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Computer program, an Iterative Scheme Using a Direct Solution, obtains double precision accuracy using a single-precision coefficient matrix. ISUDS solves a system of equations written in matrix form as AX equals B, where A is a square non-singular coefficient matrix, X is a vector, and B is a vector.
Stochastic approximation algorithms for identification of linear discrete time systems
Desensitized linear servo model following feedback control systems design using specific optimal control concepts
Linear and nonlinear control systems via state variable feedback with applications in nuclear reactor control
Two classes of large-scale systems are identified, which can always be stabilized by decentralized feedback control. For the class of systems composed of interconnected linear subsystems, we can choose local controllers for the subsystems to achieve stability of the overall system. The same linear feedback scheme can be used to stabilize a class of linear systems with bilinear interconnections. In this case, however, the scheme is used to establish a finite region of stability for the overall system. The stabilization algorithm is applied to the design of a control system for the Large-Space Telescope.
On-line system identification of linear discrete systems for implementation in a digital adaptive flight controller is considered by the conventional extended Kalman filter and a decoupling process in which the linear state estimation problem and the linear parameter identification problem are each treated separately and alternately. Input requirements for parameter identifiability are established using the standard conditions of observability for a time variant system. Experimental results for simulated linearized lateral aircraft motion are included along with the effect of different initialization and updating procedures for the priming trajectory used by the filter.
Theorems and definitions for generation of Liapunov functions for analysis of linear and nonlinear dynamic systems
Purpose: Leaf positions for dynamic multileaf collimator (DMLC) intensity modulated radiation therapy must be closely synchronized with MU delivery. For the Varian C3 series MLC controller, if the planned trajectory (leaf position vs. MU) requires velocities exceeding the capability of the MLC, the leaves fall behind the planned positions, causing the controller to momentarily hold the beam and thereby introduce dosimetric errors. We investigated the merits of a new commercial linear accelerator, TrueBeam, that integrates MLC control with prospective dose rate modulation. If treatment is delivered at dose rates so high that leaves would fall behind, the controller reduces the dose rate such that harmony between MU and leaf position is preserved. Methods: For three sets of DMLC leaf trajectories, point doses and two-dimensional dose distributions were measured in phantom using an ionization chamber and film, respectively. The first set, delivered using both a TrueBeam and a conventional C3 controller, comprised a single leaf bank closing at planned velocities of 2.4, 7.1, and 14 cm/s. The maximum achievable leaf velocity for both systems was 3 cm/s. The remaining two sets were derived from clinical fluence maps using a commercial treatment planning system for a range of planned dose rates and were delivered using TrueBeam set to the maximum dose rate, 600 MU/min. Generating trajectories using a planned dose rate that is lower than the delivery dose rate effectively increased the leaf velocity constraint used by the planning system for trajectory calculation. The second set of leaf trajectories was derived from two fluence maps containing regions of zero fluence obtained from representative beams of two different patient treatment plans. The third set was obtained from all nine fields of a head and neck treatment plan. For the head and neck plan, dose-volume histograms of the spinal cord and target for each planned dose rate were obtained. Results: For the single closing leaf bank trajectories, the TrueBeam control system reduced the dose rate such that the leaf velocity was less than the maximum. Dose deviations relative to the 2.4 cm/s trajectory were less than 3%. For the conventional controller, the leaves repeatedly fell behind the planned positions until the beam hold threshold was reached, resulting in deviations of up to 19% relative to the 2.4 cm/s trajectory. For the two clinical fluence maps, reducing the planned dose rate reduced the dose in the zero fluence regions by 15% and 24% and increased the delivery time by 5 s and 14 s. No significant differences were noted in the high and intermediate dose regions measured using film. The DVHs for the head and neck plan showed a 10% reduction in cord dose for 20 MU/min relative to 600 MU/min sequencing dose rate, which was confirmed by measurement. No difference in target DVHs were observed. The reduction in cord dose increased total treatment time by 1.8 min. Conclusions: Leaf sequencing algorithms for integrated control systems should be modified to reflect the reduced importance of maximum leaf velocity for accurate dose delivery.
Purpose: Dose accuracy has been shown to vary with dose per segment and dose rate when delivered with static multileaf collimator (SMLC) intensity modulated radiation therapy (IMRT) by Varian C-series MLC controllers. The authors investigated the impact of monitor units (MUs) per segment and dose rate on the dose delivery accuracy of SMLC-IMRT fields on a Varian TrueBeam linear accelerator (LINAC), which delivers dose and manages motion of all components using a single integrated controller. Methods: An SMLC sequence was created consisting of ten identical 10 x 10 cm{sup 2} segments with identical MUs. Beam holding between segments was achieved by moving one out-of-field MLC leaf pair. Measurements were repeated for various combinations of MU/segment ranging from 1 to 40 and dose rates of 100-600 MU/min for a 6 MV photon beam (6X) and dose rates of 800-2400 MU/min for a 10 MV flattening-filter free photon (10XFFF) beam. All measurements were made with a Farmer (0.6 cm{sup 3}) ionization chamber placed at the isocenter in a solid-water phantom at 10 cm depth. The measurements were performed on two Varian LINACs: C-series Trilogy and TrueBeam. Each sequence was delivered three times and the dose readings for the corresponding segments were averaged. The effects of MU/segment, dose rate, and LINAC type on the relative dose variation ({Delta}{sub i}) were compared using F-tests ({alpha} = 0.05). Results: On the Trilogy, large {Delta}{sub i} was observed in small MU segments: at 1 MU/segment, the maximum {Delta}{sub i} was 10.1% and 57.9% at 100 MU/min and 600 MU/min, respectively. Also, the first segment of each sequence consistently overshot ({Delta}{sub i} > 0), while the last segment consistently undershot ({Delta}{sub i} < 0). On the TrueBeam, at 1 MU/segment, {Delta}{sub i} ranged from 3.0% to 4.5% at 100 and 600 MU/min; no obvious overshoot/undershoot trend was observed. F-tests showed statistically significant difference [(1 - {beta}) =1.0000] between the Trilogy and the TrueBeam up to 10 MU/segment, at all dose rates greater than 100 MU/min. The linear trend of decreasing dose accuracy as a function of increasing dose rate on the Trilogy is no longer apparent on TrueBeam, even for dose rates as high as 2400 MU/min. Dose inaccuracy averaged over all ten segments in each beam delivery sequence was larger for Trilogy than TrueBeam, with the largest discrepancy (0.2% vs 3%) occurring for 1 MU/segment beams at both 300 and 600 MU/min. Conclusions: Earlier generations of Varian LINACs exhibited large dose variations for small MU segments in SMLC-IMRT delivery. Our results confirmed these findings. The dose delivery accuracy for SMLC-IMRT is significantly improved on TrueBeam compared to Trilogy for every combination of low MU/segment (1-10) and high dose rate (200-600 MU/min), in part due to the faster sampling rate (100 vs 20 Hz) and enhanced electronic integration of the MLC controller with the LINAC. SMLC-IMRT can be implemented on TrueBeam with higher dose accuracy per beam ({+-}0.2% vs {+-}3%) than previous generations of Varian C-series LINACs for 1 MU/segment delivered at 600 MU/min).
Optimal control of system governed by linear parabolic equation with white noise inputs, using mathematical model to generate distributed system analog
Stability conditions for multiple input-output linear time invariant feedback systems, noting open loop system impulse response characteristics
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Data-driven control strategies suffer from the necessity of training and its associated computational time and cost. This motivates the continuous increase of popularity of transfer learning based methods. In this paper, we have investigated transfer learning in the context of controller for dynamical systems. First, we have derived conditions under which controller can be transferred between two linear dynamical systems. Furthermore, we have introduced a novel algorithm to design the transferable and non-transferable control components for linear systems. Secondly, we have derived conditions under which a stabilizing controller can be transferred between two different nonlinear dynamical systems. Furthermore, we have used the notion of zero dynamics to transform the nonlinear dynamics into global normal form, to derive the transferability conditions on the controller. Finally, we have numerically evaluated the performance of our transfer learning based methods for two sets of example linear and nonlinear dynamical systems.
Ruelle gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations of Ruelle's formula have emerged that potentially enable sensitivity analysis of certain high-dimensional chaotic numerical simulations encountered in the applied sciences. In this paper, we provide full mathematical justification for the convergence of one such efficient computation, the space–split sensitivity, or S3, algorithm. In S3, Ruelle's formula is computed as a sum of two terms obtained by decomposing the perturbation vector field into a coboundary and a remainder that is parallel to the unstable direction. Such a decomposition results in a splitting of Ruelle's formula that is amenable to efficient computation. Here, we prove the existence of the S3 decomposition and the convergence of the computations of both resulting components of Ruelle's formula.
A linear motor compressor including a compressor housing and a cylinder housing having a plurality of opposing compression chambers. A piston freely reciprocates within the cylinder housing using a linear electric motor.
A truncated non-linear interferometer-based sensor system includes an input that receives an optical beam and a non-linear amplifier that generates a probe beam and a conjugate beam from the optical beam. The system's local oscillators are related to the probe beam and the conjugate beam. The system includes a sensor that transduces an input with the probe beam and the conjugate beam. The transduction detects changes in the phase of each of the probe beam and the conjugate beam. The system's phase sensitive detectors detect phase modulations between the respective local oscillators, the probe beam, and the conjugate beam and outputs phase signals based on detected phase modulations. The system measures phase signals indicative of the sensor's input resulting from a sum or difference of the phase signals. The measurement exhibits a quantum noise reduction in an intensity difference, a phase sum, or an amplitude difference quadrature.
State of linear dynamic system using noisy observations with unknown but bounded errors and system inputs, deriving recursive algorithm
One or more linear and/or curvilinear mounting rails are coupled to a structure. Each mounting rail defines a channel and at least one cartridge assembly is engaged in the channel. Each cartridge assembly includes a housing that slides within the channel. The housing defines a curvilinearly-shaped recess longitudinally aligned with the channel when the housing is in engagement therewith. The cartridge assembly also includes a cleat fitted in the recess for sliding engagement therealong. The cleat can be coupled to a fastener that passes through the mounting rail and the housing when the housing is so-engaged in the channel. The cleat is positioned in the recess by a position of the fastener.