Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks

Bonzanini, Angelo D.; Paulson, Joel A.; Makrygiorgos, Georgios; Mesbah, Ali

doi:10.1016/j.compchemeng.2020.107174

Cited by 45 publications

(38 citation statements)

References 38 publications

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“…(b) A neural approximator may be used to find the initial solution of the MPC optimisation problem, which speeds up calculations [58,59]. (c) Neural networks are able to approximate the MPC control law [60][61][62]. For training, sufficiently rich data sets are necessary, obtained for different operating points.…”

Section: Introductionmentioning

confidence: 99%

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Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Ławryńczuk

Nebeluk

2021

Sensors

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Model Predictive Control (MPC) algorithms typically use the classical L2 cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L1 norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L1 norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function; (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L1 norm even gives better performance than the classical L2 one in terms of the classical control performance indicator that measures squared control errors.

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Section: Introductionmentioning

confidence: 99%

“…Neural networks are able to approximate the MPC control law [ 60 , 61 , 62 ]. For training, sufficiently rich data sets are necessary, obtained for different operating points.…”

Section: Introductionmentioning

confidence: 99%

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Ławryńczuk

Nebeluk

2021

Sensors

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“…The feedback techniques have the ability to overcome and reduce the impact of uncertainty [59]. The LB-MPC embeds the ML method in the MPC framework to eradicate the influence of uncertain disturbances, thus improving the performance of path tracking in mobile platforms [26,60]. The LB-MPC decouples the robustness and performance requirements by employing an additional learned model and introducing it into the MPC framework along with the nominal model.…”

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

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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.

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“…Among the several approaches to cope with stochastic dynamics [44], we mention two groups of techniques, which are popular in control theory. First, the particle-based approaches [45][46][47][48][49] with scenario trees allow coping with general (not necessarily Gaussian) models. Secondly, the tube-based approaches [50][51][52][53] approxi-mate each predicted state and input by a Gaussian distribution.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

2022

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In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

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Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks

Cited by 45 publications

References 38 publications

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

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

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

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