A new method for finding closed‐form time‐domain solutions of linear time‐invariant (LTI) systems with arbitrary periodic input signals is presented. These solutions, unlike those obtained based on ...the conventional Fourier‐phasor method, have a finite number of terms in one period. To implement the proposed method, the following steps are carried out: (1) For a given system, represented by a transfer function, an impulse response, a block diagram etc., the governing differential equation relating the output of the system, y(t) $y(t)$, to its input, x(t) $x(t)$, is obtained. (2) An auxiliary differential equation is formed by simply replacing y(t) $y(t)$ with y‾(t) $\overline{y}(t)$ and equating the input side tox(t) $x(t)$ alone. The auxiliary differential equation is solved for each time segment of the input signal in one period, leaving the constant coefficients associated with the homogeneous solutions as unknowns. For an nth‐order system with an input signal consisting of q segments in one period, there are n×q $n\times q$ such unknown coefficients. (3) Continuity of y‾(t) $\overline{y}(t)$ and its derivatives, dky‾(t)/dtk, ${d}^{k}\overline{y}(t)/d{t}^{k},$ k=1,⋅⋅⋅,n−1, $k=1,\cdot \cdot \cdot ,n-1,$ at the connection points of successive segments and the periodicity conditions for the beginning and end points of the period are implemented. (4) The outcome of step 3 is a system of n×q $n\times q$ equations in terms of n×q $n\times q$ unknown coefficients described in step 2. Solving this system of equations, the solution for y‾(t) $\overline{y}(t)$ in one period is obtained. (5) Finally, using the linearity and differentiation properties of the system and the coefficients of the input side of the differential equation of the system, the total response, y(t) $y(t)$, in one period is constructed in terms of y‾(t) $\overline{y}(t)$ and its derivatives. For stable LTI systems, the proposed method can be used without any limitations.
A new method for finding closed‐form time‐domain solutions of linear time‐invariant systems with arbitrary periodic input signals is presented. Such solutions, unlike those obtained by using the Fourier‐phasor approach, have a finite number of terms in one period.
This article addresses the problem of controlling discrete-time linear time-invariant systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed ...gradient-descent-based indirect adaptive controller, used to handle parametric uncertainties, is combined with a model predictive control (MPC) algorithm, which guarantees constraint satisfaction. An estimated model of the actual uncertain plant is used for predictions of the future states. The parameters of the estimated model are updated using a gradient-descent-based adaptive update law. The errors arising due to the model mismatch between the estimated plant model and the actual uncertain plant are accounted for using a constraint tightening method in the MPC algorithm. The proposed adaptive MPC strategy is proved to be recursively feasible and the closed-loop system is proved to be bounded at all instants and asymptotically converging to the origin.
This paper proposes a new approach to studying the delay margin problem for general unstable linear time-invariant (LTI) systems, which addresses the question: What is the largest stabilizable delay ...range over all LTI controllers? The proposed approach converts the delay margin to the robust stabilization for LTI systems involving a positive uncertain parameter. The conformal mapping and Nevanlinna-Pick interpolation are employed to develop a unified numerical procedure for computing upper and lower bounds on the delay margin, and for designing robustly stabilizing controllers, aimed at maximizing the stabilizability range of the delay parameter, promised by the delay margin. The results obtained in this paper show that the proposed new approach in this paper provides an effective solution method to tackle the delay margin and applies to general unstable linear systems of finite order. The obtained upper and lower bounds of the delay margin are close to each other, illustrated by several typical linear systems and numerical examples.
Purpose
Many aspects and imperfections of gradient dynamics in MRI have been successfully captured by linear time‐invariant (LTI) models. Changes in gradient behavior due to heating, however, violate ...time invariance. The goal of this work is to study such changes at the level of transfer functions and model them by thermal extension of the LTI framework.
Methods
To study the impact of gradient heating on transfer functions, a clinical MR system was heated using a range of high‐amplitude DC and AC waveforms, each followed by measuring transfer functions in rapid succession while the system cooled down. Simultaneously, gradient temperature was monitored with an array of temperature sensors positioned according to initial infrared recordings of the gradient tube. The relation between temperatures and transfer functions is cast into local and global linear models. The models are analysed in terms of self‐consistency, conditioning, and prediction performance.
Results
Pronounced thermal effects are observed in the time resolved transfer functions, largely attributable to in‐coil eddy currents and mechanical resonances. Thermal modeling is found to capture these effects well. The keys to good model performance are well‐placed temperature sensors and suitable training data.
Conclusion
Heating changes gradient response, violating time invariance. The utility of LTI modeling can nevertheless be recovered by a linear thermal extension, relying on temperature sensing and adequate one‐time training.
Consider that an autonomous linear time-invariant (LTI) plant is given and that each member of a network of LTI observers accesses a portion of the output of the plant. The dissemination of ...information within the network is dictated by a pre-specified directed graph in which each vertex represents an observer. This paper proposes a distributed estimation scheme that is a natural generalization of consensus in which each observer computes its own state estimate of the plant using only the portion of the output vector accessible to it and the state estimates of other observers that, according to the graph, are available to it. Unlike straightforward high-order solutions in which each observer broadcasts its measurements throughout the network, the average dimension of the state of each observer in the proposed scheme does not exceed the order of the plant plus one. We determine necessary and sufficient conditions for the existence of a parameter choice for which the proposed scheme attains asymptotic omniscience of the state of the plant at all observers. The conditions reduce to certain detectability requirements that imply that if omniscience is not possible under the proposed scheme then it is not viable under any other scheme-including higher-order LTI, nonlinear, and time-varying ones-subject to the same graph.
There has been a movement to share and spread online lectures through OCW and MOOC systems. This movement would have been spread widely and adopted widely if those courses could be easily ...exchangeable with other platforms or services. If this function is available, learning activities, resources, learning outcomes can be accessed between different platforms and services. With this function, the credit exchange between different platforms or services will be easier. It also facilitates course sharing and circulation. Because the LMS is the basic platform for online classes, providing sharable and reusable learning activities, resources, and learning outcomes across the different LMSs is very demanding for online education. Analyzing LMS use in Korean universities, Moodle, Canvas, and domestic LMSs are founded to be the significant three kinds that are widely used in Korea. In this paper, a method of integrating Moodle, Canvas, and domestic LMS services is proposed. A central Moodle server is installed as the main LMS server, and the method to connect or complement with a central Moodle server is proposed for each different kind of LMS. LMS users can easily access a different kind of LMS as a form of imported course, tightly connected service, or log in as SSO. This proposition can be applied to various service fields such as KMOOC, KOCW, credit exchange, lecture exchange between universities, regional unification of online educational centers as a practical problem-solver.
In this paper, we deal with the controllability and observability of impulsive fractional linear time-invariant (IF-LTI for short) system. Our main purpose is to built some necessary and sufficient ...conditions of controllability and observability for the IF-LTI system. At the same time, we establish some conclusions of controllability and observability for a continuous fractional LTI system, which is a special case of the IF-LTI system. Examples are given to illustrate our results.
A new virus‐like particle based vaccine covering 14 types of high‐risk and disease‐inducing human papillomavirus (HPV) can offer better coverage against HPV‐induced diseases, particularly cervical ...cancers. However, the assessment of immunogenicity of the vaccine is an important task, representing not only its significant clinical characteristics, but also a major challenge, in terms of both the suitability of methods and the clinical sample testing throughput supporting clinical development. This work covers the development and evaluation of a method based on Luminex technology (a coded‐bead and flow‐cytometric approach) to assess the HPV‐type specific total immunoglobulin G (IgG). This method can evaluate the antibodies in sera post immunization against multiple types of HPV simultaneously (i.e., with multiplexing capability), save time and cost, and improve test throughput with higher sensitivity and precision than the classical, plate‐based enzyme‐linked immunoassay and competitive Luminex‐based immunoassays. Using cynomolgus monkeys as model, we demonstrated the good correlation between the results from the pseudovirion‐based neutralization assay (PBNA), and the Luminex‐based total IgG assay, supporting that the latter method can be considered as a viable, dependable replacement method for the PBNA supporting immunogenicity evaluation of HPV vaccine in preclinical development and clinical investigation.
The objective is to design output feedback event-triggered controllers to stabilize a class of nonlinear systems. One of the main difficulties of the problem is to ensure the existence of a minimum ...amount of time between two consecutive transmissions, which is essential in practice. We solve this issue by combining techniques from event-triggered and time-triggered control. The idea is to turn on the event-triggering mechanism only after a fixed amount of time has elapsed since the last transmission. This time is computed based on results on the stabilization of time-driven sampled-data systems. The overall strategy ensures an asymptotic stability property for the closed-loop system. The results are proved to be applicable to linear time-invariant (LTI) systems as a particular case.
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