Dual robust nonlinear model predictive control: A multi-stage approach

Summary In this article, we present a tube‐based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set‐membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared with robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean‐squared point estimate in the objective function the framework ensures finite‐gain ℒ2 stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and nonincreasing properties on general parameter estimation algorithms and tube/set‐based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this article, we provide similar conditions for a tube‐based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared with state of the art approaches.

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“…failure to provide theoretical guarantees regarding recursive feasibility, closed‐loop stability, and constraint satisfaction, 14‐16,18 …”

Section: Introductionmentioning

confidence: 99%

A robust adaptive model predictive control framework for nonlinear uncertain systems

Köhler

Kötting

Soloperto

et al. 2020

Intl J Robust & Nonlinear

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“…In the presence of continuous-valued uncertainty, representing all possible values of the uncertainty is infeasible. Usually, a good trade-off between robustness and computational cost is achieved by generating the scenario tree for all combinations of the minimum, nominal and maximum values of the uncertain parameters or disturbances [21,22]. This results in a box over-approximation of the true uncertainty region.…”

Section: Introductionmentioning

confidence: 99%

Robust Multi-Stage Nonlinear Model Predictive Control Using Sigma Points

2020

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We address the question of how to reduce the inevitable loss of performance that is incurred by robust multi-stage NMPC due to the lack of knowledge compared to the case where the exact plant model (no uncertainty) is available. Multi-stage NMPC in the usual setting over-approximates a continuous parametric uncertainty set by a box and includes the corners of the box and the center point into the scenario tree. If the uncertainty set is not a box, this augments the uncertainty set and results in a performance loss. In this paper, we propose to mitigate this problem by two different approaches where the scenario tree of the multi-stage NMPC is built using sigma points. The chosen sigma points help to capture the true mean and covariance of the uncertainty set more precisely. The first method computes a box over-approximation of the reachable set of the system states whereas the second method computes a box over-approximation of the reachable set of the constraint function using the unscented transformation. The advantages of the proposed schemes over the traditional multi-stage NMPC are demonstrated using simulation studies of a simple semi-batch reactor and a more complex industrial semi-batch polymerization reactor benchmark example.

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“…The first class of approaches is referred to as explicit [25][26][27][28][29] and the latter one as implicit. [30][31][32][33][34] In this work, we will use an implicit approach that is based on multi-stage NMPC framework of Thangavel et al 35,36 since, despite being computationally more demanding as an explicit dual-control strategy, it requires no a priori tuning of the objective regarding the importance of the probing and optimizing control actions. We adapt this method into the shrinking-horizon-based control for batch processes.…”

Section: Introductionmentioning

confidence: 99%

Dual-Control-Based Approach to Batch Process Operation under Uncertainty Based on Optimality-Conditions Parametrization

Paulen

Fikar

2019

Ind. Eng. Chem. Res.

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This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control.A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model parameters can be learned precisely enough to increase the robust performance of the plant. Some recently proposed approaches can be used to tackle this problem, however, this will be done at the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The dual features of the controller are incorporated through scenario-based (multi-stage) approach, which allows for modeling of the adaptive robust decision problem and for projecting this decision into predictions of the controller. The proposed approach is illustrated on a case study from batch membrane filtration.

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Dual robust nonlinear model predictive control: A multi-stage approach

Cited by 41 publications

References 33 publications

A robust adaptive model predictive control framework for nonlinear uncertain systems

A robust adaptive model predictive control framework for nonlinear uncertain systems

Robust Multi-Stage Nonlinear Model Predictive Control Using Sigma Points

Dual-Control-Based Approach to Batch Process Operation under Uncertainty Based on Optimality-Conditions Parametrization

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