Non-conservative robust Nonlinear Model Predictive Control via scenario decomposition

Lucia, Sergio; Subramanian, Sankaranarayanan; Engell, Sebastian

doi:10.1109/cca.2013.6662813

Cited by 10 publications

(12 citation statements)

References 14 publications

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“…The implementation for all cases taking scenarios greater than N r =149 was not possible owing to memory issues. Hence, some simplification assumptions as those used in or parallel computing techniques might be useful. Another way to address the problem generated by the computer effort is to use an MS‐MPC based on the three‐scenarios approach, described in Section 4.3.…”

Section: Resultsmentioning

confidence: 99%

“…Some works that address the CC‐MPC approach in water systems are and references therein. On the other hand, in the TB‐MPC, uncertainty is addressed by considering simultaneously a set of possible disturbance scenarios modeled as a rooted tree, which branches along the prediction horizon with a common initial value of the disturbances (e.g., ). This technique computes a set of control input sequences, one per each scenario in the disturbance tree, but only applies the first element from all sequences, which is the same for all the possible scenarios considered.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic model predictive control approaches applied to drinking water networks

Grosso

Velarde

Ocampo‐Martínez

et al. 2016

Optim. Control Appl. Meth.

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Control of drinking water networks is an arduous task given their size and the presence of uncertainty in water demand. It is necessary to impose different constraints for ensuring a reliable water supply in the most economic and safe ways. To cope with uncertainty in system disturbances due to the stochastic water demand/consumption, and optimize operational costs, this paper proposes three stochastic model predictive control (MPC) approaches, namely: chance-constrained MPC, tree-based MPC, and multiplescenarios MPC. A comparative assessment of these approaches is performed when they are applied to real case studies, specifically, a sector and an aggregate version of the Barcelona drinking water network in Spain.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic model predictive control approaches applied to drinking water networks

Grosso

Velarde

Ocampo‐Martínez

et al. 2016

Optim. Control Appl. Meth.

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“…Dual decomposition strategies for distributed multistage scenario optimization were presented in [7], where the individual subproblems are solved by relaxing the nonanticipativity constraints. The master problem iteratively adjusts the Lagrange multiplier (the dual variables) to coordinate the different scenarios.…”

Section: Introductionmentioning

confidence: 99%

Improving Scenario Decomposition for Multistage MPC Using a Sensitivity-Based Path-Following Algorithm

Krishnamoorthy

Suwartadi

Foss

et al. 2018

IEEE Control Syst. Lett.

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This paper proposes a computationally efficient algorithm for robust multistage model predictive control (MPC). In multistage scenario MPC, the evolution of uncertainty in the prediction horizon is represented via a scenario tree. The resulting large-scale optimization problem can be decomposed into several smaller subproblems where, for example, each subproblem solves a single scenario. Since the different scenarios differ only in the uncertain parameters, the distributed scenario MPC problem can be cast as a parametric nonlinear programming (NLP) problem. By using the NLP sensitivity, we do not need to solve all the subproblems as full NLPs. Instead they can be solved exploiting the parametric nature by a path-following predictor-corrector algorithm that approximates the NLP. This results in a computationally efficient multistage scenario MPC framework. Simulation results show that the sensitivity-based distributed multistage MPC provides a very good approximation of the fully centralized scenario MPC.

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“…In this case study, the implementation for all cases taking N s = {599, 5999} was not possible due to memory issues. Hence, some simplification assumptions as those used in [17] or parallel computing techniques might be useful.…”

Section: R E V I S E Dmentioning

confidence: 99%

“…Regarding TB-MPC, see, e.g., [17,24], uncertainty is addressed by considering simultaneously a set of possible disturbance scenarios modelled as a rooted tree, which branches along the prediction horizon. On the other hand, CC-MPC [28] is a stochastic control strategy that describes robustness in terms of probabilistic (chance) constraints, which require that the probability of violation of any operational requirement or physical constraint is below a prescribed value, representing the notion of reliability or risk of the system.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Model Predictive Control for Water Transport Networks with Demand Forecast Uncertainty

Grosso

Ocampo‐Martínez

Puig³

2017

Advances in Industrial Control

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One of the challenges in water system management is the existence of different sources of uncertainty. The availability of historical data allows to accurately predict the behaviour of the system disturbances over large horizons, but still a meaningful degree of uncertainty is present. In previous chapters, the use of MPC to tackle the complex multi-variable interactions and large-scale nature of drinking-water network control is proposed. There are several examples of MPC applied to water systems in the literature, see, e.g., [2,7,10,16, 29, 30] and references therein.In a DWN, the main management purpose is the achievement of the highest level of consumer satisfaction and service quality in line with the prevailing regulatory framework, while making best use of available resources. Hence, networks must be reliable and resilient while being subject to constraints and to continuously varying conditions with both deterministic and probabilistic nature. Customer behaviour determines the transport and storage operations within the network, and flow demands can vary in both the long and the short term, often presenting time-based patterns in some applications. Therefore, a better understanding and forecasting of demands will improve both modelling and control of DWNs.While Chaps. 12 and 13 deal with the uncertainty in the classical way of feedforward action, this chapter focuses on the way that uncertainty can be faced by using stochastic-based approaches. The simplest way to do this is by ignoring the explicit influence of disturbances or using their expected value as done in the previous chapters. However, dealing with the demand uncertainty explicitly in the control model is expected to produce more robust control strategies. In [12], a reliability-based

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Non-conservative robust Nonlinear Model Predictive Control via scenario decomposition

Cited by 10 publications

References 14 publications

Stochastic model predictive control approaches applied to drinking water networks

Stochastic model predictive control approaches applied to drinking water networks

Improving Scenario Decomposition for Multistage MPC Using a Sensitivity-Based Path-Following Algorithm

Stochastic Model Predictive Control for Water Transport Networks with Demand Forecast Uncertainty

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