Specific Growth Rate And Sliding Mode Stabilization Of Fed-Batch Processes

The subject of this paper is specific growth rate control of a fed-batch biotechnological process. The objective of the paper is to present comfortable tools and mathematical methodology that permits control stabilization of biotechnological processes with synchronized utilization of different mathematical approaches. The control design is based on the equivalent transformations to Brunovsky normal form of an enlarged Monod-Wang model, on a chattering optimal control and sliding mode control solutions. This approach permits new precise control solutions for stabilization of continuous and fed-batch cultivation processes. In the paper are investigated Monod-Wang kinetic model and it singular Monod form. The simpler Monod and Monod-Wang models are restricted forms of Wang-Yerusalimsky model. The Wang-Yerusalimsky kinetic model could be accepted as a common model. A second order sliding mode is investigated and compared with standard sliding mode algorithms. The sliding mode control permits to solve the control problems with smaller quantity of priory information and elimination of parameters and measurements noises

Resilience of dynamical systems

Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have been developed to address this issue, primarily driven by concrete applications. In particular, several disciplines suggested a web of concepts under the headline "resilience". Unfortunately, there are many different variants and explanations of resilience, and often the definitions are left relatively vague, sometimes even deliberately. Yet, to allow for a structural development of a mathematical theory of resilience that can be used across different areas, one has to ensure precise starting definitions and provide a mathematical comparison of different resilience measures. In this work, we provide a systematic review of the most relevant indicators of resilience in the context of continuous dynamical systems, grouped according to their mathematical features. The indicators are also generalized to be applicable to any attractor. These steps are important to ensure a more reliable, quantitatively comparable and reproducible study of resilience in dynamical systems. Furthermore, we also develop a new concept of resilience against certain non-autonomous perturbations to demonstrate, how one can naturally extend our framework. All the indicators are finally compared via the analysis of a classic scalar model from population dynamics to show that direct quantitative application-based comparisons are an immediate consequence of a detailed mathematical analysis.Comment: 54 pages, 18 figure

MATLAB

A well-known statement says that the PID controller is the "bread and butter" of the control engineer. This is indeed true, from a scientific standpoint. However, nowadays, in the era of computer science, when the paper and pencil have been replaced by the keyboard and the display of computers, one may equally say that MATLAB is the "bread" in the above statement. MATLAB has became a de facto tool for the modern system engineer. This book is written for both engineering students, as well as for practicing engineers. The wide range of applications in which MATLAB is the working framework, shows that it is a powerful, comprehensive and easy-to-use environment for performing technical computations. The book includes various excellent applications in which MATLAB is employed: from pure algebraic computations to data acquisition in real-life experiments, from control strategies to image processing algorithms, from graphical user interface design for educational purposes to Simulink embedded systems

Hierarchical nonlinear, multivariate, and spatially-dependent time-frequency functional methods

Notions of time and frequency are important constituents of most scientific inquiries, providing complimentary information. In an era of "big data," methodology for analyzing functional and/or image data is increasingly important. This dissertation develops methodology at the cross-section of time-frequency analysis and functional data and consists of three distinct, but related, contributions. First, we propose nonparametric methodology for nonlinear multivariate time-frequency functional data. In particular, we consider polynomial nonlinear functional data models that accommodate higher dimensional functional covariates, including time-frequency images, along with their interactions. The necessary dimension reduction for model estimation proceeds through carefully chosen basis expansions (empirical orthogonal functions) and feature-extraction stochastic search variable selection (SSVS). Properties of the methodology are examined through an extensive simulation study. Finally, we illustrate the approach through an application that attempts to characterize spawning behavior of shovelnose sturgeon in terms of high-density depth and temperature profiles. The second contribution proposes model-based time-frequency estimation through Bayesian lattice filter time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our model is estimated within the partial autocorrelation domain (i.e., through the partial autocorrelation coefficients). Additionally, all of the full conditional distributions required for our algorithm are of standard form and thus can be easily implemented using a Gibbs sampler. Further, as a by-product of the lattice filter recursions, our approach avoids undesirable matrix inversions. As such, estimation is computationally efficient and stable. We conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through several real case studies. The final project of the dissertation develops models that accommodate spatially dependent functional responses with spatially dependent image predictors. The methodology is motivated by a soil science study that seeks to model spatially correlated water content functionals as a function of electro-conductivity images. The water content curves are measured at different locations within the study field and at various depths, whereas the electro-conductivity images are spatially referenced images of wavelength by depth. Estimation is facilitated by taking a Bayesian approach, where the necessary dimension reduction for model implementation proceeds using basis function expansions along with SSVS. Finally, the methodology is illustrated through an application to our motivating data.Includes bibliographical references (pages 122-133

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Selected Topics in Gravity, Field Theory and Quantum Mechanics

Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories

A quantum measurement model of reaction-transport systems

This research develops a mesoscopic quantum measurement theoretic foundation for neutron transport theory in the presence of delayed fission and compound scattering processes. Specifically, we construct a quantization of the Pal-Bell equation of stochastic neutron transport theory from a quantum stochastic calculus for particle detection in quantum fields. This enables us to formulate a quantum theory of mesoscopic neutron transport physics that explicitly incorporates both transport mechanisms and resonance scattering into a single quantum stochastic process. The quantum stochastic process representation is shown to have a unique, trace-norm convergent perturbation expansion in the number of observed reaction events. This expansion result, and the proofs that lead to it, help to establish a variety of approximation methods that are applied to nuclear data assimilation and neutron thermalization problems