Towards dual robust nonlinear model predictive control: A multi-stage approach

Thangavel, S.; Lucia, Sergio; Paulen, Radoslav; Engell, Sebastian

doi:10.1109/acc.2015.7170773

Cited by 12 publications

(8 citation statements)

References 23 publications

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“…For some of these problems, it is the nonstandard formulation of the optimization problem that poses the main challenge. Some applications transcend the classical subdivisions; dual control combines control and learning [123,68,46], codesign of optimal trajectory and reference follower [61], multi-objective design [100,126], the use of different transcription methods on different parts of the system statespace [10].…”

Section: Nonstandard Optimization Problem Formulationsmentioning

confidence: 99%

CasADi: a software framework for nonlinear optimization and optimal control

Andersson

Gillis

Horn³

et al. 2018

Math. Prog. Comp.

2,404

976

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We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last seven years.

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Section: Nonstandard Optimization Problem Formulationsmentioning

confidence: 99%

CasADi: a software framework for nonlinear optimization and optimal control

Andersson

Gillis

Horn³

et al. 2018

Math. Prog. Comp.

2,404

976

View full text Add to dashboard Cite

show abstract

“…47 Handling the complexity of the estimation problem Clearly, the presented strategyhaving the estimation problem embedded in the constraints-is computationally tractable for only specific estimation problems, e.g., when mathematical model is linear in parameters. Here either a strategy based on approximate linear (linearization-based) estimation can be used or an approach that estimates contribution of each measurement based on parametric sensitivities 35 .…”

Section: End Formentioning

confidence: 99%

“…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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“…The proposed efficient solution method for stochastic optimal control is demonstrated on a nonlinear semibatch reactor in the presence of probabilistic model uncertainty and stochastic disturbances. An exothermic reaction takes place in a semibatch reactor equipped with a cooling jacket, where reactants A and B react to produce product C. The reactor dynamics are described by Thangavel et al, 55 ie,…”

Section: Simulation Case Studymentioning

confidence: 99%

“…Model parameters, initial conditions, and constraints on the states and inputs for the semibatch reactor case study55 …”

mentioning

confidence: 99%

An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems

Paulson

Mesbah

2017

Intl J Robust & Nonlinear

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Stochastic model predictive control hinges on the online solution of a stochastic optimal control problem. This paper presents a computationally efficient solution method for stochastic optimal control for nonlinear systems subject to (time-varying) stochastic disturbances and (time-invariant) probabilistic model uncertainty in initial conditions and parameters. To this end, new methods are presented for joint propagation of time-varying and time-invariant probabilistic uncertainty and the nonconservative approximation of joint chance constraint (JCC) on the system state. The proposed uncertainty propagation method relies on generalized polynomial chaos and conditional probability rules to obtain tractable expressions for the state mean and covariance matrix. A moment-based surrogate is presented for JCC approximation to circumvent construction of the full probability distribution of the state or the use of integer variables as required when using the sample average approximation. The proposed solution method for stochastic optimal control is illustrated on a nonlinear semibatch reactor case study in the presence of probabilistic model uncertainty and stochastic disturbances. It is shown that the proposed solution method is significantly superior to a standard random sampling method for stochastic optimal control in terms of computational requirements. Furthermore, the moment-based surrogate for the JCC is shown to be substantially less conservative than the widely used distributionally robust Cantelli-Chebyshev inequality for chance constraint approximation. KEYWORDS generalized polynomial chaos, joint chance constraint, joint propagation of probabilistic model uncertainty and stochastic disturbances, stochastic optimal control Int J Robust Nonlinear Control. 2019;29: 5017-5037.wileyonlinelibrary.com/journal/rnc

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Towards dual robust nonlinear model predictive control: A multi-stage approach

Cited by 12 publications

References 23 publications

CasADi: a software framework for nonlinear optimization and optimal control

CasADi: a software framework for nonlinear optimization and optimal control

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

An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems

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