and when using long prediction horizons. In this paper, within the algorithmic framework of the Real-Time Iteration (RTI) scheme based on multiple shooting, an inexact sensitivity updating scheme is proposed, that performs a partial update of the Jacobian of the constraints in the NLP. Such update is triggered by using a Curvature-like Measure of Nonlinearity (CMoN), so that only sensitivities exhibiting highly nonlinear behaviour are updated, thus adapting to system operating conditions and possibly reducing the computational burden. An advanced tuning strategy for the updating scheme is provided to automatically determine the number of sensitivities being updated, with a guaranteed bounded error on the Quadratic Programming (QP) solution. Numerical and control performance of the scheme is evaluated by means of two simulation examples performed on a dedicated implementation. Local convergence analysis is also presented and a tunable convergence rate is proven, when applied to the SQP method.Index Terms-nonlinear model predictive control, RTI ,partial sensitivity update optimization algorithms

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Section: B Inexact Sensitivity Schemesmentioning

confidence: 99%

“…The value of γ i cannot be computed on-line by using (23) for real time applications. However, an estimate of it can be obtained by relying on the following theorem.…”

Section: Practical Implementationmentioning

confidence: 99%

See 1 more Smart Citation

An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control

Chen

Bruschetta

Cuccato

et al. 2019

IEEE Trans. Automat. Contr.

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show abstract

“…As a result, the generation of the parameterized control low Γ depends on the optimal vector p ∈ R n n Γ which is determined from equation (3). The first part of the resulting control sequences is injected into the system at each sampling time.…”

Section: Proposed Control Scheme: a Fast Nmpc Based On Fast Solvmentioning

confidence: 99%

A New Fast NMPC Scheme for Parallel Kinematic Manipulators: Design and Real-Time Experiments

Kouki

Chemori

Bouani

2019

2019 International Conference on Signal, Control and Communication (SCC)

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This paper adresses the design of a new extension of fast nonlinear model predictive control (NMPC) for parallel manipulators. The developed controller is based on a parameterized NMPC, a fast gradient solver and a proportional derived controller (PD). The main motivation behind the proposed approach is to improve the tracking performance of fast parallel manipulators and reduce the computation time per control iteration. This control scheme is faster, in terms of computing time, than the classical NMPC and ensures the robustness of the resulting closed-loop system. To demonstrate the effectiveness of the proposed controller, real time experiments are performed on a 4-DOF parallel kinematic manipulator called VELOCE.

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“…As main arguments work, the function expects a continuous-time formulation of the objective function and constraints, limits on the decision variables and values of initial estimation, both in the decision variables and the state of the algorithm (Hessian and Lagrange multipliers). Besides the SQP algorithm, facing the formulation of optimal control problem involves solving the set of equations of the model, and evaluating the solution for the quadratic performance index [39,40]. The model solution to an initial value x m taken from the sensor readings can be found from a differential equation solver.…”

Section: Sequential Quadratic Programmingmentioning

confidence: 99%

NMPC controller applied to the operation of an internal combustion engine: formulation and solution of the optimization problem in real time

Chica

Torres

Acosta

2016

Int J Interact Des Manuf

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Numerical optimization solve problems efficiently where such efficiency is focused on the speed with which the optimal x * is achieved, is open line of research and strong work in the scientific community in order to achieve control systems in dynamic processes with response times of the order of milliseconds. A clear example of this, is the implementation of optimal controller's combustion engines. For subsequent approach to the design and implementation of nonlinear model predictive control controllers, it has made a comparison of yields algorithms quadratic programming by active set with linearization restrictions, and sequential quadratic programming with single shooting technique to solve quadratic optimization problem formulation referred to a dynamic internal combustion engine of spark ignition, in embedded systems with real-time processing.

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Fast Nonlinear Model Predictive Control with an Application in Automotive Engineering

Cited by 13 publications

References 8 publications

An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control

An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control

A New Fast NMPC Scheme for Parallel Kinematic Manipulators: Design and Real-Time Experiments

NMPC controller applied to the operation of an internal combustion engine: formulation and solution of the optimization problem in real time

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