Probabilistic performance validation of deep learning‐based robust NMPC controllers

Karg, Benjamin; Álamo, T.; Lucia, Sergio

doi:10.1002/rnc.5696

Cited by 30 publications

(15 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Second, the MPC control strategy is generated, and the calibration of MPC control parameters is performed by directly learning from the data on the basis of ML. In order for the real-time response of the controller to be realized, the sample database is trained offline by using the deep neural network [66][67][68][69]. Afterwards, nondirect measurement and the state variables for MPC are designed on the basis of ML, such as reinforcement learning [70].…”

Section: Learning-based On Model Predictive Controlmentioning

confidence: 99%

A Survey on Learning-Based Model Predictive Control: Toward Path Tracking Control of Mobile Platforms

et al. 2022

View full text Add to dashboard Cite

The learning-based model predictive control (LB-MPC) is an effective and critical method to solve the path tracking problem in mobile platforms under uncertain disturbances. It is well known that the machine learning (ML) methods use the historical and real-time measurement data to build data-driven prediction models. The model predictive control (MPC) provides an integrated solution for control systems with interactive variables, complex dynamics, and various constraints. The LB-MPC combines the advantages of ML and MPC. In this work, the LB-MPC technique is summarized, and the application of path tracking control in mobile platforms is discussed by considering three aspects, namely, learning and optimizing the prediction model, the controller design, and the controller output under uncertain disturbances. Furthermore, some research challenges faced by LB-MPC for path tracking control in mobile platforms are discussed.

show abstract

Section: Learning-based On Model Predictive Controlmentioning

confidence: 99%

A Survey on Learning-Based Model Predictive Control: Toward Path Tracking Control of Mobile Platforms

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In a learning-based MPC setting, recent works such as (Hertneck et al, 2018;Rosolia et al, 2018;Karg et al, 2021) discuss a few probabilistic considerations. In this paper, we bring in a novel stochastic sampling-based design for differentiable predictive control architecture along with chance constraints for closed-loop state evolution and provide appropriate probabilistic guarantees motivated from (Hertneck et al, 2018).…”

Section: Probabilistic Guaranteesmentioning

confidence: 99%

“…While Lenz et al (2015) discussed a recurrent neural model for learning latent dynamics for MPC. In a learning-based MPC setting, various forms of probabilistic guarantees are discussed in recent works such as Hertneck et al (2018); Rosolia et al (2018); Karg et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Learning Stochastic Parametric Differentiable Predictive Control Policies

Drgoňa¹,

Mukherjee²,

Tuor³

et al. 2022

Preprint

View full text Add to dashboard Cite

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical controltheoretic methods. To address this challenge, we present a scalable alternative called stochastic parametric differentiable predictive control (SP-DPC) for unsupervised learning of neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the SP-DPC problem's value function is backpropagated through the closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy which allows for direct model-based policy optimization. We provide theoretical probabilistic guarantees for policies learned via the SP-DPC method on closed-loop stability and chance constraints satisfaction. Furthermore, we demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

show abstract

“…As discussed in [2], this result may be alternatively derived by applying the scenario approach with discarded constraints [8,6]. Adaptations of this result have been used in the context of chance constrained optimization [4,20], and stochastic model predictive control [17,15,19].…”

Section: Uncertainty Quantification Using Probabilistic Maximizationmentioning

confidence: 99%

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

Mirasierra¹,

Mammarella²,

Dabbene³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.

show abstract

Probabilistic performance validation of deep learning‐based robust NMPC controllers

Cited by 30 publications

References 61 publications

A Survey on Learning-Based Model Predictive Control: Toward Path Tracking Control of Mobile Platforms

A Survey on Learning-Based Model Predictive Control: Toward Path Tracking Control of Mobile Platforms

Learning Stochastic Parametric Differentiable Predictive Control Policies

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

Contact Info

Product

Resources

About