Output stabilization of fermentation processes: A binary control system approach

Two types of continuous fermentation processes for product formation are considered. The processes are described by three nonlinear differential equations with uncertain parameters. Binary control design for theses processes is proposed. The asymptotic output stabilization problems are solved. The control design is carried out with direct use of nonlinear model and microbiological expert knowledge. The good system robustness to parameter uncertainties and external disturbance is demonstrated by simulation investigations.     

Metabolic engineering in silico

This review briefs on the main directions in the field of mathematical modeling of metabolic processes aimed at a rational design of genetically modified organisms. The class of generalized Hill functions is described, and their application to modeling of nonlinear processes in Escherichia coli metabolic systems is illustrated by several examples. A model for the pyrimidine biosynthesis in E. coli, taking into account the nonlinear effects of a negative allosteric regulation of enzyme activities involved in the control of the subsequent stages by the end products of synthesis, is considered. It has been shown that the model displays its own continuous oscillation mode of functioning with a period of approximately 50 min, which is close to the duration of E. coli cell cycle. The need in considering the nonlinear effects in the models as essential elements in the function of metabolic systems far from equilibrium is discussed.     

Non-linear control of continuous bioreactors

Control of bioreactors has achieved importance in the recent years. This may be due to the fact that they are difficult to control which may be attributed to its nonlinear dynamic behavior. The model parameters of the bioreactor also vary in an unpredictable manner. The complexity of the biochemical processes inhibits the accurate modeling and also the lack of suitable sensors make the process state difficult to characterize. Considerable emphasis has been placed on the control of fed-batch fermentors because of their prevalence in industries. However, when production of biomass is to be optimized, continuous operation is desirable. Several procedures are available for the nonlinear control of processes, viz., differential geometric approach, internal model control approach, reference synthesis technique, predictive control design, etc., but the major disadvantage of these approaches is the computational time required to perform the prediction optimization. In this study, a nonlinear controller based on a polynomial discrete time model (NARMAX) is evaluated for its performance on a fermentor. It can be shown that a nonlinear self-tuning controller based on NARMAX model can be extended to the control of fermentors. The response is smooth for both load and setpoint changes even when process parameters are assumed to be zero and uncertainty in parameters are present and in the presence of controller constraints. The control action can be made more or less robust by changing the design parameters appropriately. Therefore, nonlinear self-tuning controller is suitable for control of industrial processes.     

Dynamic output feedback stabilization for nonlinear systems based on standard neural network models

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.     

Connecting geographical distributions with population processes

The geographical distribution of a species is determined by a large number of complex processes operating over spatial scales spanning 10 orders of magnitude. Patterns in population processes have been described at numerous scales. We show that two patterns, measured at different scales, jointly allow us to infer heretofore unknown patterns in the distribution of demographic patterns across the geographical range of a species. The resulting model describes three fundamentally different modes of geographical variation in vital rates of populations. One mode is characterized by a positive nonlinear relationship between the maximum rate of population growth and the intensity of intraspecific competition across a geographical range. That is, populations that grow rapidly are also those where individuals experience the greatest per capita negative effect of the presence of other individuals. The second mode of behaviour is described by a negative nonlinear relationship between maximum growth rate and density dependence. Under this scenario, populations with low capacity to grow rapidly have highest intensities of intraspecific competitive effects. A third mode of behaviour is characterized by a weak positive relationship between growth rate and intraspecific competition, with very little geographical variation in maximum growth rate. A survey of studies relating temporal means and variances in population abundance for a variety of species indicate that the second mode of geographical variation in population dynamics across species ranges is the most common, though a few species appear to be characterized by the third mode.     

U.S. Environmental Protection Agency's revised guidelines for carcinogen risk assessment: evaluating a postulated mode of carcinogenic action in guiding dose-response extrapolation

There are new opportunities to using data from molecular and cellular studies in order to bring together a fuller biological understanding of how chemicals induce neoplasia. In 1996, the Environmental Protection Agency (EPA) published a proposal to replace its 1986 Guidelines for Carcinogen Risk Assessment to take advantage of these new scientific advances in cancer biology. The analytical framework within the new guidelines focuses on an understanding of the mode of carcinogenic action. Mode of action data come into play in a couple of ways in these new guidelines. For example, such information can inform the dose-response relationship below the experimental observable range of tumours. Thus, mode of action data can be useful in establishing more appropriate guidance levels for environmental contaminants. It is the understanding of the biological processes that lead to tumour development along with the response data derived from experimental studies that can help discern the shape of the dose-response at low doses (linear vs. nonlinear). Because it is experimentally difficult to establish "true thresholds" from others with a nonlinear dose-response relationship, the proposed guidelines take a practical approach to depart from low-dose linear extrapolation procedures when there is sufficient experimental support for a mode of action consistent with nonlinear biological processes (e.g., tumours resulting from the disruption of normal physiological processes).     

U.S. Environmental Protection Agency's revised guidelines for carcinogen risk assessment: evaluating a postulated mode of carcinogenic action in guiding dose–response extrapolation

There are new opportunities to using data from molecular and cellular studies in order to bring together a fuller biological understanding of how chemicals induce neoplasia. In 1996, the Environmental Protection Agency (EPA) published a proposal to replace its 1986 Guidelines for Carcinogen Risk Assessment to take advantage of these new scientific advances in cancer biology. The analytical framework within the new guidelines focuses on an understanding of the mode of carcinogenic action. Mode of action data come into play in a couple of ways in these new guidelines. For example, such information can inform the dose–response relationship below the experimental observable range of tumours. Thus, mode of action data can be useful in establishing more appropriate guidance levels for environmental contaminants. It is the understanding of the biological processes that lead to tumour development along with the response data derived from experimental studies that can help discern the shape of the dose–response at low doses (linear vs. nonlinear). Because it is experimentally difficult to establish “true thresholds” from others with a nonlinear dose–response relationship, the proposed guidelines take a practical approach to depart from low-dose linear extrapolation procedures when there is sufficient experimental support for a mode of action consistent with nonlinear biological processes (e.g., tumours resulting from the disruption of normal physiological processes).     

LFT models of continuous biotechnological processes

The aim of the paper is to obtain suitable state-space models of continuous biotechnological processes (CBTP) in the framework of Linear Fractional Transformation (LFT). The LFT models are starting point in most of the advanced robust control design and analysis methods. Therefore, a linearized process model in the state-space is used whose elements are supposed to vary within certain bounds to represent the nonlinear behaviour of the real plant. The performance specifications are defined in the frequency domain through weighting functions. Two LFT models of CBTP are obtained ready for controller design aimed to optimize robust stability margins and robust performance, respectively.     

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ₁-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.     

On the modeling of the performances of the human brain in a two-choice task involving decoding and memorization of simple visual patterns

The quantitative, aspects of the decoding and storage processes of simple visual patterns by the human brain are considered, on the basis of the performances obtained in a set of two-choice experiments. Strings of patterns (colored lights or simple geometrical patterns) were used in which the densities of the two patterns throughout the string were either constant or asymmetric. The subjects were required to indicate the pattern which was presented more frequently. A nonlinear model for the storage and decision processes was devised from these data which accurately predicted the performance under experimental conditions different from those originally used. Among the prominent features of the brain processes suggested by the model are the necessity for a nonlinear summation of the decoded information and its decay with time.Finally, it is shown that the experimental design allows a quantitative evaluation of those factors which are relevant to the decoding of patterns of different complexities.     

Foundations for the design and implementation of synthetic genetic circuits

Synthetic gene circuits are designed to program new biological behaviour, dynamics and logic control. For all but the simplest synthetic phenotypes, this requires a structured approach to map the desired functionality to available molecular and cellular parts and processes. In other engineering disciplines, a formalized design process has greatly enhanced the scope and rate of success of projects. When engineering biological systems, a desired function must be achieved in a context that is incompletely known, is influenced by stochastic fluctuations and is capable of rich nonlinear interactions with the engineered circuitry. Here, we review progress in the provision and engineering of libraries of parts and devices, their composition into large systems and the emergence of a formal design process for synthetic biology.     

Mathematical model for transient isoelectric focusing of simple ampholytes

A mathematical model describing transient processes in isoelectric focusing (IEF) of L biprotic ampholytes is presented. The model is a generalization of our previous research on steady slate in IEF and consists of L nonlinear partial differential equations coupled with 2L+2 algebraic equations. Constraints imposed by the mode of operation, viz., constant current. voltage or power, are described. Due to the nonlinearity of the equations, analysis of the model requires computer simulation. Model equations suitable for computer implementation are derived.     

Machine learning-based model predictive controller design for cell culture processes

The biopharmaceutical industry continuously seeks to optimize the critical quality attributes to maintain the reliability and cost-effectiveness of its products. Such optimization demands a scalable and optimal control strategy to meet the process constraints and objectives. This work uses a model predictive controller (MPC) to compute an optimal feeding strategy leading to maximized cell growth and metabolite production in fed-batch cell culture processes. The lack of high-fidelity physics-based models and the high complexity of cell culture processes motivated us to use machine learning algorithms in the forecast model to aid our development. We took advantage of linear regression, the Gaussian process and neural network models in the MPC design to maximize the daily protein production for each batch. The control scheme of the cell culture process solves an optimization problem while maintaining all metabolites and cell culture process variables within the specification. The linear and nonlinear models are developed based on real cell culture process data, and the performance of the designed controllers is evaluated by running several real-time experiments.     

Formation and stability of dissipative structures

The nonlinear interaction of the disturbed wave packet modes has been analysed within nonlinear parabolic equation. There has also been designed the approach to a limit cycle regime of an isolated mode, the analytical stability criterion of the obtained solutions having separated the existance spheres of isolated and multimode regimes. Stochastization and self-organization processes taking place during the formation of dissipative structures have been studied by methods of random function theory.     

Optimization of glucose isomerase reactor: optimum operating temperature mode

The optimum temperature operation mode required to achieve high fructose productivity is studied for immobilized glucose isomerase (GI) packed bed reactor. In this study, the reactor design equation based on reversible Michaelis-Menten kinetics assumes both thermal enzyme deactivation and substrate protection. The optimization problem is formulated as a discretized constrained nonlinear programming problem (NLP). The formulation is expressed in terms of maximization of fructose productivity as the objective function subject to reactor design equation, kinetic parameter equations, substrate protection factor equation and feasibility constraints. The constraints are discretized along the reactor operating period by employing piecewise polynomial approximations. Approximately 7% improvement in terms of fructose productivity is achieved when running the reactor at the optimum decreasing temperature operation mode as compared to the constant optimum isothermal operation.     

Design of Full-Adder and Full-Subtractor Using Metal-Insulator-Metal Plasmonic Waveguides

The metal-insulator-metal (MIM) waveguides are considered best among all plasmonic waveguides for propagation of optical signal to deep sub-wavelength scale. In this paper, MIM plasmonic waveguides based Mach-Zehnder interferometer (MZI) is developed. It possesses nonlinear Kerr material in one of its linear arm for controlling of optical signal with light intensity. Self phase modulation (SPM) and cross phase modulation (XPM) processes inside nonlinear MZI are used to design novel and compact full-adder and full-subtractor. Analysis and verification of proposed devices are carried out using FDTD and MATLAB simulations.     

Neural chaos and schizophrenia

Recent data indicate that random-like processes are related to the defects in the organization of semantic memory in schizophrenia which is more disorganized and less definable than those of controls with more semantic links and more bizarre and atypical associations. These aspects of schizophrenic cognition are similar to characteristics of chaotic nonlinear dynamical systems. In this context, the hypothesis tested in this study is that dynamic changes of electrodermal activity (EDA) as a measure of brain and autonomic activity may serve as a characteristic which can be used as an indicator of possible neural chaotic process in schizophrenia. In the present study, bilateral EDA in rest conditions were measured in 40 schizophrenic patients and 40 healthy subjects. Results of nonlinear and statistical analysis indicate left-side significant differences of positive largest Lyapunov exponents in schizophrenia patients compared to the control group. This might be interpreted that the neural activity during rest in schizophrenic patients is significantly more chaotic than in the control group. The relationship was confirmed by surrogate data testing. These data suggest that increased neural chaos in patients with schizophrenia may influence brain processes that can cause random-like disorganization of mental processes.     

The nature of robustness in development

A trait is robust to a genetic or environmental variable if its variation is weakly correlated with variation in that variable. The source of robustness lies in the fact that the developmental processes that give rise to complex traits are nonlinear. A consequence of this nonlinearity is that not all genes are equally correlated with the trait whose ontogeny they control. Here we explore how developmental mechanisms determine and alter the correlation structure between genes and the traits that they control. A formula is developed by which the correlation of a gene or environmental variable with a trait can be calculated if the mechanism that gives rise to the trait is known. The nature of robustness and the ways in which robustness can evolve are discussed in the context of the problems that arise in the analysis of inherently nonlinear systems.     

Dipteran insect flight dynamics. Part 1 Longitudinal motion about hover

This paper presents a reduced-order model of longitudinal hovering flight dynamics for dipteran insects. The quasi-steady wing aerodynamics model is extended by including perturbation states from equilibrium and paired with rigid body equations of motion to create a nonlinear simulation of a Drosophila-like insect. Frequency-based system identification tools are used to identify the transfer functions from biologically inspired control inputs to rigid body states. Stability derivatives and a state space linear system describing the dynamics are also identified. The vehicle control requirements are quantified with respect to traditional human pilot handling qualities specification. The heave dynamics are found to be decoupled from the pitch/fore/aft dynamics. The haltere-on system revealed a stabilized system with a slow (heave) and fast subsidence mode, and a stable oscillatory mode. The haltere-off (bare airframe) system revealed a slow (heave) and fast subsidence mode and an unstable oscillatory mode, a modal structure in agreement with CFD studies. The analysis indicates that passive aerodynamic mechanisms contribute to stability, which may help explain how insects are able to achieve stable locomotion on a very small computational budget.