Advanced-step multistage nonlinear model predictive control: Robustness and stability

Yu, Zhou; Biegler, Lorenz T.

doi:10.1016/j.jprocont.2019.10.006

Cited by 20 publications

(12 citation statements)

References 28 publications

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“…The gradient and Hessian of the function Q θ needed in (19) require one to compute the sensitivities of the optimal value of NLP (15). Let us define the Lagrange function L θ associated to the RNMPC problem (15) as follows:…”

Section: B Sensitivity Analysismentioning

confidence: 99%

“…Researchers in [18] proposed to use a tube-based MPC with a Min-Max differential inequality. Multi-stage or Scenario-tree NMPC scheme was proposed in [19], [20] as a real-time NMPC that accounts for the uncertain influence and generates decisions to control a nonlinear plant in a robust sense. These approaches remain challenging for problems that are not of small scale.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Robust NMPC using Reinforcement Learning

Esfahani¹,

Kordabad²,

Gros³

2021

Preprint

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We present a Reinforcement Learning-based Robust Nonlinear Model Predictive Control (RL-RNMPC) framework for controlling nonlinear systems in the presence of disturbances and uncertainties. An approximate Robust Nonlinear Model Predictive Control (RNMPC) of low computational complexity is used in which the state trajectory uncertainty is modelled via ellipsoids. Reinforcement Learning is then used in order to handle the ellipsoidal approximation and improve the closed-loop performance of the scheme by adjusting the MPC parameters generating the ellipsoids. The approach is tested on a simulated Wheeled Mobile Robot (WMR) tracking a desired trajectory while avoiding static obstacles.

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Section: B Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate Robust NMPC using Reinforcement Learning

Esfahani¹,

Kordabad²,

Gros³

2021

Preprint

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show abstract

“…Its application has already been demonstrated on CSTR, quadtank, and semi-batch reactor examples. 23,33 Compared to the aforementioned robust NMPCs, multistage NMPC shows a less conservative control policy because each scenario considers a separate sequence of control inputs to counteract the effect of uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…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. Its application has already been demonstrated on CSTR, quadtank, and semi‐batch reactor examples 23,33 . Compared to the aforementioned robust NMPCs, multistage NMPC shows a less conservative control policy because each scenario considers a separate sequence of control inputs to counteract the effect of uncertainties.…”

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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“…These RL control policies can provide different strategies to handle uncertainties compared to robust MPC schemes such as min‐max MPC, 32 tube‐based MPC, 33 and scenario‐tree MPC 34 where the optimization problems need to be solved at each sample time considering the possible scenarios from current state. Here, it is worth noting that there exist several strategies to reduce the online computational load of MPC such as advanced‐step MPC, 35,36 MPC using neighboring‐extremal updates strategy, 37 and explicit MPC 38 . Although RL approach cannot consider input and state constraints explicitly, there are several methods for considering constraints.…”

Section: Introductionmentioning

confidence: 99%

Model‐based reinforcement learning for nonlinear optimal control with practical asymptotic stability guarantees

Kim

Lee

2020

AIChE Journal

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We propose a new reinforcement learning approach for nonlinear optimal control where the value function is updated as restricted to control Lyapunov function (CLF) and the policy is improved using a variation of Sontag's formula. The practical asymptotic stability of the closed‐loop system is guaranteed during the training and at the end of training without requiring an additional actor network and its update rule. For a single‐layer neural network (NN) with exact basis functions, the approximate function converges to the optimal value function, resulting in the optimal controller. When a deep NN is used, the level set shapes of the trained NN become similar to those of the optimal value function. Because Sontag's formula with CLF is equivalent to the optimal controller when the given CLF has the same level set shapes as the optimal value function, Sontag's formula with the trained NN provides a nearly optimal controller.

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Advanced-step multistage nonlinear model predictive control: Robustness and stability

Cited by 20 publications

References 28 publications

Approximate Robust NMPC using Reinforcement Learning

Approximate Robust NMPC using Reinforcement Learning

Multistage nonlinear model predictive control for pumping treatment in hydraulic fracturing

Model‐based reinforcement learning for nonlinear optimal control with practical asymptotic stability guarantees

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