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PubMed2002

Theory for the optimal control of time-averaged quantities in quantum systems.

We present a variational theory for the optimal control of quantum systems with relaxation over a finite time interval. In our approach, which is a nontrivial generalization of previous formulations and which contains them as limiting cases, the optimal control field fulfills a high-order Euler-Lagrange differential equation, which guarantees the uniqueness of the solution. We solve this equation numerically and also analytically for some limiting cases. The theory is applied to two-level quantum systems with relaxation, for which we determine quantitatively how relaxation effects limit the control of the system.

Journal Article↗
PubMed1999

Thermodynamic framework for discrete optimal control in multiphase flow systems.

Bellman's method of dynamic programming is used to synthesize diverse optimization approaches to active (work producing) and inactive (entropy generating) multiphase flow systems. Thermal machines, optimally controlled unit operations, nonlinear heat conduction, spontaneous relaxation processes, and self-propagating wave fronts are all shown to satisfy a discrete Hamilton-Jacobi-Bellman equation and a corresponding discrete optimization algorithm of Pontryagin's type, with the maximum principle for a Hamiltonian. The extremal structures are always canonical. A common unifying criterion is set for all considered systems, which is the criterion of a minimum generated entropy. It is shown that constraints can modify the entropy functionals in a different way for each group of the processes considered; thus the resulting structures of these functionals may differ significantly. Practical conclusions are formulated regarding the energy savings and energy policy in optimally controlled systems.

Journal Article↗
PubMed2002

Human motion planning based on recursive dynamics and optimal control techniques.

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

Algorithms↗
PubMed2005

Mathematical model for optimal control in wastewater discharges: the global performance.

In this work we show how mathematical models and optimal control techniques can help us to solve some problems of environmental engineering, more precisely, water pollution problems arising from wastewater discharges into coastal areas or rivers. We deal with a complete two-dimensional mathematical model for the evolution of pollutant concentration in a shallow water domain. By integrating this model we obtain a zero-dimensional one and we use it to study the global performance of the system in a realistic situation. Finally, by using the two-dimensional model, we recall two optimal control problems related to the wastewater disposal problem.

Models, Theoretical↗
PubMed2003

Hybrid adaptive optimal control of anaerobic fluidized bed bioreactor for the de-icing waste treatment.

Hybrid adaptive control strategy was developed and tested for the degradation of propylene glycol, a major component in de-icing waste, in an anaerobic fluidized bed bioreactor (AFBR). A linearized model with time-varying parameters was first employed to describe the dynamic behavior of the AFBR using a recursive off-line system identification method. A hybrid adaptive control strategy was then tested using a recursive off-line system identification routine followed by an on-line adaptive optimal control algorithm. The objective of the controller was to achieve the desired set point value of the propionate concentration (stand-alone control output variable) by manipulating the dilution rate (control input variable). To do so, the optimal control law was developed by minimizing a cost function with constraint equations. This novel idea was successfully applied to the underlying system for 200 h. The set point (700 mg HPrl(-1)) was achieved even in the case where the feed concentration suddenly increased by 50% (9000 mg HPrl(-1) to 13500 mg HPrl(-1)).

Algorithms↗
PubMed2006

Direct descent curvature optimal control with a modification algorithm and its application to nonlinear process.

This paper presents a direct descent second order or direct descent curvature algorithm with some modifications for the optimal control computations. This algorithm is compared with Hamiltonian methods in the literature. The proposed algorithm has generated numerically robust solutions with respect to conjugate points. The weighting matrix updating scheme was developed to improve the second-order optimal control algorithm, tested the performance of the algorithm, and shown on the benchmark and industrial process. The time-varying optimal feedback (TVOFB) gains are also generated along the trajectory as byproducts. If the trajectory deviates from the optimal trajectory for any reason (i.e., changing of system parameters, step disturbance into the plant, changing of initial conditions), it is held on the optimal trajectory by means of the optimal feedback. Simulations have been given for controlling the Van der Pol and bioreactor system, which are nonlinear benchmark systems.

Journal Article↗
PubMed2003

Biomechanical modeling and optimal control of human posture.

The present work describes the biomechanical modeling of human postural mechanics in the saggital plane and the use of optimal control to generate open-loop raising-up movements from a squatting position. The biomechanical model comprises 10 equivalent musculotendon actuators, based on a 40 muscles model, and three links (shank, thigh and HAT-Head, Arms and Trunk). Optimal control solutions are achieved through algorithms based on the Consistent Approximations Theory (Schwartz and Polak, 1996), where the continuous non-linear dynamics is represented in a discrete space by means of a Runge-Kutta integration and the control signals in a spline-coefficient functional space. This leads to non-linear programming problems solved by a sequential quadratic programming (SQP) method. Due to the highly non-linear and unstable nature of the posture dynamics, numerical convergence is difficult, and specific strategies must be implemented in order to allow convergence. Results for control (muscular excitations) and angular trajectories are shown using two final simulation times, as well as specific control strategies are discussed.

Algorithms↗
PubMed2005

Improved excitation schemes for multiple-quantum magic-angle spinning for quadrupolar nuclei designed using optimal control theory.

We have investigated the use of optimal control theory for the design of improved multiple-quantum excitation schemes for the popular multiple-quantum magic-angle spinning NMR experiment for quadrupolar nuclei with half-integer quadrupolar spin. The advantage of the new low-power experiments, termed OCFASTER, is demonstrated by sensitivity improvements approaching 50% for 87Rb in RbClO4 and RbNO3 as compared to FASTER and standard strong-pulse excitation schemes.

Computer Simulation↗
PubMedDate not supplied

Human energy - optimal control of disturbance rejection during constrained standing.

An optimal control system that enables a subject to stand without hand support in the sagittal plane was designed. The subject was considered as a double inverted pendulum structure with a voluntarily controlled degree of freedom in the upper trunk and artificially controlled degree of freedom in the ankle joints. The control system design was based on a minimization of cost function that estimated the effort of the ankle joint muscles through observation of the ground reaction force position relative to the ankle joint axis. By maintaining the centre of pressure close to the ankle joint axis the objective of the upright stance is fulfilled with minimal ankle muscle energy cost. The performance of the developed controller was evaluated in a simulation-based study. The results were compared with the responses of an unimpaired subject to different disturbances in the sagittal plane. The proposed cost function was shown to produce a reasonable approximation of human natural behaviour.

Algorithms↗
PubMed1992

Conductivity interface modelling with dipoles by means of optimal control and boundary element methods in impedance tomography.

Optimal control techniques have been combined with Alessandrini's singular perturbation method and Wexler's algorithm to reconstruct images in impedance imaging. We have also considered an integral formulation of the potential problem, which has led us to introduce an array of dipoles whose position, orientation and length can be optimised to model the conductivity discontinuities.

Algorithms↗
PubMed1989

[The application of an optimal control model in the study of migration].

"An optimal control model has been applied in the study of migration among regions [in Indonesia. The author finds that the] population in Indonesia is not well distributed: more than half...live in Java. Since migration can mean reducing or increasing the total population in a region, so a [better] distribution of the population will overcome the problem, [by relocating the population] to a certain region (such as Irian Jaya, Kalimantan and others)." (SUMMARY IN ENG)

Asia↗
PubMed2005

Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy.

A mathematical model for the depletion of bone marrow under cancer chemotherapy is analyzed as an optimal control problem. The control represents the drug dosage of a single chemotherapeutic agent and pharmacokinetic equations which model its plasma concentration are included. The drug dosages enter the objective linearly. It is shown that optimal controls are bang-bang, i.e. alternate the drug dosages at full dose with rest-periods in between, and that singular controls which correspond to treatment schedules with varying dosages at less than maximum rate are not optimal. Numerical simulations are given to illustrate the effect of the pharmacokinetic equations on the dosages.

Algorithms↗
PubMed2006

Experimental implementation of identification-based optimizing control of a simulated moving bed process.

Experimental implementation of an optimizing controller based on identified model for the separation of nucleosides in a laboratory scale simulated moving bed (SMB) unit is reported in this study. The manipulative variables are the three external and one internal flow rates while the outputs are productivity, solvent consumption, and purities of extract and raffinate streams averaged over a switching period. The feedback information is the concentration profile of extract and raffinate measured online using two ultraviolet (UV) detectors. Experimental results show that the designed controller is able to operate the SMB units under optimal condition fulfilling the purity requirements. Besides, the controller demonstrated excellent performance in terms of rejecting disturbances that may occur during SMB operations.

Chromatography↗
PubMed2001

Optimal control by least squares support vector machines.

Support vector machines have been very successful in pattern recognition and function estimation problems. In this paper we introduce the use of least squares support vector machines (LS-SVM's) for the optimal control of nonlinear systems. Linear and neural full static state feedback controllers are considered. The problem is formulated in such a way that it incorporates the N-stage optimal control problem as well as a least squares support vector machine approach for mapping the state space into the action space. The solution is characterized by a set of nonlinear equations. An alternative formulation as a constrained nonlinear optimization problem in less unknowns is given, together with a method for imposing local stability in the LS-SVM control scheme. The results are discussed for support vector machines with radial basis function kernel. Advantages of LS-SVM control are that no number of hidden units has to be determined for the controller and that no centers have to be specified for the Gaussian kernels when applying Mercer's condition. The curse of dimensionality is avoided in comparison with defining a regular grid for the centers in classical radial basis function networks. This is at the expense of taking the trajectory of state variables as additional unknowns in the optimization problem, while classical neural network approaches typically lead to parametric optimization problems. In the SVM methodology the number of unknowns equals the number of training data, while in the primal space the number of unknowns can be infinite dimensional. The method is illustrated both on stabilization and tracking problems including examples on swinging up an inverted pendulum with local stabilization at the endpoint and a tracking problem for a ball and beam system.

Feedback↗
PubMed2001

Reliability of optimal control strategies for photochemical air pollution.

This study illustrates how consideration of modeling uncertainties can affect optimal control strategies for urban ozone. Control strategies are investigated for illustrative cases of air parcel trajectories ending at Azusa, CA, and Riverside, CA, on August 28, 1987. The control strategies are designed to achieve a specified air quality target with a given reliability, considering uncertainties in the California Institute of Technology's trajectory model and its inputs, including uncertainties in emissions and in the SAPRC-97 chemical mechanism. A decoupled stochastic optimization scheme is used to solve the chance-constrained programming problem. Least-cost control strategies derived using nominal model inputs and parameter values have low reliability for some target O3 concentrations when uncertainties are taken into account. For the case considered, reducing volatile organic compound (VOC) emissions from motor vehicles is identified as the least-cost approach to meeting O3 targets at Azusa. However, the optimal control strategies for Riverside depend on the target O3 concentrations and the level of reliability required. Consideration of model uncertainty is found to shift the focus from VOC controls to nitrogen oxide controls for the Riverside trajectory.

Air Pollution↗
PubMed1992

Modelling the optimal control of cyclical leg movements induced by functional electrical stimulation.

An optimal control strategy for FES-induced cyclical leg movements in paraplegics is proposed. The control of the cyclical movement of a freely swinging leg is considered as an example. Quadriceps and the flexion withdrawal reflex are stimulated in order to generate a cyclical movement, of which the forward swing resembles the swing phase of gait. Optimal stimulation patterns are determined on the basis of an optimization criterion and a dynamic model of the system. The criterion is based on desired movement parameters and a minimal duration of the stimulation bursts. The movement parameters should ensure the generation of the desired cyclical movement: a desired hip angle range, sufficient foot clearance during the forward swing and knee extension at the beginning of the backward swing. Minimal duration of the stimulation bursts is assumed to yield minimal fatigue. A dynamic model, describing the dynamics of the neural system, the muscles and the leg, was constructed and its parameters identified on the basis of preliminary experiments and literature. Optimal timing of the quadriceps and flexion reflex stimulation bursts was determined by means of computer simulation. These simulations predicted that the flexion reflex should be stimulated in a short burst approximately 150 ms before the start of the forward swing. The quadriceps should be stimulated approximately starting 200 ms before the end of the forward swing in order to ensure knee extension at the beginning of the backward swing. The duration of one cycle of the movement was between 1300 and 1500 ms in these simulations. These results predict that the movement specified by the functional objectives can be realised using only two channels of stimulation. On the basis of the optimal timing, an adaptive control strategy can be designed, which varies the stimulation burst width when muscles fatigue.

Biomechanical Phenomena↗
PubMed2006

Isotope selective photoionization of NaK by optimal control: theory and experiment.

We present a joint theoretical and experimental study of the maximization of the isotopomer ratio (23)Na(39)K(23)Na(41)K using tailored phase-only as well as amplitude and phase modulated femtosecond laser fields obtained in the framework of optimal control theory and closed loop learning (CLL) technique. A good agreement between theoretically and experimentally optimized pulse shapes is achieved which allows to assign the optimized processes directly to the pulse shapes obtained by the experimental isotopomer selective CLL approach. By analyzing the dynamics induced by the optimized pulses we show that the mechanism involving the dephasing of the wave packets between the isotopomers (23)Na (39)K and (23)Na (41)K on the first excited state is responsible for high isotope selective ionization. Amplitude and phase modulated pulses, moreover, allow to establish the connection between the spectral components of the pulse and corresponding occupied vibronic states. It will be also shown that the leading features of the theoretically shaped pulses are independent from the initial conditions. Since the underlying processes can be assigned to the individual features of the shaped pulses, we show that optimal control can be used as a tool for analysis.

Journal Article↗