FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs

Zanelli, Andrea; Domahidi, Alexander; Jerez, Juan L.; Morari, Manfred

doi:10.1080/00207179.2017.1316017

Cited by 171 publications

(119 citation statements)

References 41 publications

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“…Constraints are introduced based on Remark 3 considering a maximum probability of individual constraint violation of 2.28%, corresponding to a 2-σ confidence bound. The MPC optimization problem (18) is solved using FORCES Pro [38], [39]. Fig.…”

Section: A Gp-based Reference Tracking Controllermentioning

confidence: 99%

Cautious Model Predictive Control Using Gaussian Process Regression

Hewing

Kabzan

Zeilinger

2020

IEEE Trans. Contr. Syst. Technol.

415

334

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Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.

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Section: A Gp-based Reference Tracking Controllermentioning

confidence: 99%

Cautious Model Predictive Control Using Gaussian Process Regression

Hewing

Kabzan

Zeilinger

2020

IEEE Trans. Contr. Syst. Technol.

415

334

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“…We use dynamic constraint tightening for the first N shrink = 30 time steps and consider 10 inducing inputs to reduce the complexity of GP evaluations. The FORCES Pro solver [22], [23] was used to solve the underlying optimization problem, in which the maximum number of iterations was limited to 60 to ensure consistent maximum solve times. A delay compensation of one time step is used to compensate for the solver computation time.…”

Section: B Controller Implementationmentioning

confidence: 99%

Learning-Based Model Predictive Control for Autonomous Racing

Kabzan

Hewing

Liniger

et al. 2019

IEEE Robot. Autom. Lett.

300

155

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In this paper, we present a learning-based control approach for autonomous racing with an application to the AMZ Driverless race car gotthard. One major issue in autonomous racing is that accurate vehicle models that cover the entire performance envelope of a race car are highly nonlinear, complex and complicated to identify, rendering them impractical for control. To address this issue, we employ a relatively simple nominal vehicle model, which is improved based on measurement data and tools from machine learning. The resulting formulation is an online learning data-driven Model Predictive Controller, which uses Gaussian Processes regression to take residual model uncertainty into account and achieve safe driving behavior. To improve the vehicle model online, we select from a constant inflow of data points according to a criterion reflecting the information gain, and maintain a small dictionary of 300 data points. The framework is tested on the full-size AMZ Driverless race car, where it is able to improve the vehicle model and reduce lap times by 10% while maintaining safety of the vehicle.

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“…Since the input MB scheme considers more state and path constraints, its time for solving QP is slightly higher than that of nonuniform grid scheme. It is interesting to compare performance of a specific parameterization of scheme B that shows similar computational time to that of scheme C. This can be achieved by increasing the number of intervals for non-uniform grid NMPC (scheme B) to M = 42 with I =[0, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,28,32,35,37,40,42,44,46,48,50,52,55,60,65,70,75,80] The state and control trajectories are shown in Fig. 4 and the KKT values are shown in Fig.…”

Section: A Control Of An Inverted Pendulummentioning

confidence: 99%

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Chen

Scarabottolo²,

Bruschetta³

et al. 2020

IET Control Theory & Applications

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Move blocking (MB) is a widely used strategy to reduce the degrees of freedom of the Optimal Control Problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretization steps. In this paper, we focus on developing computationally efficient MB schemes for multiple shooting based nonlinear model predictive control (NMPC). The degrees of freedom of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretization accuracy and level of sparsity is maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretization nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the nonuniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimization accuracy and constraints fulfillment is shown by means of simulations with two different problems.

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FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs

Cited by 171 publications

References 41 publications

Cautious Model Predictive Control Using Gaussian Process Regression

Cautious Model Predictive Control Using Gaussian Process Regression

Learning-Based Model Predictive Control for Autonomous Racing

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

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