scholarly journals Optimal control in liver kinetics

1986 ◽  
Vol 27 (3) ◽  
pp. 361-369 ◽  
Author(s):  
A. M. Fink
Keyword(s):  
Optimal Control ◽  
Minimization Problem ◽  
Enzymatic Reaction ◽  
The Body ◽  
Minimum Problem ◽  
Density Functions ◽  
Intermediate Form

AbstractWe solve a minimization problem in liver kinetics posed by Bass, et al., in this journal, (1984), pages 538–562. The problem is to choose the density functions for the location of two enzymes, in order to minimize the concentration of an intermediate form of a substance at the outlet of the liver. This form may be toxic to the rest of the body, but the second enzyme renders it harmless. It seems natural that the second enzyme should be downstream from the first. However, we can show that the minimum problem is sometimes solved by an overlap of the supports of the two density functions. Even more surprising is that, for certain forms of the kinetic functions and high levels of transformation of the first enzymatic reaction, some of the first enzyme should be located downstream from all the second enzyme. This suggests that the first reaction should be relatively slow.

A Non-Normality Measure of the Condition Number for Monitoring and Control

1997 ◽  
Vol 119 (2) ◽  
pp. 217-222 ◽  
Author(s):  
Kunsoo Huh ◽  
Jeffrey L. Stein
Keyword(s):  
Optimal Control ◽  
Condition Number ◽  
Minimization Problem ◽  
Monitoring And Control ◽  
Proper Selection ◽  
Modal Structure ◽  
L2 Norm ◽  
And Control ◽  
Normality Measure ◽  
Selection Of

Because the behavior of the condition number can have highly steep and multi-modal structure, optimal control and monitoring problems based on the condition number cannot be easily solved. In this paper, a minimization problem is formulated for κ2(P), the condition number of an eigensystem (P) of a matrix in terms of the L2 norm. A new non-normality measure is shown to exist that guarantees small values for the condition number. In addition, this measure can be minimized by proper selection of controller and observer gains. Application to the design of well-conditioned controller and observer-based monitors is illustrated.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Vehicular Optimal Control

2018 ◽  
pp. 391-426
Author(s):  
David J. N. Limebeer ◽  
Matteo Massaro
Keyword(s):  
Optimal Control ◽  
Minimization Problem ◽  
Optimization Problems ◽  
Structural Features ◽  
Minimum Time ◽  
Time Of Arrival ◽  
Hybrid Powertrain ◽  
Multi Stage ◽  
Time Minimization ◽  
Minimum Time Problems

Chapter 9 deals with the solution of minimum-time and minimum-fuel vehicular optimal control problems. These problems are posed as fuel usage optimization problems under a time-of-arrival constraint, or minimum-time problems under a fuel usage constraint. The first example considers three variants of a simple fuel usage minimization problem under a time-of-arrival constraint. The first variant is worked out theoretically, and serves to highlight several of the structural features of these problems; the other two more complicated variants are solved numerically.The second example is also a multi-stage fuel usage minimization problem under a timeof- arrival constraint.More complicated track and vehicle models are then employed; the problem is solved numerically. The third problem is a lap time minimization problem taken from Formula One and features a thermoelectric hybrid powertrain. The fourth and final problem is a minimum-time closed-circuit racing problem featuring a racing motorcycle and rider.

Near-Optimal Time-Domain Control of Small Buoys in Irregular Waves

2014 ◽  
Author(s):  
Umesh A. Korde ◽  
R. Cengiz Ertekin
Keyword(s):  
Optimal Control ◽  
Impulse Response ◽  
Time Domain ◽  
The Body ◽  
Irregular Waves ◽  
Single Frequency ◽  
Impulse Response Functions ◽  
Control Force ◽  
Response Functions ◽  
Absorbed Power

Within the linear theory framework, smooth optimal control for maximum energy conversion in irregular waves requires independent synthesis of two non-causal impulse response functions operating on the body oscillations near the free surface, and one non-causal impulse response function relating the exciting force to the incident wave profile at the body. Full cancellation of reactive forces and matching of radiation damping thus requires knowledge or estimation of device velocity into the future. As suggested in the literature, the control force can be synthesized in long-crested waves by suitably combining the ‘full’ impulse response functions with wave surface elevation information at an appropriately determined distance up-wave of the device. This paper applies the near-optimal control approach investigated earlier by one of the authors (Korde, UA, Applied Ocean Research, to appear) to small floating cylindrical buoys. Absorbed power performance is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Time domain absorbed power results are discussed.

Enzyme-Mediated Oscillatory Drug Release through Hydrogel Membranes

1995 ◽  
Vol 394 ◽  
Author(s):  
John P. Baker ◽  
Ronald S. Siegel
Keyword(s):  
Drug Release ◽  
Hormone Replacement ◽  
Enzymatic Reaction ◽  
Human Growth ◽  
Product Inhibition ◽  
The Body ◽  
Acute Tolerance ◽  
Variable Permeability ◽  
Pulsatile Delivery ◽  
Membrane Oscillator

AbstractImplantable polymeric drug-delivery devices have been constructed to deliver drugs at welldefined rates. Typically, these devices have been designed to deliver drugs at a constant rate, or in response to the concentration of a certain body metabolite. For some drugs, pulsatile delivery is sought. For example, under normal conditions, human growth hormone is released in the body in periodic bursts. Current treatments for HGH deficiency often fail because HGH is not administered following the endogenous pattern. Thus, pulsatile hormone-replacement therapy should be considered. Also, it may be useful to deliver in a periodic, pulsatile manner drugs that exhibit significant acute tolerance.Currently, an oscillator is under development that is fueled by endogenous compounds and contains a variable-permeability membrane. The membrane's permeability to the substrate of an enzymatic reaction is assumed to be dependent on the concentration of the product of the reaction in a manner that displays product inhibition. Under certain conditions, this negative-feedback control can lead to oscillations in the membrane's permeability to substrate. If the membrane's permeability to a drug is simultaneously affected, then this will lead to oscillatory drug release.We report encouraging initial studies. A simple theoretical model has been developed for the membrane oscillator, and results of simulations based on the model are discussed.Diffusion-cell studies have been performed with a variable-permeability poly(N-isopropylacrylamide- co-methacrylic acid) hydrogel membrane. Using glucose as a probe solute, the results show that lowering the pH induces hydrogel volume collapse and cessation of glucose permeation across the membrane.

Effect of the sulfur-containing compounds on the quinoid process of adrenaline autoxidation; potential neuroprotectors

2019 ◽  
Vol 65 (4) ◽  
pp. 316-323
Author(s):  
T.V. Sirota
Keyword(s):  
Antioxidant Properties ◽  
Enzymatic Reaction ◽  
The Body ◽  
Biologically Active ◽  
Treatment And Prevention ◽  
Multistep Process ◽  
Ic50 Values ◽  
Sulfur Containing ◽  
Sulfur Containing Compounds

The superoxide-generating reaction of adrenaline autoxidation in an alkaline medium, used in vitro to identify the antioxidant properties of various compounds, simulates the complex multistep process of quinoid oxidation of catecholamines (CA) in the body. Sulfur-containing cysteine (Cys) and reduced glutathione (GSH), as well as oxidized glutathione (GSSG), have been shown to inhibit this process. The studied substances were considered as inhibitors of quinoid oxidation and are evaluated as antioxidants. The IC50 values for Cys and GSH were close to 7.5 mM. Inhibition by GSSG was weaker; represented approximately 50-70% of Cys and GSH. Other sulfur-containing compounds that differ in chemical structure, the amino acids taurine and methionine were ineffective. The interest in this model and the search for effective compounds acting on this reaction is associated with one of the mechanisms of the etiopathogenesis of Parkinson's disease (PD) discussed in the literature, which occurs when the biochemical transformations of dopamine CA and its quinoid oxidation process are violated. Cys, GSH and GSSG in the model system inhibit quinoid oxidation of adrenaline, as a result of which the formation of superoxide (O2 ·-) is also inhibited. Experiments with the superoxide-generating enzymatic reaction xanthine xanthioxidase, the chemistry of which is different and not related to formation of quinoid metabolites, showed that the studied substances did not inhibit O2 ·- formation in this model. Thus, it was established that the biologically active sulfur-containing compounds Cys, GSH and GSSG are specific inhibitors of quinoid oxidation of CA, and are likely to be able to play the role of a neuroprotector. It is proposed to use these compounds in the treatment and prevention of PD by activating their biosynthesis in the body.

A General Model to Chemo-Mechanical Equilibrium of a Geo-Synthetic Polymeric Membrane

2007 ◽  
Vol 345-346 ◽  
pp. 1031-1034
Author(s):  
Michele Buonsanti
Keyword(s):  
Minimization Problem ◽  
General Model ◽  
Chemical Potential ◽  
Axial Strain ◽  
Practical Importance ◽  
Fem Simulation ◽  
Polymeric Membrane ◽  
Minimum Problem ◽  
External Agent ◽  
Equilibrium Phases

The interaction between two or more independent causes of materials degradation results in a duplex mode of materials degradation. The materials degradation rate whether expressed in loss of material or loss of mechanical strength is often faster than the sum of each form of materials degradation acting separately. For this reason, duplex modes of materials degradation are of great practical importance. Synergisms between unrelated forms of materials degradation are not immediately obvious and have in some instances been only recently recognized. In this paper a chemically aggressive environment over a geo-synthetic polymeric membrane is investigated. The membrane free energy depends upon the mono-axial strain and the degree of reaction with an external agent. We suppose chemical potential assigned and the minimization problem is formulated. Practically the minimum problem is non-convex, and coexistence of equilibrium phases is possible. The proposed general model is able to describe the complex phenomenon when polymeric geo-synthetic membrane are undergoing to heterogeneous and complex action of the package system built in dump of urban waste. Finally a FEM simulation is compared with minimization problem theoretical results.

Modeling of Active Flexible Suspensions by Mobility and Transfer Matrix

2011 ◽  
Vol 383-390 ◽  
pp. 2366-2371
Author(s):  
Jun Chuan Niu ◽  
Hao Nan Guo ◽  
Meng Li
Keyword(s):  
Optimal Control ◽  
Optimal Design ◽  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
The Body ◽  
Impedance Method ◽  
Multi Objective Optimization ◽  
Vehicle Model ◽  
Numerical Examples ◽  
Proposed Model

For simplicity and not losing generality, a half-vehicle model with 4 rigid DOFs is presented by mobility or impedance method and transfer matrix technology, which bring the flexibility of the body to the proposed model easily and conveniently, instead of complex differential and state space equations. Based on the multi-objective optimization, a synthetic cost function is proposed to investigate the dynamic characteristics and achieve the optimal control of suspensions. The numerical examples are performed to show the validity and efficiency of the presented model, and some valuable conclusions are also obtained to guide the optimal design of suspensions.

On Hammersley's minimum problem for a rolling sphere

1986 ◽  
Vol 99 (3) ◽  
pp. 529-534 ◽  
Author(s):  
A. M. Arthurs ◽  
G. R. Walsh
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Control Theory ◽  
Shortest Path ◽  
Optimal Control Theory ◽  
Nonlinear Differential Equations ◽  
Equation Of Motion ◽  
Minimum Problem ◽  
End Conditions ◽  
Rolling Sphere

AbstractThe problem posed by Hammersley (1983) of finding the shortest path along which a sphere can roll from one prescribed state to another is formulated by using quaternion calculus of variations and optimal control theory. This leads to a system of coupled nonlinear differential equations with prescribed end conditions. From the resulting expression for the curvature, it is shown that the differential equation of the required path in intrinsic coordinates is the same as the equation of motion of a simple pendulum, giving a solution in terms of elliptic integrals.

scholarly journals Synthesis of the law of optimal control of the system of active dynamic stabilization of the movement of a self-propelled vehicle with a mounted working body

2020 ◽  
Vol 1 (5) ◽  
pp. 5-12
Author(s):  
P.V. Sirotin ◽  
Keyword(s):  
Optimal Control ◽  
The Body ◽  
System Control ◽  
Stabilization System ◽  
Stabilization Method ◽  
Emergency Braking ◽  
Total Energy Balance ◽  
The Law ◽  
Quadratic Integral ◽  
Linearized Model

The paper is devoted to the development of systems and technical devices for reduction of dy-namic loads acting on operators and the supporting system of self-propelled vehicles. The goal of the paper is to develop an algorithm and a law of optimal control of the stabilization system. The set of tasks to be solved for this is determined, the requirements for the information field are highlight-ed, the element base of the stabilization system is substantiated. The problem of optimal control of the stabilization system is formulated. The development of a law of control of the stabilization sys-tem of the movement of self-propelled wheeled vehicles based on the principle of active inertial vi-bration damping is presented. The law of optimal control of the stabilization system with the possi-bility of correcting the requirements for attenuation and the type of transient process was developed. On the basis of quadratic integral criteria, the indicators for assessing the quality of system control are distinguished. It is substantiated that for the system of stabilization of the harvester body it is necessary to regulate the output variables, such as the angular velocity of the body and the angle of the longitudinal inclination of the harvester body. A linearized model of the longitudinal-angular motion of the combine is considered, the equations that connect the laws of the disturbed motion of the body and the law of optimal control are presented. With the help of simulation modeling, the effectiveness of the proposed stabilization method and the law of control of the stabilization system in terms of reducing the longitudinal angles of inclination of the body when driving on an asphalt-concrete highway and a dirt road are shown. The effectiveness of the proposed law of control for suppressing the pitch of the combine body during emergency braking is shown. The calculated values of the power spent on control of the stabilization system for the considered driving modes are given. On the basis of calculations, it is shown that in the total energy balance of the combine, the power consumption for control is insignificant, which confirms the efficiency of the proposed stabilization method and the law of control. Conclusions are drawn, stages and directions of further research are determined.

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