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Results for “optimal control”

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At least 145 records · Page 8Linked to original sources

PubMed1999

Optimal control of FES-assisted standing up in paraplegia using genetic algorithms.

A practical system for Functional Electrical Stimulation (FES) assisted standing up in paraplegia should involve only a minimum of manual set up and tuning. An improved tuning method, using a genetic algorithm (GA) is proposed and demonstrated using computer simulation. Specifically, the GA adjusts the parameters of fuzzy logic (FL) and gain-scheduling proportional integral derivative (GS-PID) controllers that electrically stimulate the hip and knee musculature during the sit-stand maneuver. These new GA designed controllers were found to be effective in coordinating volitional and FES control according to formulated criteria. The latter was based on the deviations from a desired trajectory of the knee and hip joints and the magnitude of the voluntary upper body forces. The magnitude of the average arm forces were slightly higher when compared with the open-loop maximal stimulation of the hip and knee musculature; however, the terminal knee velocities were significantly reduced to less than 10 degrees /s. For practical implementation, the number of trials required to optimize the FL and GS-PID controllers can be reduced by a proposed pre-training procedure using a computer model scaled to the individual. The GA designed controllers remain near optimal provided the model-subject mismatch is small.

Algorithms↗

PubMed1976

Optimal control of a semibatch fermentation.

This work is concerned with the optimization study of the semibatch fermentation by which an amino acid is produced. The particular fermentation studied is the synthesis of lysine by the auxotrophic mutant. Applying Green's theorem to the maximization problem was proposed, and it succeeded in determining the feed rate of the substrate that maximized the production rate of the desired product.

Amino Acids↗

PubMed2004

Age-structured optimal control in population economics.

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (both age-dependent). By using a new maximum principle for age-structured control systems we derive meaningful results for the optimal migration and saving rate in an aging population. The model used in the numerical calculations is calibrated for Austria.

Adult↗

PubMed2006

On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control.

Numerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a by-product we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.

Journal Article↗

PubMed2025

Optimal Control of Directional False Discovery Rates in Large-Scale Testing.

The high-throughput biomedical technology enables measurement of thousands of gene expression levels contemporaneously. A major task in analyzing these gene expression data is to identify both over-expressed and under-expressed genes. The popular two-group models select the non-null genes without further classifying them as overexpression or underexpression. Consequently, two-group decision rules are unable to constrain the numbers of falsely discovered over-expressed or under-expressed genes respectively. We propose a general three-group model that allows dependence between the test statistics and develop a decision rule that separately controls the two types of false discoveries. We show that the optimal decision rule in our three-group model has a special monotonic structure. By making use of this monotonic structure, we can linearize the two-directional false discovery rate constraints. We prove that our decision rule optimizes the expected number of true discoveries while controlling the proportions of falsely discovered over-expressed and under-expressed genes at desired levels simultaneously. The data-driven versions of the proposed procedures are suggested, and their consistency is established. Comparisons with state-of-the-art approaches and applications to genomic studies show that our procedures work well.

Humans↗

PubMed2004

Generalized monotonically convergent algorithms for solving quantum optimal control problems.

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.

Journal Article↗

PubMed2004

Optimal control law for classical and multiconjugate adaptive optics.

Classical adaptive optics (AO) is now a widespread technique for high-resolution imaging with astronomical ground-based telescopes. It generally uses simple and efficient control algorithms. Multiconjugate adaptive optics (MCAO) is a more recent and very promising technique that should extend the corrected field of view. This technique has not yet been experimentally validated, but simulations already show its high potential. The importance for MCAO of an optimal reconstruction using turbulence spatial statistics has already been demonstrated through open-loop simulations. We propose an optimal closed-loop control law that accounts for both spatial and temporal statistics. The prior information on the turbulence, as well as on the wave-front sensing noise, is expressed in a state-space model. The optimal phase estimation is then given by a Kalman filter. The equations describing the system are given and the underlying assumptions explained. The control law is then derived. The gain brought by this approach is demonstrated through MCAO numerical simulations representative of astronomical observation on a 8-m-class telescope in the near infrared. We also discuss the application of this control approach to classical AO. Even in classical AO, the technique could be relevant especially for future extreme AO systems.

Journal Article↗

PubMed1999

Optimization algorithm performance in determining optimal controls in human movement analyses.

The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a "tracking" problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed for superior to the conventional routines by converging more rapidly and avoiding local minima.

Algorithms↗

PubMed2006

A simple approach to optimal control of invasive species.

The problem of invasive species and their control is one of the most pressing applied issues in ecology today. We developed simple approaches based on linear programming for determining the optimal removal strategies of different stage or age classes for control of invasive species that are still in a density-independent phase of growth. We illustrate the application of this method to the specific example of invasive Spartina alterniflora in Willapa Bay, WA. For all such systems, linear programming shows in general that the optimal strategy in any time step is to prioritize removal of a single age or stage class. The optimal strategy adjusts which class is the focus of control through time and can be much more cost effective than prioritizing removal of the same stage class each year.

Plant Development↗

PubMed1998

Optimal control of the cell dynamics in the granulosa of ovulatory follicles.

The aim of this paper is to seek for the optimal cellular changes in the granulosa of ovarian follicles, leading to ovulation in minimal time. The granulosa cell population consists of proliferating, differentiated and apoptotic cells. Cell numbers are ruled by a system of differential equations, in which the control variables are the cell cycle exit and apoptosis rates. The conditions for ovulation are represented by three different constraints on the granulosa final state. We prove that the optimal strategy consists in applying permanently the minimal apoptosis rate and in switching the cell cycle exit rate from its minimal bound to its maximal one. We finally apply the optimal strategy on data providing the changes in the total cell number of ewe follicles during their terminal development.

Animals↗

PubMed1995

Optimal control for an above-knee prosthesis with two degrees of freedom.

Our previous research and clinical tests of a self-contained powered above-knee prosthesis (AKP) showed that a knee joint with one degree of freedom (DOF) increases the energy cost of walking with respect to able-bodied subjects. Better symmetry of the gait can improve performance, so we suggest here the integration of a second powered DOF into the knee joint mechanism to control the internal-external rotation of the shank-foot complex. The control for the AKP with two DOFs is based on a method of optimal tracking. The data used for analysis were collected in able-bodied subjects braced with an ankle splint to experimentally duplicate a gait like that of amputees using a two-DOF prosthesis. The simulation showed the following: (1) the technique of optimal programming can be used for simulation of the artificial leg during locomotion; (2) the optimal tracking method is an efficient tool for selection of actuators for the above-knee prosthesis, ensuring that the tracking remains within limits. Limitation of joint torque is desirable in order to reduce the size of the motor, but beyond a certain point limiting maximal torques lead to tracking errors that are associated with higher energy costs and hence the need for a larger power source. The errors are also associated with higher forces at the interface between the socket and the prosthesis. The optimal tracking method allows the optimization of tracking with constraints on the size of the motor used and its energy cost.

Adult↗

PubMedDate not supplied

Optimal control of a birth and death epidemic process.

We employ a birth and death process to describe the spread of an infectious disease through a closed population. Control of the epidemic can be effected at any instant by varying the birth and death rates to represent quarantine and medical care programs. An optimal strategy is one which minimizes the expected discounted losses and costs resulting from the epidemic process and the control programs over an infinite horizon. We formulate the problem as a continuous-time Markov decision model. Then we present conditions ensuring that optimal quarantine and medical care program levels are nonincreasing functions of the number of infectives in the population. We also analyze the dependence of the optimal strategy on the model parameters. Finally, we present an application of the model to the control of a rumor.

Communicable Disease Control↗

PubMed2006

Optimal control and anti-control of the nonlinear dynamics of a rigid block.

This paper deals with control and anti-control of overturning of a rigid block subjected to a generic periodic excitation. Attention is focused on two relevant thresholds, corresponding to heteroclinic bifurcation and immediate overturning, and representing lower and upper bounds of the region where toppling can occur. The two opposite problems of increasing (control) or decreasing (anti-control) of these two curves by properly modifying the shape of the excitation are investigated in depth and the optimal excitations permitting their maximum variations are determined. The notions of 'global' and 'one-side' control (anti-control) are utilized and their different importance for the various cases is discussed. The effects of control (anti-control) of one curve on the uncontrolled (non-anti-controlled) curve are also investigated, both analytically and with numerical overturning charts. A good agreement is seen to occur.

Algorithms↗

PubMed2001

System analysis for optimal control of a wastewater treatment benchmark.

The paper presents an analysis and optimisation of a wastewater treatment benchmark. The benchmark is a simulation environment defining a plant layout, simulation model, influent data, test procedures and evaluating criteria that should be used for comparing different control strategies. In this paper an analysis of the benchmark which addresses the influences of potential manipulated variables on control performance under different operating conditions is presented. In the study optimisation is used to define the optimal values of the manipulated variables under constant as well as dynamic influent conditions. The results indicate that such an analysis and optimisation give important information about the manipulated variables under varying influent conditions and consequently about possible control strategies.

Computer Simulation↗

PubMed2006

Excited-state dynamics of carotenoids in light-harvesting complexes. 2. Dissecting pulse structures from optimal control experiments.

Dispersed multipump-probe (PPP) spectroscopy was used to explore the role of saturation, annihilation, and structured pulses in recent coherent control experiments on the light-harvesting 2 complex from Rhodopseudomonas acidophila (Herek et al. Nature 2002, 417, 533). We discuss the complimentary aspects between the PPP technique and coherent control studies, in particular the ability to dissect complicated pulse structures and the utility in exploring incoherent mechanisms. With the aid of a simple multistate model involving only population dynamics, we illustrate how the optimized structured pulses may be explained in terms of an interplay between excited-state populations, saturation, and annihilation. Furthermore, we discuss the experimental conditions that are required for incoherent effects to contribute to control experimental signals, with particular emphasis on pulse intensities, and show that the optimization of a ratio of conservative signals (i.e., not modulated by external dynamics) is required to exclude saturation effects from coherent control studies.

Carotenoids↗

PubMed2004

A SISO mixed H2/l1 optimal control problem and its solution.

Study of the SISO mixed H(2)/l(1) problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l(2) norm with solvable suboptimal solutions and solvable superoptimal solutions.

Algorithms↗

PubMedDate not supplied

A semiclosed-loop optimal control system for blood glucose level in diabetics.

In this manuscript, the well-known Bergman nonlinear mathematical model of the plasma glucose/insulin interaction is adopted and a semi closed-loop optimal technique is proposed for the correction of hyperglycemia in diabetic subjects. Computer simulations are used to evaluate the effectiveness of the proposed technique and to demonstrate its superiority in controlling hyperglycemia over other existing algorithms.

Algorithms↗

PubMed2003

Optimal control of spin dynamics in the presence of relaxation.

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? In this paper, we give analytical answers to the above questions. Unexpected gains in sensitivity are reported for one of the most commonly used experimental building blocks in NMR spectroscopy. Surprisingly, in the case when longitudinal relaxation is small, the relaxation optimized pulse elements (ROPE) that transfer maximum polarization between coupled spins are longer than conventional sequences.

Journal Article↗