The Design of Optimum Controllers for Linear Processes With Energy Limitations

1963 ◽  
Vol 85 (2) ◽  
pp. 181-192 ◽  
Author(s):  
Bernard Friedland
Keyword(s):  
Energy Consumption ◽  
Discrete Time ◽  
Continuous Time ◽  
Analog Computer ◽  
Minimum Time ◽  
Linear Processes

A special-purpose analog computer which can be used as the optimum controller for linear processes with energy-limited control inputs is described. The computer may be used to force the process state to a desired state in minimum time; or to minimize the terminal error at a specified time; or to minimize the energy consumption, if the error can be reduced to zero in the specified time. Continuous-time and discrete-time processes are both considered.

Markovian contact processes

1978 ◽  
Vol 10 (01) ◽  
pp. 85-108 ◽  
Author(s):  
Denis Mollison
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Birth Process ◽  
Linear Processes ◽  
Contact Processes ◽  
Spatial Spread ◽  
Non Linear ◽  
And Migration ◽  
Contact Distribution ◽  
Continuous Time Processes

Markovian contact processes (mcp's) include some of the commoner models for the spatial spread of population processes, such as the ‘simple’ and ‘general’ epidemics, percolation processes, and birth, death and migration processes. They are here set in a framework which relates them to each other, and to a particular basic model, the contact birth process (cbp); indeed they are defined as modifications of the cbp. The immediate advantage of this is that bounds for the velocity of the cbp, which can be obtained from the linear equation describing its expected numbers (provided the contact distribution has exponentially bounded tail) apply also to general mcp's. Existence of moments (and for some processes their time-derivatives) of St (θ), the distance to the furthest individual in an arbitrary direction θ, can also be deduced whenever the corresponding moment of the contact distribution exists. An important subclass consists of population-monotone mcp's, for which the distributions of St can be shown to be subconvolutive, so that the work of Hammersley (1974) can be applied to obtain convergence theorems for St /t; and these can be extended to convergence of the convex hull of the set of inhabited points. These results are particularly valuable because they apply to some non-linear processes, e.g. the simple epidemic. Some special results on the cbp (Section 6) emphasize the differences between linear and non-linear spatial stochastic processes. Although the paper is written throughout in terms of continuous-time processes, the results on subconvolutive distributions are actually more easily applied in the discrete-time case. (Conversely, the approach used in the accompanying paper by Biggins (pp. 62–84), which is written in terms of discrete-time processes, can be extended to deal also with continuous-time processes.)

Markovian contact processes

1978 ◽  
Vol 10 (1) ◽  
pp. 85-108 ◽  
Author(s):  
Denis Mollison
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Birth Process ◽  
Linear Processes ◽  
Contact Processes ◽  
Spatial Spread ◽  
Non Linear ◽  
And Migration ◽  
Contact Distribution ◽  
Continuous Time Processes

Markovian contact processes (mcp's) include some of the commoner models for the spatial spread of population processes, such as the ‘simple’ and ‘general’ epidemics, percolation processes, and birth, death and migration processes. They are here set in a framework which relates them to each other, and to a particular basic model, the contact birth process (cbp); indeed they are defined as modifications of the cbp. The immediate advantage of this is that bounds for the velocity of the cbp, which can be obtained from the linear equation describing its expected numbers (provided the contact distribution has exponentially bounded tail) apply also to general mcp's. Existence of moments (and for some processes their time-derivatives) of St(θ), the distance to the furthest individual in an arbitrary direction θ, can also be deduced whenever the corresponding moment of the contact distribution exists.An important subclass consists of population-monotone mcp's, for which the distributions of St can be shown to be subconvolutive, so that the work of Hammersley (1974) can be applied to obtain convergence theorems for St/t; and these can be extended to convergence of the convex hull of the set of inhabited points. These results are particularly valuable because they apply to some non-linear processes, e.g. the simple epidemic. Some special results on the cbp (Section 6) emphasize the differences between linear and non-linear spatial stochastic processes.Although the paper is written throughout in terms of continuous-time processes, the results on subconvolutive distributions are actually more easily applied in the discrete-time case. (Conversely, the approach used in the accompanying paper by Biggins (pp. 62–84), which is written in terms of discrete-time processes, can be extended to deal also with continuous-time processes.)

Multi-dimensional Linear Processes

2015 ◽  
Author(s):  
Arno Berger ◽  
Theodore P. Hill
Keyword(s):  
Differential Equations ◽  
Discrete Time ◽  
Continuous Time ◽  
Benford’S Law ◽  
Linear Processes ◽  
Continuous Time Systems ◽  
Benford's Law ◽  
The One ◽  
Time Systems

Chapter 6 studied models based solely on the one-dimensional processes, however, for many applications, these models are often too simple and have to be replaced with or complemented by more sophisticated multi-dimensional models. This chapter studies Benford's law in the simplest deterministic multi-dimensional processes, namely, linear processes in discrete and continuous time. Despite their simplicity, these systems provide important models for many areas of science. Through far-reaching generalizations of results from earlier chapters, they will be shown to very often conform to Benford's law in that their dynamics is an abundant source of Benford sequences and functions. As in the previous chapter, the properties of continuous-time systems (i.e., differential equations) are analogous to those of discrete-time systems, and the chapter focuses on the latter in every but its last section.

Design of Programmable Wideband Low Pass Filter with Continuous-Time/Discrete-Time Hybrid Architecture

2017 ◽  
Vol E100.C (10) ◽  
pp. 858-865 ◽  
Author(s):  
Yohei MORISHITA ◽  
Koichi MIZUNO ◽  
Junji SATO ◽  
Koji TAKINAMI ◽  
Kazuaki TAKAHASHI
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Architecture ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

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