Controllability of semilinear stochastic delay systems with distributed delays in control

Karthikeyan, S.; Sathya, M.; Balachandran, K.

doi:10.1007/s00498-017-0206-9

Cited by 5 publications

(4 citation statements)

References 38 publications

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“…Problem 2. Find a control vector ῡ(τ) ∈ C 1 ([0, +∞)) and a vector function ξ(τ) ∈ C 1 ([0, +∞)) satisfying (10) and the conditions…”

Section: Auxiliary Systemmentioning

confidence: 99%

“…Since the late 1960s, many researchers have studied BVPs for linear stationary, nonstationary linear, bilinear, semilinear, and nonlinear systems of ordinary differential equations with delayed control and/or system state. In recent years, the problem of controllability has been considered for impulsive [8], stochastic [8][9][10], integro-differential [11], and fractional [12,13] dynamic systems with delays.…”

Section: Introductionmentioning

confidence: 99%

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A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

Kvitko

Eremin

2022

Symmetry

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In this paper, a class of controllable nonlinear stationary systems of ordinary differential equations with an account of external perturbations is studied. The control satisfies given restrictions, and there is a fixed delay in it. An algorithm to construct a control transferring a system from a certain initial state to an arbitrary neighborhood of the origin is proposed. The algorithm has both numerical and analytical stages and is easy to implement. A constructive sufficient Kalman-type condition of possibility of the transfer is derived. The algorithm efficiency is demonstrated by solving a robot manipulator controlling problem.

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“…Problem 2. Find a control vector ῡ(τ) ∈ C 1 ([0, +∞)) and a vector function ξ(τ) ∈ C 1 ([0, +∞)) satisfying (10) and the conditions…”

Section: Auxiliary Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

Kvitko

Eremin

2022

Symmetry

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“…Several practical applications are examined using fixed-point theory in fractional calculus as well [38][39][40][41][42]. We build on the ideas of [4,17,[43][44][45][46][47][48] in this work to examine the exponential stability for differential systems with numerous control delays and also their relative controllability, respectively.…”

Section: Introductionmentioning

confidence: 99%

Results on relative controllability for nonlinear system with multi‐delays in control

Vinodkumar,

Hemalatha

2023

Math Methods in App Sciences

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This study uses a delayed matrix exponential to illustrate the solution of both linear and nonlinear delay problems using permutable matrices. We outline several prerequisites that are necessary to ensure the exponential stability of the trivial solution of delay systems. The conditions that are necessary and sufficient for the linear system to possess relative controllability are established by introducing a delayed Grammian matrix‐like criterion. A sufficient condition is obtained by Krasnoselskii's fixed point theorem for the relative controllability of nonlinear systems. Numerical examples provided at the end of the paper demonstrate the validity of our theoretical findings.

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“…Nonlinear Time-Varying Discrete Stochastic Systems. The stochastic control system has the characteristics of uncertainty [30], such as the autonomous control system of unmanned aerial vehicle (UAV) [31], which is affected by unstable wind [32], electromagnetic interference [33], noise signal [34], and so on in the process of operation, resulting in its control system with nonlinear, discrete, time-varying, stochastic, and other characteristics [35]. A stochastic system can be represented in the form of Equations (1) and (2) [36].…”

Section: Introductionmentioning

confidence: 99%

Control Optimization of Stochastic Systems Based on Adaptive Correction CKF Algorithm

Zhang

2020

International Journal of Aerospace Engineering

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Standard cubature Kalman filter (CKF) algorithm has some disadvantages in stochastic system control, such as low control accuracy and poor robustness. This paper proposes a stochastic system control method based on adaptive correction CKF algorithm. Firstly, a nonlinear time-varying discrete stochastic system model with stochastic disturbances is constructed. The control model is established by using the CKF algorithm, the covariance matrix of standard CKF is optimized by square root filter, the adaptive correction of error covariance matrix is realized by adding memory factor to the filter, and the disturbance factors in nonlinear time-varying discrete stochastic systems are eliminated by multistep feedback predictive control strategy, so as to improve the robustness of the algorithm. Simulation results show that the state estimation accuracy of the proposed adaptive cubature Kalman filter algorithm is better than that of the standard cubature Kalman filter algorithm, and the proposed adaptive correction CKF algorithm has good control accuracy and robustness in the UAV control test.

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Controllability of semilinear stochastic delay systems with distributed delays in control

Cited by 5 publications

References 38 publications

A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

Results on relative controllability for nonlinear system with multi‐delays in control

Control Optimization of Stochastic Systems Based on Adaptive Correction CKF Algorithm

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