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Results for “optimal control”

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PubMed2006

Optimal control of ultrafast laser driven many-electron dynamics in a polyatomic molecule: N-methyl-6-quinolone.

We report time-dependent configuration interaction singles calculations for the ultrafast laser driven many-electron dynamics in a polyatomic molecule, N-methyl-6-quinolone. We employ optimal control theory to achieve a nearly state-selective excitation from the S(0) to the S(1) state, on a time scale of a few ( approximately 6) femtoseconds. The optimal control scheme is shown to correct for effects opposing a state-selective transition, such as multiphoton transitions and other, nonlinear phenomena, which are induced by the ultrashort and intense laser fields. In contrast, simple two-level pi pulses are not effective in state-selective excitations when very short pulses are used. Also, the dependence of multiphoton and nonlinear effects on the number of states included in the dynamical simulations is investigated.

Journal Article↗

PubMed1985

Optimal control applications in the chemotherapy of multiple myeloma.

There is an increasing interest in the use of therapeutic devices which deliver chemotherapeutic agents in a continuous manner. In this paper the Gompertz model of cancer growth with a loss term depending on a cancer chemotherapeutic agent is applied to human multiple myeloma. Three different performance criteria are introduced which measure the influence of the anti-cancer drug in driving the tumor population level to a desired target level. Engineering optimal control theory is used to produce expressions for the continuous-time optimal control. A comparison is made between the natures of the controller for the three problems considered. Parameter values used in the models are based on patient data. Results of the present study may be useful in the construction of algorithms for use with drug delivery devices that incorporate a microprocessor. Use of such devices may be useful in improving the treatment schedules and treatment outcome of cancer patients.

Antineoplastic Agents↗

PubMed2005

Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system.

Optimality principles of biological movement are conceptually appealing and straightforward to formulate. Testing them empirically, however, requires the solution to stochastic optimal control and estimation problems for reasonably realistic models of the motor task and the sensorimotor periphery. Recent studies have highlighted the importance of incorporating biologically plausible noise into such models. Here we extend the linear-quadratic-gaussian framework--currently the only framework where such problems can be solved efficiently--to include control-dependent, state-dependent, and internal noise. Under this extended noise model, we derive a coordinate-descent algorithm guaranteed to converge to a feedback control law and a nonadaptive linear estimator optimal with respect to each other. Numerical simulations indicate that convergence is exponential, local minima do not exist, and the restriction to nonadaptive linear estimators has negligible effects in the control problems of interest. The application of the algorithm is illustrated in the context of reaching movements. A Matlab implementation is available at www.cogsci.ucsd.edu/~todorov.

Afferent Pathways↗

PubMed2002

A six-month multicentre, double-blind, bromocriptine-controlled study of the safety and efficacy of ropinirole in the treatment of patients with Parkinson's disease not optimally controlled by L-dopa.

OBJECTIVES: To compare the safety and efficacy of ropinirole and bromocriptine as adjunct therapy in patients with Parkinson's disease (PD) not optimally controlled by L-dopa. METHODS: A randomised, double-blind trial in which 555 patients were assigned to three treatment groups according to the level of daily dosage of L-dopa, presence of motor fluctuations, and use of dopamine agonist before study entry. Patient response was defined as at least a 20% reduction in daily L-dopa dose plus: for patients with no prior treatment and no motor fluctuations, a 20% reduction in UPDRS motor score; for patients with motor fluctuations, a 20% reduction in time spent "off"; and for patients already taking an agonist, an improvement on the CGI scale. RESULTS: Safety assessments showed no significant differences in the two treatment groups for patients without prior dopamine-agonist therapy. In the group of patients with prior dopamine-agonist therapy, more patients reported adverse events in the ropinirole group (90% versus 79%, p < 0.001). The proportions of responders tended to be higher in ropinirole groups compared with bromocriptine groups and, in the subgroup with motor fluctuations, this difference was statistically significant (9.1% versus 0.0%, respectively; p < 0.05). CONCLUSIONS: Both drugs were well tolerated. In patients receiving a relatively high dose of L-dopa and requiring the addition of a dopamine agonist to control motor fluctuations or dyskinesias, ropinirole was significantly more effective than bromocriptine.

Adult↗

PubMed1990

An optimal control model for maximum-height human jumping.

To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).

Biomechanical Phenomena↗

PubMed1991

Optimal control system for the intra-aortic balloon pump.

An optimal control system for the intra-aortic balloon pump (IABP) is presented. Control of the IABP is based on a performance index formulated to reflect a tradeoff between maximising cardiac oxygen supply and minimising cardiac oxygen consumption. In the performance index, mean diastolic pressure (MDP) was used to represent oxygen availability and peak systolic pressure (PSP) was used to represent oxygen consumption. An algorithm, implemented using an 8-bit microcomputer, changes the deflation time of the IABP to maximise this performance index by using an optimisation technique that employs both a search and an approximation. The search produces three equally spaced points which define a region that includes the maximum of the performance index. From these points, the optimum deflation time is estimated by a quadratic approximation. The algorithm has been successfully tested using performance index curves generated by computer simulations.

Algorithms↗

PubMed1994

Dosage regimen calculations with optimal control theory.

In clinical pharmacokinetics, dosage regimen calculation involves determination of either: (1) the drug amount to be administered according to a set time schedule, or (2) the time schedule to be used for appropriate drug amounts. The goal is to guarantee that the time profile of circulating drug levels is between the thresholds of toxicity and efficacy. For the first case, solutions are obtained by using the property of linearity when it holds. Herein, we present several results concerning the second case. The optimal control theory allows determination of switching times between the minimal and maximal input rates in order to ensure the fastest transition from an initial state to the therapeutic levels. Fundamental results are reported and the approach is developed for drugs administered by intravenous infusion. By means of the phase trajectories, general graphical rules are presented to design the optimal control and to determine the reachable areas. A numerical example is given, comparisons of the method with others are attempted and potential developments are pointed out.

Drug Administration Schedule↗

PubMed1999

A multi-phase optimal control technique for the simulation of a human vertical jump.

A multi-phase optimal control technique is presented that can be used to solve dynamic optimization problems involving musculoskeletal systems. The biomechanical model consists of a set of differential equations describing the dynamics of the multi-body system and the generation of the dynamic forces of the human muscles. Within the optimization technique, subintervals can be defined in which the differential equations are continuous. At the boundaries the dimension of the state- and control vector as well as the dimension of the right-hand side may change. The problem is solved by a multiple shooting approach which converts the problem into a non-linear program. The method is applied to simulate a human jump movement.

Computer Simulation↗

PubMed2004

Improving solid-state NMR dipolar recoupling by optimal control.

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.

Carbon Isotopes↗

PubMed1986

Energy cost minimization in left ventricular ejection: an optimal control model.

A new optimization model for explaining the observed left ventricular ejection patterns is presented. In the system model, arterial load is described by a modified windkessel load. The ejection pattern for a given cardiac output with fixed stroke volume and duration of ejection is predicted by minimizing a criterion that describes the total ventricular O2 consumption. The ejection patterns of the model closely resemble the observed ejection patterns. Also, the model predictions for changes in the values of the system parameters are qualitatively correct. The results strongly suggest that the control of ejection pattern satisfies the principle of energy cost minimization.

Animals↗

PubMed2005

Optimal control simulations reveal mechanisms by which arm movement improves standing long jump performance.

Optimal control simulations of the standing long jump were developed to gain insight into the mechanisms of enhanced performance due to arm motion. The activations that maximize standing long jump distance of a joint torque actuated model were determined for jumps with free and restricted arm movement. The simulated jump distance was 40 cm greater when arm movement was free (2.00 m) than when it was restricted (1.60 m). The majority of the performance improvement in the free arm jump was due to the 15% increase (3.30 vs. 2.86 m/s) in the take-off velocity of the center of gravity. Some of the performance improvement in the free arm jump was attributable to the ability of the jumper to swing the arms backwards during the flight phase to alleviate excessive forward rotation and position the body segments properly for landing. In restricted arm jumps, the excessive forward rotation was avoided by "holding back" during the propulsive phase and reducing the activation levels of the ankle, knee, and hip joint torque actuators. In addition, swinging the arm segments allowed the lower body joint torque actuators to perform 26 J more work in the free arm jump. However, the most significant contribution to developing greater take-off velocity came from the additional 80 J work done by the shoulder actuator in the jump with free arm movement.

Arm↗

PubMed2005

Optimal control of ultrafast cis-trans photoisomerization of retinal in rhodopsin via a conical intersection.

Optimal control simulation is applied to the cis-trans photoisomerization of retinal in rhodopsin within a two-dimensional, two-electronic-state model with a conical intersection [S. Hahn and G. Stock, J. Phys. Chem. B 104, 1146 (2000)]. For this case study, we investigate coherent control mechanisms, in which laser pulses work cooperatively with a conical intersection that acts as a "wave-packet cannon." Optimally designed pulses largely consist of shaping subpulses that prepare a wave packet, which is localized along a reaction coordinate and has little energy in the coupling mode, through multiple electronic transitions. This shaping process is shown to be essential for achieving a high target yield although the envelopes of the calculated pulses depend on the local topography of the potential-energy surfaces around the conical intersection and the choice of target. The control mechanisms are analyzed by considering the motion of reduced wave packets in a nuclear configuration space as well as by snapshots of probability current-density maps.

Journal Article↗

PubMed2006

Biodegradation of high 4-chlorophenol concentrations in a discontinuous reactor fed with an optimally controlled influent flow rate.

This work presents the results of the application of an optimally controlled influent flow rate strategy to biodegrade, in a discontinuous reactor, high concentrations of 4-chlorophenol used as toxic compound model. The influent is fed into the reactor in such a way as to obtain the maximal degradation rate, thus avoiding the inhibition of the microorganisms. The optimal strategy was able to manage increments of toxic concentrations in the influent up to 7,000 mg 4CP/L without any problem. It was shown not only that higher concentrations of toxic could be treated, but also that a reduction in degradation time (around 52%) and in the supplied air volume was obtained.

Bacteria, Anaerobic↗

PubMed2006

Optimal control in a model of dendritic cell transfection cancer immunotherapy.

We construct a population dynamics model of the competition among immune system cells and generic tumor cells. Then, we apply the theory of optimal control to find the optimal schedule of injection of autologous dendritic cells used as immunotherapeutic agent. The optimization method works for a general ODE system and can be applied to find the optimal schedule in a variety of medical treatments that have been described by a mathematical model.

Algorithms↗

PubMed2006

Quantum optimal control of molecular isomerization in the presence of a competing dissociation channel.

The quantum optimal control of isomerization in the presence of a competing dissociation channel is simulated on a two-dimensional model. The control of isomerization of a hydrogen atom is achieved through vibrational transitions on the ground-state surface as well as with the aid of an excited-state surface. The effects of different competing dissociation channel configurations on the isomerization control are explored. Suppression of the competing dissociation dynamics during the isomerization control on the ground-state surface becomes easier with an increase in the spatial separation between the isomerization and dissociation regions and with a decrease in the dissociation channel width. Isomerization control first involving transfer of amplitude to an excited-state surface is less influenced by the dissociation channel configuration on the ground-state surface, even in cases where the excited-state surface allows for a moderate spreading of the excited wave packet.

Journal Article↗

PubMed1994

Optimal control of antagonistic muscle stiffness during voluntary movements.

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an 'N'-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.

Arm↗

PubMed1995

An optimal control model for analyzing human postural balance.

The question posed in this study is whether optimal control and state estimation can explain selection of control strategies used by humans, in response to small perturbations to stable upright balance. To answer this question, a human sensorimotor control model, compatible with previous work by others, was assembled. This model incorporates linearized equations and full-state feedback with provision for state estimation. A form of gain-scheduling is employed to account for nonlinearities caused by control and biomechanical constraints. By decoupling the mechanics and transforming the controls into the space of experimentally observed strategies, the model is made amenable to the study of a number of possible control objectives. The objectives studied include cost functions on the state deviations, so as to control the center of mass, provide a stable platform for the head, or maintain upright stance, along with a cost function on control effort. Also studied was the effect of time delay on the stability of controls produced using various control strategies. An objective function weighting excursion of the center of mass and deviations from the upright stable position, while taking advantage of fast modes of the system, as dictated by inertial parameters and musculoskeletal geometry, produces a control that reasonably matches experimental data. Given estimates of sensor performance, the model is also suited for prediction of uncertainty in the response.

Biomechanical Phenomena↗

PubMed2003

Preventing coronary events by optimal control of blood pressure and lipids in patients with the metabolic syndrome.

We estimated the coronary heart disease (CHD) events that are preventable by treatment of lipids and blood pressure in patients with metabolic syndrome (MetS), a contributor to coronary heart disease (CHD). Among patients aged 30 to 74 years (without diabetes or CHD) in the United States, MetS was defined by National Cholesterol Education Program criteria. CHD events over a period of 10 years were estimated by Framingham algorithms. Events that could be prevented by statistically "controlling" blood pressure, low-density lipoprotein (LDL) cholesterol, and high-density lipoprotein (HDL) cholesterol to either normal or optimal levels according to national guidelines were calculated. Of 7.5 million men and 9.0 million women aged 30 to 74 years with MetS, approximately 1.5 million men and 0.45 million women, if untreated, developed CHD events in 10 years. In men and women, blood pressure control to normal levels "prevented" 28.1% and 12.5% of CHD events, respectively (p <0.01); control to optimal levels resulted in preventing 28.2% and 45.2% of events, respectively (p <0.01). Control of HDL cholesterol to normal levels resulted in preventing 25.3% of events in men and 27.3% in women; optimal control prevented 51.2% and 50.6% of events, respectively. Control of LDL cholesterol to normal levels prevented 9.3% of events in men and 9.8% of events in women; control to optimal levels prevented 46.2% and 38.1% of events (p <0.05), respectively. Control of all 3 risk factors to normal levels resulted in preventing 51.3% of events for men and 42.6% for women; control to optimal levels resulted in preventing 80.5% and 82.1% of events, respectively. Thus, many CHD events in patients with MetS may be preventable by nominal or optimal control of lipids and/or blood pressure.

Adult↗