Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

A systolic evaluator for linear, quadratic, and cubic expressions

High-speed evaluation of a large number of linear, quadratic, and cubic expressions is very important for the modeling and real-time display of objects in computer graphics. Using VLSI techniques, chips called pixel planes have actually been built by H. Fuchs and his group to evaluate linear expressions. In this paper, we describe a topological variant of Fuchs' pixel planes which can evaluate linear, quadratic, cubic, and higher-order polynomials. In our design, we make use of local interconnections only, i.e., interconnections between neighboring processing cells. This leads to the concept of tiling the processing cells for VLSI implementation.

Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

Linear chirp control of infrared signal in a biased semiconductor thin film

Ultrashort light-matter interactions between a linear chirped pulse and a biased semiconductor thin film GaAs are investigated. Using different chirped pulses, the dependence of infrared spectra on chirp rate is demonstrated for a 5 fs pulse. It is found that the infrared spectra can be controlled by the linear chirp of the pulse. Furthermore, the infrared spectral intensity could be enhanced by two orders of magnitude via appropriately choosing values of the linear chirp rates. Our results suggest a possible scheme to control the infrared signal.

Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments.

Improvement in clinical step and shoot intensity modulated radiation therapy delivery accuracy on an integrated linear accelerator control system

Purpose: The dose delivery accuracy of 30 clinical step and shoot intensity modulated radiation therapy plans was investigated using the single integrated multileaf collimator controller of the Varian Truebeam linear accelerator (linac) (Varian Medical Systems, Palo Alto, CA) and compared with the dose delivery accuracy on a previous generation Varian 2100CD C-Series linac.

Methods and Materials: Ten prostate, 10 prostate and pelvic node, and 10 head-and-neck cases were investigated in this study. Dose delivery accuracy on each linac was assessed using Farmer ionization chamber point dose measurements, 2-dimensional planar ionization chamber array measurements, and the corresponding Varian dynamic log files. Absolute point dose measurements, fluence delivery accuracy, leaf position accuracy, and the overshoot effect were assessed for each plan.

Results: Absolute point dose delivery accuracy increased by 1.5% on the Truebeam compared with the 2100CD linac. No improvement in fluence delivery accuracy between the linacs, at a gamma criterion of 3%/3 mm was measured using the 2-dimensional ionization chamber array, with median (interquartile range) gamma passing rates of 98.99% (97.70%-99.72%) and 99.28% (98.26%-99.75%) for the Truebeam and 2100CD linacs, respectively. Varian log files also showed no improvement in fluence delivery between the linacs at 3%/3 mm, with median gamma passing rates of 99.97% (99.93%-99.99%) and 99.98% (99.94%-100%) for the Truebeam and 2100CD linacs, respectively. However, log files revealed improved leaf position accuracy and fluence delivery at 1%/1 mm criterion on the Truebeam (99.87%; 99.78%-99.94%) compared with the 2100CD linac (97.87%; 91.93%-99.49%). The overshoot effect, characterized on the 2100CD linac, was not observed on the Truebeam.

Conclusions: The integrated multileaf collimator controller on the Varian Truebeam improves clinical treatment delivery accuracy of step and shoot intensity modulated radiation therapy fields compared with delivery on a Varian C-series linac. © 2014.

Identifying the predictors of employee health and satisfaction in an NPM environment : testing a comprehensive and non-linear demand-control-support model

The Demand-Control-Support (DCS) model is investigated in the context of police officers working within an organization that has relatively widespread uptake of New Public Management (NPM) practices. A survey of 479 police officers from two geographic regions was undertaken and the results indicate that the DCS offers a simple, yet powerful, framework for identifying the conditions to be managed in an NPM-oriented environment. Job control and work-based support predict all four target variables, strengthening the view that decision-making latitude and support from supervisors and colleagues represent critical resources for promoting the well-being, satisfaction and commitment of public sector employees.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

Equilibrium existence in the circle model with linear quadratic transport cost

We treat the problem of existence of a location-then-price equilibrium in the circle model with a linear quadratic type of transportation cost function which can be either convex or concave. We show the existence of a unique perfect equilibrium for the concave case when the linear and quadratic terms are equal and of a unique perfect equilibrium for the convex case when the linear term is equal to zero. Aside from these two cases, there are feasible locations by the firms for which no equilibrium in the price subgame exists. Finally, we provide a full taxonomy of the price equilibrium regions in terms of weights of the linear and quadratic terms in the cost function.