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Results for “optimal control”

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PubMed2006

Continuous hybridoma bioreactor: sensitivity analysis and optimal control.

Animal cell culture has already established itself as a mature technology able to make a wide range of valuable products, the actual focus being to find the competitive bioreactor design and operating conditions for increasing production. A complex analysis, implying sensitivity calculus and optimal control computation, is done for a system composed of a continuous perfectly mixed bioreactor, with cell recirculation, a cell separator, a mixer and a purge. The bioreactor's sensitivity to the control parameters is measured by a new concept, entropic density, developed from the notion of Shannon entropy. An optimization procedure based on a genetic-algorithms approach is applied for the computation of the inlet flow profile in time, which guarantees optimum monoclonal-antibody production. Our studies, including the present one, proved that the best approach to obtain high production is to use a hybrid operating sequence: fed-batch mode followed by the continuous mode.

Antibodies, Monoclonal↗

PubMed2005

Tailoring the optimal control cost function to a desired output: application to minimizing phase errors in short broadband excitation pulses.

The de facto standard cost function has been used heretofore to characterize the performance of pulses designed using optimal control theory. The freedom to choose new, creative quality factors designed for specific purposes is demonstrated. While the methodology has more general applicability, its utility is illustrated by comparison to a consistently chosen example--broadband excitation. The resulting pulses are limited to the same maximum RF amplitude used previously and tolerate the same variation in RF homogeneity deemed relevant for standard high-resolution NMR probes. Design criteria are unchanged: transformation of I(z)--> I(x) over resonance offsets of +/-20 kHz and RF variability of +/-5%, with a peak RF amplitude equal to 17.5 kHz. However, the new cost effectively trades a small increase in residual z magnetization for improved phase in the transverse plane. Compared to previous broadband excitation by optimized pulses (BEBOP), significantly shorter pulses are achievable, with only marginally reduced performance. Simulations transform I(z) to greater than 0.98 I(x), with phase deviations of the final magnetization less than 2 degrees, over the targeted ranges of resonance offset and RF variability. Experimental performance is in excellent agreement with the simulations.

Algorithms↗

PubMed2005

Fourier transform measurement of two-photon excitation spectra: applications to microscopy and optimal control.

We report a novel Fourier transform method for measuring two-photon excitation spectra. We demonstrate this method using simple dye molecules and discuss its applications in two-photon fluorescence microscopy and optimal control. This method facilitates an intuitive interpretation of recent control experiments in terms of tuning the nonlinear spectrum of the exciting laser source.

Equipment Design↗

PubMed1994

Brain magnetic resonance imaging in children with optimally controlled hyperphenylalaninaemia.

This study was undertaken to investigate whether the white-matter changes on MRI and the EEG abnormalities detectable in treated adolescents and adults with hyperphenylalaninaemia (HPA) can be detected in younger children on an optimally controlled diet. The study included 17 children, 7-12 years of age, with HPA. The MRI of five healthy children were included in the blind evaluation of the MR images. According to mutation genotype and dietary tolerance of phenylalanine, 9 patients have severe HPA and 8 have moderate HPA, all requiring dietary treatment. Mild white-matter hyperintensity was detected in 1 of the 5 healthy children and in 10 of 17 patients. EEG was abnormal in 2 patients. This group of children was compared with a previously reported group of adolescents with HPA who had been treated according to the same dietary regimen. MRI changes and EEG abnormalities were significantly less frequent in the group of children than in the group of adolescents. It is suggested that the more frequent MRI changes and EEG abnormalities seen in adolescents are related to the fact that a relaxation of the dietary treatment after the age of 8 years is often accepted.

Adolescent↗

PubMed1991

Pump function of the heart as an optimal control problem.

In order to model the pump function of the heart the left ventricle is represented as an elastic thick-walled cylinder contracting symmetrically. The acceleration is included in the mathematical formalism describing the contraction of the myocardium and optimal control theory is used to solve the differential equation of motion of the cylindrical wall in such a way as to minimize a given performance index. Application of the equations to experimental data published in the literature is discussed. The mathematical formalism presents a new way to study the time variation of the volume ejected from the left ventricle. Methods to quantify the pump function of the heart are suggested.

Biomechanical Phenomena↗

PubMed2005

Sensitivity enhancement in NMR of macromolecules by application of optimal control theory.

NMR of macromolecules is limited by large transverse relaxation rates. In practice, this results in low efficiency of coherence transfer steps in multidimensional NMR experiments, leading to poor sensitivity and long acquisition times. The efficiency of coherence transfer can be maximized by design of relaxation optimized pulse sequences using tools from optimal control theory. In this paper, we demonstrate that this approach can be adopted for studies of large biological systems, such as the 800 kDa chaperone GroEL. For this system, the 1H-15N coherence transfer module presented here yields an average sensitivity enhancement of 20-25% for cross-correlated relaxation induced polarization transfer (CRIPT) experiments.

Chaperonin 60↗

PubMed1987

Optimal control analysis of a cancer chemotherapy problem.

The biologically based model due to Cox and co-workers is used in this study of a cancer chemotherapy problem involving the continuous delivery of an anticancer drug. A performance criterion is introduced to measure the effectiveness of therapy while penalizing excessive usage of drug. Optimal control theory is used to obtain information on the nature of the controller, which is related to the amount of drug to be infused from a drug-delivery device.

Antineoplastic Agents↗

PubMed2006

Sustainable ecosystem management using optimal control theory: part 2 (stochastic systems).

Sustainable development of ecosystems through external ecosystem management is assuming importance for the environmentalists. To that effect, previous work by the authors looked at the option of manipulating population dynamics of the species in an ecosystem to achieve sustainability. Fisher information is used as the quantifying measure of sustainability and optimal control theory is used to derive the control profiles. However, that work considered only deterministic systems. Uncertainty being prevalent in all systems, particularly in natural systems, this paper extends that work to analyse uncertain systems. Predator-prey models are used to model the species populations and different control philosophies are compared. Ito mean reverting process is used to model the stochastic process, and stochastic maximum principle is used to derive the control profiles. The results for the objective of FI variance minimization qualitatively agree with those for the deterministic system, while the results for the FI maximization objective differ. It is observed that the instability associated with the FI maximization objective for deterministic systems is absorbed by the noise introduced by the uncertainty. Quantitatively, it is observed that the degree of uncertainty, along with its presence, is also important to identify the most appropriate management strategy.

Animals↗

PubMed1986

Optimal control of gas exchange.

A major difficulty in evaluating the optimization theory of leaf gas exchange under conditions of water deficit has been that of obtaining suitable experimental data. Mathematical solutions to three formulations of optimal stomatal control are presented which can be tested experimentally. First, it is assumed that the movement of stomata and changes in environmental factors are slow compared to changes in the internal CO(2) concentration. The optimization problem is solved under this assumption, and the procedures for testing the solution experimentally are described. Second, instantaneous stomatal response is postulated and the solution suggests that very rapid oscillations provide optimal CO(2) uptake. Third, variable stomatal dynamics are postulated and the mathematical solution shown to be similar to that of the second case. The second and third cases can also be tested empirically.

Journal Article↗

PubMed2004

Chebyshev series for designing RF pulses employing an optimal control approach.

Magnetic resonance imaging (MRI) provides bidimensional images with high definition and selectivity. Selective excitations are achieved applying a gradient and a radio frequency (RF) pulse simultaneously. They are modeled by the Bloch differential equation, which has no closed-form solution. Most methods for designing RF pulses are derived from approximation of this equation or are based on iterative optimization methods. The approximation methods are only valid for small tip angles and the optimization-based algorithms yield better results, but they are computationally intensive. To improve the solutions and to reduce processing time, a method for designing RF pulses using a pseudospectral approach is presented. The Bloch equation is expanded in Chebyshev series, which can be solved using a sparse linear algebraic system. The method permits three different formulations derived from the optimal control theory, minimum distance, minimum energy, or minimum time, which are solved as algebraic constrained minimization problems. The results were validated through simulated and real experiments of 90 degrees and 180 degrees RF pulses. They show improvements compared to the corresponding solutions obtained using the Shinnar-Le Roux method. The minimum time formulation produces the best performance for 180 degrees pulses, reducing the excitation length in 4% and the RF pulse energy in 3%.

Algorithms↗

PubMed1981

Optimal control evaluation of left ventricular systolic dynamics.

A model of the contracting left ventricle was developed, in which the left ventricle was represented as a time-varying compliance. The vascular load included the nonlinear (Bernoulli) resistance of the aortic valve, blood inertance, and a Windkessel model of the arterial tree. Owing to the obligatory aerobic nature of the heart, oxygen consumption can be used to characterize the energy utilized by the myocardium. An adaptive control law was developed for determining the systolic time course of ventricular pressure and volume that minimizes cardiac oxygen consumption. Three main determinants of myocardial oxygen consumption were included in the integral criterion function: developed wall tension, inotropic state, and external (mechanical) work. The optimal control problem was solved using the Pontryagin maximum principle. The model could predict, in good agreement with experimentally obtained data, systolic time course of ventricular pressure and volume, as well as directional changes in the duration of isovolumic contraction and ejection phase under various conditions of end-diastolic volume, mean aortic pressure, and inotropic state.

Animals↗

PubMed2001

An optimal control strategy for crop growth in advanced life support systems.

A feedback control method for regulating crop growth in advanced life support systems is presented. Two models for crop growth are considered, one developed by the agricultural industry and used by the Ames Research Center, and a mechanistic model, termed the Energy Cascade model. Proportional and pointwise-optimal control laws are applied to both models using wheat as the crop and light intensity as the control input. The control is particularly sensitive to errors in measurement of crop dry mass. However, it is shown that the proposed approach is a potentially viable way of controlling crop growth as it compensates for model errors and problems associated with applying the desired control input due to environmental disturbances. Grant numbers: NGT5-50229.

Biomass↗

PubMed2004

Optimal control of multiphoton ionization processes in aligned I2 molecules with time-dependent polarization pulses.

Multiphoton ionization processes in aligned I2 molecules are actively controlled by the homemade pulse shaping system, with which a time-dependent polarization pulse can be generated and controlled. We find a correlation between a femtosecond time-dependent polarization pulse and the production efficiency of evenly or oddly charged molecular ions. We achieve much better controllability of the correlation with a time-dependent polarization pulse than with a pulse having a fixed ellipticity. The results suggest the existence of an unknown tunnel ionization mechanism which is characteristic of a time-dependent polarization pulse. Our experiments point to new directions in optimal control studies with molecular systems, as discussed in the text.

Journal Article↗

PubMed1983

Optimal control of antagonistic muscles.

Recently, a model for a pair of antagonistic muscles has been studied (Oğuztöreli and Stein, 1982). In the present paper we formulate and investigate the minimization of the costs associated with the time to complete the movement, the oscillation about the endpoint, the energy costs to the muscles to complete the movement, the cost to the nervous system to supply the inputs, and the cost of reliability in the face of perturbing forces. To solve these optimization problems the maximum principle of Pontryagin is employed. In all of these optimization problems, except the energy optimal problem, the optimal controls (active states or nervous inputs) are of the bang-bang type.

Animals↗

PubMedDate not supplied

[The use of the optimal control method for correcting lipid metabolism].

The paper discusses an optimal artificial control of lipid metabolism which is the most important element of human life. The fact that the solution of this problem contributes to a decrease in risk of developing some diseases in the pilots and cosmonauts and an increase in human adaptive potentialities is particularly emphasized. An approximated algorithm of solving an assigned model problem and the results of computational experiments are presented.

Aerospace Medicine↗

PubMed2005

Optimal control of redundant muscles in step-tracking wrist movements.

An important question in motor neuroscience is how the nervous system controls the spatiotemporal activation patterns of redundant muscles in generating accurate movements. The redundant muscles may not only underlie the flexibility of our movements but also pose the challenging problem of how to select a specific sequence of muscle activation from the huge number of possible activations. Here, we propose that noise in the motor command that has an influence on task achievement should be considered in determining the optimal motor commands over redundant muscles. We propose an optimal control model for step-tracking wrist movements with redundant muscles that minimizes the end-point variance under signal-dependent noise. Step-tracking wrist movements of human and nonhuman primates provide a detailed data set to investigate the control mechanisms in movements with redundant muscles. The experimental EMG data can be summarized by two eminent features: 1) amplitude-graded EMG pattern, where the timing of the activity of the agonist and antagonist bursts show slight variations with changes in movement directions, and only the amplitude of activity is modulated; and 2) cosine tuning for movement directions exhibited by the agonist and antagonist bursts, and the discrepancy found between a muscle's agonist preferred direction and its pulling direction. In addition, it is also an important observation that subjects often overshoot the target. We demonstrate that the proposed model captures not only the spatiotemporal activation patterns of wrist muscles but also trajectory overshooting. This suggests that when recruiting redundant muscles, the nervous system may optimize the motor commands across the muscles to reduce the negative effects of motor noise.

Biomechanical Phenomena↗

PubMed1994

New ideas for solving identification and optimal control problems related to biomedical systems.

Many bio-medical models lead to differential systems where some parameters have to be identified from partial observation on the system's solution. For two- or three-compartment models parameters to be identified can be explicitly calculated (when uniqueness is ensured) from the algebraic relation obtained by using classical methods. However, when the number of compartments is greater than three, numerical techniques are necessary. In this work we propose new numerical methods based on Adomian's method for solving identification and optimal control problems associated to biomedical systems.

Algorithms↗

PubMed2006

Optimal control in a dissipative system: vibrational excitation of CO/Cu(100) by IR pulses.

The question as to whether state-selective population of molecular vibrational levels by shaped infrared laser pulses is possible in a condensed phase environment is of central importance for such diverse fields as time-resolved spectroscopy, quantum computing, or "vibrationally mediated chemistry." This question is addressed here for a model system, representing carbon monoxide adsorbed on a Cu(100) surface. Three of the six vibrational modes are considered explicitly, namely, the CO stretch vibration, the CO-surface vibration, and a frustrated translation. Optimized infrared pulses for state-selective excitation of "bright" and "dark" vibrational levels are designed by optimal control theory in the framework of a Markovian open-system density matrix approach, with energy flow to substrate electrons and phonons, phase relaxation, and finite temperature accounted for. The pulses are analyzed by their Husimi "quasiprobability" distribution in time-energy space.

Journal Article↗