Nonlinear model predictive control with explicit back-offs for Gaussian process state space models

Bradford, Eric; Imsland, Lars; Rio‐Chanona, Ehecatl Antonio del

doi:10.1109/cdc40024.2019.9029443

Cited by 10 publications

(12 citation statements)

References 27 publications

(40 reference statements)

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“…The conditions (18) and (19) were applied to ensure V (0) = 0 and ∂ x V (0) = 0. The condition (20) was introduced for the following lemma, and it is not restrictive, because nonzero kernel functions k(x, x d ) = 0 for any x can be employed; examples include squared-exponential kernels.…”

Section: A Reducing the Hji Equation To An Algebraic Matrix Equationmentioning

confidence: 99%

“…Because of (75), M HJI = 0 is a sufficient condition for H HJI (x) = 0 to be satisfied for all x ∈ R nx . Next, substituting (18) and (19) into Φ(x)k vec (x) yields Φ(0)k vec (0) = 0. Note that Φ(x)k vec (x) is a linear combination of ∂ x k(x,…”

Section: B Proof Of Theoremmentioning

confidence: 99%

“…Various methods have been developed to control kernelbased system models. Model predictive control [14]- [19] can design (sub-) optimal controllers to minimize cost functions. Local (sub-) optimal controllers near reference trajectories have been calculated using differential dynamic programming [20] and an iterative linear quadratic regulator [21].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kernel-Based Hamilton–Jacobi Equations for Data-Driven Optimal and H-Infinity Control

2020

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This paper presents a data-driven method for designing optimal controllers and robust controllers for unknown nonlinear systems. Mathematical models for the realization of the control are difficult to develop owing to a lack of knowledge regarding such systems. The proposed multidisciplinary method, based on optimal control theory and machine learning with kernel functions, facilitates designing appropriate controllers using a data set. Kernel-based system models are useful for representing nonlinear systems. An optimal and an H-infinity controller can be designed by solving Hamilton-Jacobi (HJ) equations, which unfortunately, are difficult to solve owing to the nonlinearity and complexity of the kernelbased models. The objective of this study consists of overcoming two challenges. The first challenge is to derive exact solutions to the HJ equations for a class of kernel-based system models. A key technique in overcoming this challenge is to reduce the HJ equations to easily solvable algebraic matrix equations, from which optimal and H-infinity controllers are designed. The second challenge is to control an unknown system using the obtained controllers, wherein the system is identified as a kernel-based model. Additionally, this study analyzes probabilistic stability of the feedback system with the proposed controllers. Numerical simulations demonstrate control performances of both the derived optimal and Hinfinity controllers and stability of the feedback system.

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Section: A Reducing the Hji Equation To An Algebraic Matrix Equationmentioning

confidence: 99%

Section: B Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kernel-Based Hamilton–Jacobi Equations for Data-Driven Optimal and H-Infinity Control

2020

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“…In this paper we extend a method first proposed in [10,11] to the hybrid modelling case. The approach determines explicit back-offs to tighten constraints offline using closed-loop Monte Carlo (MC) simulations for finite horizon control problems.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes

Bradford

Imsland

Reble

et al. 2021

Recent Advances in Model Predictive Control

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Nonlinear model predictive control (NMPC) is an efficient approach for the control of nonlinear multivariable dynamic systems with constraints, which however requires an accurate plant model. Plant models can often be determined from first principles, parts of the model are however difficult to derive using physical laws alone. In this paper a hybrid Gaussian process (GP) first principles modeling scheme is proposed to overcome this issue, which exploits GPs to model the parts of the dynamic system that are difficult to describe using first principles. GPs not only give accurate predictions, but also quantify the residual uncertainty of this model. It is vital to account for this uncertainty in the control algorithm, to prevent constraint violations and performance deterioration. Monte Carlo samples of the GPs are generated offline to tighten constraints of the NMPC to ensure joint probabilistic constraint satisfaction online. Advantages of our method include fast online evaluation times, possibility to account for online learning alleviating conservativeness, and exploiting the flexibility of GPs and the data efficiency of first principle models. The algorithm is verified on a case study involving a challenging semi-batch bioreactor.

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“…Others are devoted to design robust NMPC schemes such as min-max NMPC, 27,28 tube-based NMPC, 29,30 and NMPC modified with back-off constraints. 31,32 Here, we introduce multistage NMPC 22 to address parametric uncertainty by discretizing the uncertainty and modeling the evolution of uncertainty realizations with a scenario tree. Solving a larger optimization problem based on the generated scenario tree, multistage NMPC is able to provide an optimal closed-loop feedback control for the process, even when the realization of uncertainty for the next step is unknown.…”

Section: Introductionmentioning

confidence: 99%

Multistage nonlinear model predictive control for pumping treatment in hydraulic fracturing

Lin

Eason²,

Biegler

2021

AIChE Journal

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Hydraulic fracturing has gained increasing attention as it allows the constrained natural gas and crude oil to flow out of low-permeability shale formations and significantly increase production. Perilous operating states of extremely high pressure also raise some safety concerns, requiring us to formulate an appropriate dynamic model, and provide a careful engineering control to ensure safe operating conditions. Moreover, uncertainties due to spatially varying rock properties increase the difficulties in control of the fracturing process. In this work, we formulate a first-principles model by considering the fracture evolution, mass transport of substances in the slurry, changing fluid properties, and the monitored operating pressure on the ground level.Next, we implement nonlinear model predictive control (NMPC) to control the process under a set of final requirements and process constraints. Our results show that the performance of standard NMPC degrades when the rock uncertainty causes the parameter mismatch between the process and the predictive model in the controller.With standard NMPC, designed with a nominal model, the process fails to meet the terminal requirements of fracture geometry, and pressure is violated in one of the parameter mismatch cases. Therefore, we resort to multistage NMPC, which considers uncertainty evolution in a scenario tree with separate control sequences to address constraint violations. We demonstrate that multistage NMPC presents good performance by showing constraint satisfaction whether the uncertain rock parameter realization is time-invariant or time-variant. We also simulate the process with multistage NMPC including different numbers of scenarios and compare their control performance. Our investigation demonstrates that multistage NMPC effectively manages parametric uncertainties attributed to non-homogeneous rock formation, and provides a promising control strategy for the hydraulic fracturing process.

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Nonlinear model predictive control with explicit back-offs for Gaussian process state space models

Cited by 10 publications

References 27 publications

Kernel-Based Hamilton–Jacobi Equations for Data-Driven Optimal and H-Infinity Control

Kernel-Based Hamilton–Jacobi Equations for Data-Driven Optimal and H-Infinity Control

Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes

Multistage nonlinear model predictive control for pumping treatment in hydraulic fracturing

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