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PubMed2005

Linear theory for control of nonlinear stochastic systems.

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of nonlinear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exists a critical noise value that separates regimes where optimal control yields qualitatively different solutions. The path integral can be computed efficiently by Monte Carlo integration or by a Laplace approximation, and can therefore be used to solve high dimensional stochastic control problems.

Journal Article↗

PubMed2002

Time-optimal chaos control by center manifold targeting.

Ott-Grebogi-Yorke control and its map-based variants work by targeting the (linear) stable subspace of the target orbit so that after one application of the control the system will be in this subspace. I propose an n-step variation, where n is the dimension of the system, that sends any initial condition in a controllable region directly to the target orbit instead of its stable subspace. This method is time optimal, in that, up to modeling and measurement error, the system is completely controlled after n iterations of the control procedure. I demonstrate the procedure using a piecewise linear and a nonlinear two-dimensional map, and indicate how the technique may be extended to maps and flows of higher dimension.

Journal Article↗

PubMed1989

Formation and control of optimal trajectory in human multijoint arm movement. Minimum torque-change model.

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.

Arm↗

PubMed1990

Artificial blood circulation: stabilization, physiological control, and optimization.

The requirements for creating an efficient Artificial Blood Circulation System (ABCS) have been determined. A hierarchical three-level adaptive control system is suggested for ABCS to solve the following problems: stabilization of the circulation conditions, left and right pump coordination, physiological control for maintaining a proper relation between the cardiac output and the level of gas exchange required for metabolism, and optimization of the system behavior. The adaptations to varying load and body parameters will be accomplished using the signals which characterize the real-time computer-processed values of correlations between the changes in hydraulic resistance of blood vessels, or the changes in aortic pressure, and the oxygen (or carbon dioxide) concentration.

Adaptation, Physiological↗

PubMed2006

Terahertz-laser control of large amplitude vibrational motion in the sub-one-cycle pulse limit.

We investigate the control of state-selective population transfer in the THz spectral range generated by sub-one-cycle pulse excitation. To this end we developed a zero-net-force modification of the optimal control algorithm which allows us to extend the algorithm into the ultrashort pulse domain. By combining the analysis of the control landscapes and that of optimal control theory, we were able to formulate a general mechanism suitable for laser control by ultrashort pulses. The strategy consists of a superposition of two pi-pulses with carrier envelope phases of phi = pi/2. The first pulse is effectively in resonance with the targeted transition, while the second one, fired at around the minimum of the first pulse second lobe, removes leaking to the dipole-coupled background state. To compensate for the pulses ultrashort duration, the carrier frequencies of both pulses are red-shifted from the spectroscopic resonance.

Journal Article↗

PubMed2006

Control strategy optimization for attainment and exposure mitigation: case study for ozone in Macon, Georgia.

Implementation of more stringent 8-hour ozone standards has led the U.S. Environmental Protection Agency to designate nonattainment status to 474 counties nationwide, many of which had never previously violated air quality standards. As states select emission control measures to achieve attainment in these regions, their choices pose significant implications to local economies and the health of their citizens. Considering a case study of one such nonattainment region, Macon, Georgia, we develop a menu of potential controls that could be implemented locally or in neighboring parts of the state. The control menu offers the potential to control about 20-35% of ozone precursor emissions in most Georgia regions, but marginal costs increase rapidly beyond 15-20%. We link high-order ozone sensitivities with the control menu to identify cost-optimized strategies for achieving attainment and for alternative goals such as reducing spatially averaged or population-weighted ozone concentrations. Strategies targeted toward attainment of Macon ozone would prioritize local reductions of nitrogen oxides, whereas controls in the more densely populated Atlanta region are shown to be more effective for reducing statewide potential population exposure to ozone. A U.S. EPA-sanctioned approach for demonstrating ozone attainment with photochemical models is shown to be highly dependent on the choice of a baseline period and may not foster optimal strategies for assuring attainment and protecting human health.

Air Pollution↗

PubMed2003

[Control of blood pressure in diabetic patients in primary care setting. DIAPA study].

BACKGROUND AND OBJECTIVE: We aimed to assess the blood pressure (BP) control in patients with diabetes mellitus (DM) treated in primary care (PC) and to establish the factors associated with a suboptimal control of BP. PATIENTS AND METHOD: This was a multicenter, transverse study. Ninety investigators included 875 patients with DM (57.8% women), with a mean (SD) age of 64 (11.8) years. BP was measured according to the Sixth Report of Joint National Committee (JNC-VI) and Word Health Organization/International Society Hypertension (WHO/ISH) recommendations, calculating the arithmetic mean of three consecutive measurements. Patients with a previous established diagnosis were considered to be hypertensive, and an optimal control was considered when BP values were lower than 130/85 mmHg. RESULTS: 66.7% (n = 583) patients with DM were previously diagnosed of hypertension (HT); 86.3% (CI 95%: 83.0-89.1) of those with type 2 DM and 87.8% (CI95%: 70.9-96.0) of those with type 1 DM did not have an optimal control of BP at the visit (BP >= 130 and/or 85 mmHg). 56.8% (CI 95%: 50.1-63.3) of those with type 2 DM and 23.8% (CI 95%: 12.6-39.8) of those with type 1 DM with unknown HT had a BP >= 130 and/or 85 mmHg at the visit. The median of antihypertensive drugs used was 1 (1-2). In a multivariate analysis, age, higher body mass index (BMI), higher cholesterol levels and uric acid were associated with a worse BP control (p < 0.001). CONCLUSIONS: In our study, 66.7% of patients with DM attended in PC had known HT and only 13.6% had an optimal BP control. Diabetic patients with HT were undertreated, with a median of one antihypertensive drug.

Aged↗

PubMed2003

Regression of hypertensive nephropathy during three years of optimal blood pressure control.

Hypertensive nephropathy is among the leading causes of end-stage renal disease. Once renal function is severely impaired, the effects of strict control of blood pressure on the recovery of renal function remain elusive. Published case series suggest that optimal control of blood pressure results in regression of renal failure to some extent. In the present case of biopsy-proven hypertensive nephropathy we show that renal function can substantially improve over time if blood pressure is optimally controlled. Glomerula filtration rate continuously improved in our patient from 20 ml/min at presentation to 80 ml/min over a period of three years using a fivefold antihypertensive regimen. Hypertensive retinopathy regressed from stage III to stage I, and left ventricular hypertrophy decreased from an initial septum thickness of 19 mm to 12 mm within that period of time. This case clearly illustrates that optimal control of blood pressure is mandatory in patients with pre-terminal renal failure due to hypertensive nephropathy. Such intervention can lead to a regression of hypertension-associated end-organ injury.

Adrenergic alpha-Antagonists↗

PubMed2006

Quantum control of molecular vibrational and rotational excitations in a homonuclear diatomic molecule: a full three-dimensional treatment with polarization forces.

The optimal control of the vibrational excitation of the hydrogen molecule [Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)] utilizing polarization forces is extended to three dimensions. The polarizability of the molecule, to first and higher orders, is accounted for using explicit ab initio calculations of the molecular electronic energy in the presence of an electric field. Optimal control theory is then used to design infrared laser pulses that selectively excite the molecule to preselected vibrational-rotational states. The amplitude of the electric field of the optimized pulses is restricted so that there is no significant ionization during the process, and a new frequency sifting method is used to simplify the frequency spectrum of the pulse. The frequency spectra of the optimized laser pulses for processes involving rotational excitation are more complex than those relating to processes involving only vibrational excitation.

Journal Article↗

PubMed1996

Risk-sensitive optimal harvesting and control of biological populations

Theory recently developed elsewhere is introduced, to a more applied and biological audience, for the optimal control of linear systems with a risk-sensitive exponential of a quadratic (LEQG) cost function, and for the optimal control of fully nonlinear systems through the risk-sensitive maximum principle (RSMP). The LEQG theory is extended, in this study, to give solutions for locally optimal stochastic control of nonlinear systems. Examples and applications are given of the extended theory, using simple, heuristic logistic models and more complex multicohort models of fisheries. Implementations of the nonlinear RSMP are described. The results show how the theories can be applied to biological harvesting and control problems. They also shed some light upon the character of the dynamics of the risk-sensitive optimal solutions, which have been little explored. Keywords: population dynamics; resource management; fisheries; risk.

Journal Article↗

PubMed2005

Dynamic motion planning for the design of robotic gait rehabilitation.

In this paper we examine a method to control the stepping motion of a paralyzed person suspended over a treadmill using a robot attached to the pelvis. A leg swing motion is created by moving the pelvis without contact with the legs. The problem is formulated as an optimal control problem for an underactuated articulated chain. The optimal control problem is converted into a discrete parameter optimization and an efficient gradient-based algorithm is used to solve it. Motion capture data from an unimpaired human subject is compared to the simulation results from the dynamic motion optimization. Our results suggest that it is feasible to drive repetitive stepping on a treadmill by a paralyzed person by assisting in torso movement alone. The optimized, pelvic motion strategies are comparable to "hip-hiking" gait strategies used by people with lower limb prostheses or hemiparesis. The resulting motions can be found at the web site http://ww.eng.uci.edu/-chwang/project/stepper/stepper.html.

Computer Simulation↗

PubMed2002

A decision-tree to optimise control measures during the early stage of a foot-and-mouth disease epidemic.

A decision-tree was developed to support decision making on control measures during the first days after the declaration of an outbreak of foot-and-mouth disease (FMD). The objective of the tree was to minimise direct costs and export losses of FMD epidemics under several scenarios based on livestock and herd density in the outbreak region, the possibility of airborne spread, and the time between first infection and first detection. The starting point of the tree was an epidemiological model based on a deterministic susceptible-infectious-recovered approach. The effect of four control strategies on FMD dynamics was modelled. In addition to the standard control strategy of stamping out and culling of high-risk contact herds, strategies involving ring culling within 1 km of an infected herd, ring-vaccination within 1 km of an infected herd, and ring-vaccination within 3 km of an infected herd were assessed. An economic model converted outbreak and control effects of farming and processing operations into estimates of direct costs and export losses. Ring-vaccination is the economically optimal control strategy for densely populated livestock areas whereas ring culling is the economically optimal control strategy for sparsely populated livestock areas.

Animal Husbandry↗

PubMed2002

Synthesis of a robust broadband duct ANC system using convex programming approach.

A robust active controller using spatially feedforward structure is proposed for broadband attenuation of noise in ducts. To meet the requirements of performance and robust stability in the presence of plant uncertainties, an H2 cost function and an H(infinity) constrain are employed in the synthesis of the controller. The design is then converted into a convex programming problem using Q-parametrization and frequency discretization. An optimal controller that satisfies the quadratic cost functions and linear inequality constraints can be found by sequential quadratic programming. The optimal controller was implemented via a digital signal processor (DSP) and verified by experiments. Experiment results showed that the system attained 16.5 dB maximal attenuation and 5.9 dB total attenuation in the frequency band 200-600 Hz.

Journal Article↗

PubMed2006

Psychological adaptation after marital disruption: the effects of optimism and perceived control.

The present study explored the extent to which the two personality factors--perceived control and dispositional optimism--are related to psychological adaptation after marital disruption. A sample of 658 recently divorced individuals participated in the study by filling in an anonymous questionnaire. Bivariate findings revealed that perceived control and optimism were strongly related to psychological adaptation. However, when both predictors were included in a multiple regression analysis, optimism had a much larger effect than perceived control. The findings clearly indicate that personality factors account for a substantial proportion of the variance in adaptation to marital disruption.

Adaptation, Psychological↗

PubMed2002

Multisensory fusion and the stochastic structure of postural sway.

We analyze the stochastic structure of postural sway and demonstrate that this structure imposes important constraints on models of postural control. Linear stochastic models of various orders were fit to the center-of-mass trajectories of subjects during quiet stance in four sensory conditions: (i) light touch and vision, (ii) light touch, (iii) vision, and (iv) neither touch nor vision. For each subject and condition, the model of appropriate order was determined, and this model was characterized by the eigenvalues and coefficients of its autocovariance function. In most cases, postural-sway trajectories were similar to those produced by a third-order model with eigenvalues corresponding to a slow first-order decay plus a faster-decaying damped oscillation. The slow-decay fraction, which we define as the slow-decay autocovariance coefficient divided by the total variance, was usually near 1. We compare the stochastic structure of our data to two linear control-theory models: (i) a proportional-integral-derivative control model in which the postural system's state is assumed to be known, and (ii) an optimal-control model in which the system's state is estimated based on noisy multisensory information using a Kalman filter. Under certain assumptions, both models have eigenvalues consistent with our results. However, the slow-decay fraction predicted by both models is less than we observe. We show that our results are more consistent with a modification of the optimal-control model in which noise is added to the computations performed by the state estimator. This modified model has a slow-decay fraction near 1 in a parameter regime in which sensory information related to the body's velocity is more accurate than sensory information related to position and acceleration. These findings suggest that: (i) computation noise is responsible for much of the variance observed in postural sway, and (ii) the postural control system under the conditions tested resides in the regime of accurate velocity information.

Adult↗

PubMed2003

Dynamic optimization: inverse analysis for the Yurchenko layout vault in women's artistic gymnastics.

The use of dynamic optimization to compute the trajectory of joint torques is not popular due to the large amount of computation required, the choice of initial "guesstimates" of torque values and the mathematical sophistication required to understand the technique. Modern optimal control algorithms circumvent most of these objections to the method. It is our aim to demonstrate that the dynamic optimization technique is feasible for complex movements, using the Yurchenko layout vault as an example. A dynamic optimization method to compute joint torques so that the histories of the angular orientations of the model segments closely approximate the corresponding observed angular coordinate histories is demonstrated with the Yurchenko layout vault using an optimal control package. The objective function used is a measure of distance of fitted segment angles to the data, plus the distance of the fitted whole body centre of mass (CM), from the whole body CM computed from the data. Including the CM into the objective function, facilitates the optimization process so as to obtain a set of torques which reproduced the data. The paper shows that the approach works well for the task examined, that is, where the dynamics of the system change during a movement (impact to postflight).

Adolescent↗

PubMed1991

Control and optimization of apheresis procedures in a COBE 2997 cell separator.

To obtain more efficient operation of a COBE Model 2997 clinical cell separator using either a Single Stage II (SS II) or a Dual Stage separation chamber, modifications were made to allow complete computer control. Product cell density was detected using an optical sensor and controlled by automatic feedback through a microcomputer interface. Control was accomplished by automatically adjusting the red blood cell (RBC) and plasma product flow rates using a proportional-integral (PI) algorithm. Results show that, using either chamber, the product cell density can be maintained at a preselected value for extended periods of time without operator intervention. This system allowed investigation of optimal operating regions for plateletpheresis and leukapheresis procedures. The effects of centrifuge rpm and controller set point on centrifuge operation were investigated using a second order factorial experimental design. Theoretical significance of model parameters was assessed with the aid of a hindered settling model and simple reasoning about the interface position relative to the collection port. The results suggest that, in either chamber, the optimum operating region for plateletpheresis procedures occurs at moderate controller set points and high centrifuge rpm. The resultant operating efficiency and product purity values are approximately 63 percent and 0.65 respectively in the SS II chamber and approximately 70 percent and 0.70 respectively in the Dual Chamber. In the SS II, the optimum operating region for leukapheresis procedures occurred at high controller set point values for any centrifuge rpm above 1200 with an operating efficiency near 100 percent. However, in the Dual Chamber, the optimum operating region for leukapheresis procedures occurred at high controller set points and high centrifuge rpm's, again providing an operating efficiency near 100 percent.

Animals↗

PubMed2003

Does adjuvant radiation therapy increase loco-regional control after optimal resection of soft-tissue sarcoma of the extremities?

Adjuvant radiotherapy (RT) is routinely recommended for most soft-tissue sarcomas (STS) of the extremities. However, its impact on local control is not clearly established after wide complete excision. We performed a retrospective analysis of patients who underwent wide resection in our institution (first or second resection in cases of incomplete surgery) and either did or did not receive adjuvant RT. All histological specimens of patients operated upon between 1975 and 1996 were carefully analysed and only patients with free tumour margins (ftm) were retained for the analysis. The histopathological classification was as follows: minimal resection (mR) (ftm<10 mm) and optimal resection (oR) (ftm >/=10 mm). There were 133 patients with a median age of 44 years (range 16-88 years). The median tumour size was 6 cm (range 1-20 cm) with 28, 44 and 28% of stage I, II and III lesions, respectively. 93 patients (70%) were reoperated upon and residual tumour was found in 55% of the patients (51/93). 69 patients (17 oR and 52 mR) received adjuvant RT and 64 patients did not (54 oR and 10 mR). Other patient characteristics (age, tumour size, stage, deep-seated lesion, histoprognostic grade, adjuvant chemotherapy) were similar in both the RT and no-RT groups. Median follow-up was 10 years (3-25 years). The 5- and 10-year local relapse-free survival rates were 78 and 71%, respectively. 33 patients relapsed locally: 11 in the RT group and 22 patients in the control group (P=0.01). In the univariate analysis, adjuvant RT was correlated with relapse-free survival, while tumour grade and tumour margin status were correlated with overall survival. The multivariate analysis demonstrated a favourable impact of RT and negative influence of malignant fibrous histiocytoma (MFH) on local relapse-free survival; the tumour grade was correlated with overall survival. RT had a positive influence on local control exclusively in patients with mR resection (P=0.005) and in patients with residual tumour cells after re-excision (P=0.001). RT had no influence on 5- and 10-year overall survival. The 5- and 10-year overall survival for the entire population were 77 and 67%, respectively. Optimal resection seems to be the best predictive parameter for a favourable outcome in localised STS. Adjuvant RT is indicated after mR resection and for residual tumour after definitive surgery, but its role after oR resection (primary resection or no residual tumour after re-excision) should be evaluated in a prospective randomised trial.

Adolescent↗