scholarly journals Multiloop Multirate Continuous‐Discrete Drone Stabilization System: An Equivalent Single‐Rate Model

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 129
Author(s):  
Vadim Kramar ◽  
Aleksey Kabanov ◽  
Vasiliy Alchakov
Keyword(s):  
Discrete System ◽  
Rational Functions ◽  
Discrete Systems ◽  
Lateral Motion ◽  
Stabilization System ◽  
Rate Model ◽  
Common Multiple ◽  
Structural Invariant ◽  
Equivalent Models ◽  
Motion Stabilization

The article discusses the UAV lateral motion stabilization system, as a MIMO multiloop multirate continuous-discrete system, specified in the form of an input–output model in the domain of discrete Laplace transform or in the form of a structural diagram. Approaches to the construction of equivalent T and NT single-rate models for MIMO multiloop multirate continuous-discrete systems are considered. Here, T is the largest common divisor of the sampling periods of the system, N is a natural number that is the smallest common multiple of the numbers characterizing the sampling periods of the system. The resulting impulse representations of the outputs of equivalent models are in the form of rational functions. The basis for the construction of these models is a matrix of sampling densities—a structural invariant of sampling chains. An example of the construction of the indicated matrix and an equivalent single-rate model are given. Obtaining equivalent single-rate models for MIMO multiloop multirate systems allows us to extend the methods of research and synthesis of MIMO continuous and continuous-discrete systems to a common theoretical base—the theory of polynomials and rational functions, which are typical elements of the description of these classes of systems.

On perturbed stochastic discrete systems

1974 ◽  
Vol 11 (3) ◽  
pp. 385-393 ◽  
Author(s):  
B.G. Pachpatte
Keyword(s):  
Asymptotic Behavior ◽  
Probability Measure ◽  
Measure Space ◽  
Discrete System ◽  
Discrete Systems ◽  
Image Position ◽  
Probability Measure Space

The object of this paper is to study a stochastic discrete system, including an operator T, of the formas a perturbation of the linear stochastic discrete systemwhere ω ∈ Ω, the supporting set of probability measure space (Ω, A, P) and n ∈ N, the set of nonnegative integers. We are concerned vith the existence, uniqueness, boundedness, and asymptotic behavior of random solutions of the above equation.

Exact solutions for a discrete system arising in traffic flow

1990 ◽  
Vol 428 (1874) ◽  
pp. 49-69 ◽  
Keyword(s):  
Exact Solutions ◽  
Traffic Flow ◽  
Discrete System ◽  
Time Lag ◽  
Discrete Systems ◽  
Travelling Wave ◽  
System Of Equations ◽  
Periodic Waves ◽  
Travelling Wave Solutions ◽  
Nonlinear System Of Equations

This paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by G. F. Newell as a model for car­- following in traffic flow. In particular, Newell found exact solutions for shock waves and related phenomena. Here, exact solutions representing periodic waves and solitary waves are obtained. The method relates travelling wave solutions to the Toda and Kac-van-Moerbeke discrete systems. In this and other ways, much of the interest is in the general phenomena possible in discrete systems, here including also a time lag, rather than in just the specific traffic flow setting.

scholarly journals On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Lei Liu
Keyword(s):  
Discrete System ◽  
Original System ◽  
Discrete Systems ◽  
Topological Transitivity ◽  
Weak Mixing ◽  
Basic Properties ◽  
Weakly Mixing

Blanchard and Huang introduced the notion of weakly mixing subset, and Oprocha and Zhang gave the concept of transitive subset and studied its basic properties. In this paper our main goal is to discuss the weakly mixing subsets and transitive subsets in set-valued discrete systems. We prove that a set-valued discrete system has a transitive subset if and only if original system has a weakly mixing subset. Moreover, we give an example showing that original system has a transitive subset, which does not imply set-valued discrete system has a transitive subset.

Periodic solutions of higher-dimensional discrete systems

2004 ◽  
Vol 134 (5) ◽  
pp. 1013-1022 ◽  
Author(s):  
Zhan Zhou ◽  
Jianshe Yu ◽  
Zhiming Guo
Keyword(s):  
Positive Integer ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Second Order ◽  
Higher Dimensional ◽  
Image Position

Consider the second-order discrete system where f ∈ C (R × Rm, Rm), f(t + M, Z) = f(t, Z) for any (t, Z) ∈ R × Rm and M is a positive integer. By making use of critical-point theory, the existence of M-periodic solutions of (*) is obtained.

scholarly journals Bifurcation and Chaos Analysis for a Discrete Ecological Developmental Systems

2021 ◽  
Author(s):  
Xiaowei Jiang ◽  
Chaoyang Chen ◽  
Xian-He Zhang ◽  
Ming Chi ◽  
Huaicheng Yan
Keyword(s):  
Discrete System ◽  
Period Doubling ◽  
Discrete Systems ◽  
Flip Bifurcation ◽  
Maximum Lyapunov Exponent ◽  
Step Size ◽  
Developmental Systems ◽  
Bifurcation And Chaos ◽  
The Rich ◽  
Theoretical Results

Abstract This work concentrates on the dynamic analysis including bifurcation and chaos of a discrete ecological developmental systems. Specifically, it is a prey-predator-scavenger (PPS) system, which is derived by Euler discretization method. By choosing the step size h as a bifurcation parameter, we determine the set consist of all system’s parameters, in which the system can undergo flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB). The theoretical results are verified by some numerical simulations. It is shown that the discrete systems exhibit more interesting behaviors, including the chaotic sets, quasiperiodic orbits, and the cascade of period-doubling bifurcation in orbits of periods-2, 4, 8, 16. Finally, corresponding to the two bifurcation behaviors discussed, the maximum Lyapunov exponent is numerically calculated, which further verifies the rich dynamic characteristics of the discrete system.

Newton’s iterative formula for finding an equation solution as an abstract problem of the modal synthesis theory

2021 ◽  
Author(s):  
Keyword(s):  
Discrete System ◽  
Decomposition Method ◽  
Control Method ◽  
Discrete Systems ◽  
Modal Control ◽  
New Approach ◽  
Equation Solution ◽  
Modal Synthesis ◽  
Linear Discrete System ◽  
Linear Discrete Systems

A new approach to obtain an iterative Newton formula for finding an equation solution, by using modal control theory for linear discrete systems when solving problems of observation or identification is presented. The decomposition method as a modal control method, which allows obtaining analytical solutions, is used. Keywords Newton’s iterative formula; numerical solution of the equation; decomposition method of modal synthesis; linear discrete system

On the Equivalence of Discrete Systems in Time-Optimal Control

1963 ◽  
Vol 85 (2) ◽  
pp. 204-210 ◽  
Author(s):  
E. Polak
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Pulse Width ◽  
Discrete System ◽  
Discrete Systems ◽  
Order Linear Differential Equation ◽  
Optimal Control Strategy ◽  
Pulse Width Modulated ◽  
Time Optimal ◽  
Linear Differential

It is shown in this paper that under a transformation which maps the state space of a system onto a sequence space in a one-to-one manner, time-optimal discrete regulator systems with different dynamics and modulators can be brought to equivalence and that this fact may be used to construct an optimal control strategy for one system from the known optimal control strategy of another one. In particular, the optimal control strategy for a pulse-width-modulated discrete system with a plant described by an nth order linear differential equation is derived in this manner.

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