A simultaneous approach for singular optimal control based on partial moving grid

Chen, Weifeng; Ren, Yinyin; Zhang, Guijun; Biegler, Lorenz T.

doi:10.1002/aic.16584

Cited by 21 publications

(17 citation statements)

References 34 publications

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“…In addition to multimodality [ 131 , 133 , 134 , 158 ], other numerical and computational issues in nonlinear optimal control include complicated control profiles with multiple and very sensitive switching points [ 143 , 163 ], discontinuous dynamics [ 142 ], path constraints [ 139 , 165 ] and singular arcs [ 88 , 139 , 166 ], and the need of good initial guesses [ 131 ]. Even small nonlinear optimal control problems can be non-trivial, exhibiting unusual behavior due to the existence of local solutions and extreme sensitivity to initial guesses [ 130 ].…”

Section: Methodsmentioning

confidence: 99%

Using optimal control to understand complex metabolic pathways

Tsiantis

Banga

2020

BMC Bioinformatics

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Background Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria. Results Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. Conclusions We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

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Section: Methodsmentioning

confidence: 99%

Using optimal control to understand complex metabolic pathways

Tsiantis

Banga

2020

BMC Bioinformatics

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“…In addition to multimodality, other numerical and computational issues in optimal control include complicated control profiles with multiple and very sensitive switching points, discontinuous dynamics, path constraints and singular arcs [86,148].…”

Section: Challenges and Pitfalls In Numerical Optimal Controlmentioning

confidence: 99%

Using optimal control to understand complex metabolic pathways

Tsiantis

Banga

2020

Preprint

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Background: We revisit the idea of explaining and predicting dynamics in biochemical pathways from first-principles. A promising approach is to exploit optimality principles that can be justified from an evolutionary perspective. In the context of the cell, several previous studies have explained the dynamics of simple metabolic pathways exploiting optimality principles in combination with dynamic models, i.e. using an optimal control framework. For example, dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point.Results: Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework based on multicriteria optimal control which has been designed with scalability and efficiency in mind, extending several recent methods. This framework includes mechanisms to avoid common pitfalls, such as local optima, unstable solutions or excessive computation time. We illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. Conclusions:We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we show how the multicriteria approach allows us to consider general cost/benefit trade-offs that have been likely favored by evolution. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction networks.

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“…Benchmark problems are standard repositories in many scientific disciplines such as systems biology [1,2], reservoir modeling [3,4,5,6], drilling [7,8], optimization [9,10], dynamic optimization [11,12], singular optimal control [13,14], combined scheduling and control [15,16,17,18], and others [19,20,21]. The benchmark problems serve as a consistent measure of innovations that are proposed to increase profitability or improve some aspect of control or optimization performance.…”

Section: Introductionmentioning

confidence: 99%

Benchmark temperature microcontroller for process dynamics and control

Park

Martin

Kelly³

et al. 2020

Computers & Chemical Engineering

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Standard benchmarks are important repositories to establish comparisons between competing model and control methods, especially when a new method is proposed. This paper presents details of an Arduino micro-controller temperature control lab as a benchmark for modeling and control methods. As opposed to simulation studies, a physical benchmark considers real process characteristics such as the requirement to meet a cycle time, discrete sampling intervals, communication overhead with the process, and model mismatch. An example case study of the benchmark is quantifying an optimization approach for a PID controller with 5.4% improved performance. A multivariate example shows the quantified performance improvement by using model predictive control with a physics-based model, an autoregressive time series model, and a Hammerstein model with an artificial neural network to capture the static nonlinearity. These results demonstrate the potential of a hardware benchmark for transient modeling and regulatory or advanced control methods.

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A simultaneous approach for singular optimal control based on partial moving grid

Cited by 21 publications

References 34 publications

Using optimal control to understand complex metabolic pathways

Using optimal control to understand complex metabolic pathways

Using optimal control to understand complex metabolic pathways

Benchmark temperature microcontroller for process dynamics and control

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