Topic Editors

Prof. Dr. Chang-Hua Lien
Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan
Prof. Dr. Hamid Reza Karimi
Department of Mechanical Engineering, Politecnico di Milano, via La Masa 1, 20156 Milan, Italy
Prof. Dr. Sundarapandian Vaidyanathan
Research and Development Centre, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062, Tamil Nadu, India

Analysis and Controls of Time-Delay Systems with Perturbations: Theory and Application

Abstract submission deadline
closed (30 April 2022)
Manuscript submission deadline
30 June 2022
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7476

Topic Information

Dear Colleagues,

The field of time-delay systems with perturbations is receiving a lot of interest in terms of modeling and analysis of practical systems. Specifically, the main focus is on performance analysis and controller design of time-delay systems across many fields of science and engineering. To include the uncertain properties of systems, systems with perturbances are used to present the variations and nonlinearities. Instability and poor performance will be caused by those main factors.

The focus of this Special Issue is addressing recent progress in both theoretical and practical developments on topics relating to the analysis, design, implementation, and technology of time-delay systems with perturbations. Topics that are invited for submission include (but are not limited to):

  • Linear fractional perturbations;
  • Switching signal designs and switched systems;
  • Sampling and data-hold;
  • Parallel distributed compensator and T–S fuzzy systems;
  • Complex systems;
  • Chaotic and hyperchaotic systems;
  • Fractional-order dynamical systems;
  • Networked control systems;
  • Linear parameter varying systems;
  • Mixed performances and controls;
  • Fault diagnosis for time-delay systems;
  • Case studies.

Prof. Dr. Changhua Lien
Prof. Dr. Hamid Reza Karimi
Prof. Dr. Sundarapandian Vaidyanathan
Topic Editors

Keywords

  • time-delay systems
  • linear fractional perturbations
  • robust controls
  • samplings
  • chaotic systems
  • fractional-order dynamical systems
  • mixed performances
  • fuzzy controls
  • switching strategies
  • analysis

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Fractal and Fractional
fractalfract
3.577 2.8 2017 19.8 Days 1600 CHF Submit
Mathematics
mathematics
2.592 2.9 2013 19 Days 1800 CHF Submit
Axioms
axioms
1.824 2.6 2012 22.4 Days 1400 CHF Submit
Symmetry
symmetry
2.940 4.3 2009 16.9 Days 1800 CHF Submit

Published Papers (13 papers)

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Article
Tumour-Natural Killer and CD8+ T Cells Interaction Model with Delay
Mathematics 2022, 10(13), 2193; https://doi.org/10.3390/math10132193 - 23 Jun 2022
Abstract
The literature suggests that effective defence against tumour cells requires contributions from both Natural Killer (NK) cells and CD8+ T cells. NK cells are spontaneously active against infected target cells, whereas CD8+ T cells take some times to activate [...] Read more.
The literature suggests that effective defence against tumour cells requires contributions from both Natural Killer (NK) cells and CD8+ T cells. NK cells are spontaneously active against infected target cells, whereas CD8+ T cells take some times to activate cell called as cell-specific targeting, to kill the virus. The interaction between NK cells and tumour cells has produced the other CD8+ T cell, called tumour-specific CD8+ T cells. We illustrate the tumour–immune interaction through mathematical modelling by considering the cell cycle. The interaction of the cells is described by a system of delay differential equations, and the delay, τ represent time taken for tumour cell reside interphase. The stability analysis and the bifurcation behaviour of the system are analysed. We established the stability of the model by analysing the characteristic equation to produce a stability region. The stability region is split into two regions, tumour decay and tumour growth. By applying the Routh–Hurwitz Criteria, the analysis of the trivial and interior equilibrium point of the model provides conditions for stability and is illustrated in the stability map. Numerical simulation is carried out to show oscillations through Hopf Bifurcation, and stability switching is found for the delay system. The result also showed that the interaction of NK cells with tumour cells could suppress tumour cells since it can increase the population of CD8+ T cells. This concluded that the inclusion of delay and immune responses (NK-CD8+ T cells) into consideration gives us a deep insight into the tumour growth and helps us understand how their interactions contribute to kill tumour cells. Full article
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Article
Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays
Mathematics 2022, 10(11), 1885; https://doi.org/10.3390/math10111885 - 31 May 2022
Abstract
In this paper, by adopting sliding mode control, an adaptive memoryless control scheme has been developed for uncertain Rössler chaotic systems with unknown time delays. Firstly, the proposed adaptive control can force the trajectories of controlled Rössler time-delayed chaotic systems into the specified [...] Read more.
In this paper, by adopting sliding mode control, an adaptive memoryless control scheme has been developed for uncertain Rössler chaotic systems with unknown time delays. Firstly, the proposed adaptive control can force the trajectories of controlled Rössler time-delayed chaotic systems into the specified sliding manifold. Then, the Riemann sum is introduced to analyze the stability of the equivalent dynamics in the sliding manifold. The control performance can be predicted even if the controlled systems have unmatched uncertainties and unknown time delays, which have not been well addressed in the literature. Numerical simulations are included to demonstrate the feasibility of the proposed scheme. Full article
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Article
State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays
Mathematics 2022, 10(10), 1725; https://doi.org/10.3390/math10101725 - 18 May 2022
Cited by 1
Abstract
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix [...] Read more.
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method. Full article
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Article
A Note on the Reverse Order Law for g-Inverse of Operator Product
Axioms 2022, 11(5), 226; https://doi.org/10.3390/axioms11050226 - 12 May 2022
Abstract
The generalized inverse has many important applications in aspects of the theoretical research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the reverse order laws for the generalized inverse of [...] Read more.
The generalized inverse has many important applications in aspects of the theoretical research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the reverse order laws for the generalized inverse of the operator product. In this paper, we study the reverse order law for the g-inverse of an operator product T1T2T3 using the technique of matrix form of bounded linear operators. In particular, some necessary and sufficient conditions for the inclusion T3{1}T2{1}T1{1}(T1T2T3){1} is presented. Moreover, some finite dimensional results are extended to infinite dimensional settings. Full article
Article
Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles
Mathematics 2022, 10(9), 1399; https://doi.org/10.3390/math10091399 - 22 Apr 2022
Abstract
In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) [...] Read more.
In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations. Full article
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Article
Robust State Estimation for Uncertain Discrete Linear Systems with Delayed Measurements
Mathematics 2022, 10(9), 1365; https://doi.org/10.3390/math10091365 - 19 Apr 2022
Abstract
Measurement delays and model parametric uncertainties are meaningful issues in actual systems. Addressing the simultaneous existence of random model parametric uncertainties and constant measurement delay in the discrete-time linear systems, this study proposes a novel robust estimation method based on the combination of [...] Read more.
Measurement delays and model parametric uncertainties are meaningful issues in actual systems. Addressing the simultaneous existence of random model parametric uncertainties and constant measurement delay in the discrete-time linear systems, this study proposes a novel robust estimation method based on the combination of Kalman filter regularized least-squares (RLS) framework and state augmentation. The state augmentation method is elaborately designed, and the cost function is improved by considering the influence of modelling errors. A recursive program similar to the Kalman filter is derived. Meanwhile, the asymptotic stability conditions of the proposed estimator and the boundedness conditions of its error covariance are analyzed theoretically. Numerical simulation results show that the proposed method has a better processing capability for measurement delay and better robustness to model parametric uncertainties than the Kalman filter based on nominal parameters. Full article
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Article
Tuning of PID Control for the Double Integrator Plus Dead Time Model by Modified Real Dominant Pole and Performance Portrait Methods
Mathematics 2022, 10(6), 971; https://doi.org/10.3390/math10060971 - 18 Mar 2022
Cited by 2
Abstract
The paper discusses the proportional-integral-derivative (PID) controller from the viewpoint of (a) the analytical tuning of the PID controller for the double integrator plus dead time (DIPDT) model and (b) the numerical tuning using the performance portrait method (PPM). In the first case, [...] Read more.
The paper discusses the proportional-integral-derivative (PID) controller from the viewpoint of (a) the analytical tuning of the PID controller for the double integrator plus dead time (DIPDT) model and (b) the numerical tuning using the performance portrait method (PPM). In the first case, the already published tuning with multiple real dominant pole, extended by integrated tuning procedures, which incorporate the inevitable low-pass filters by delay equivalences, is elaborated for modified sets of real poles. By considering several such modified sets of real poles, resulting in several new sets of controller parameters, the design can be better adapted to the requirements of the control tasks solved and to the limitations of the existing control loop hardware. In a noisy and uncertain environment, the balance between speed of setpoint and disturbance responses and acceptable excessive controller effort can thus be improved. The effectiveness of the analytical design can be evaluated using the numerical performance portrait method (PPM). For an already generated performance portrait (PP), it can offer a broad spectrum of controller settings that satisfy various design constraints. However, the results of the analytical design are still important as they facilitate the initial steps in the elaboration of the PPM and in explaining the nature of PID control. The developed controller tuning are compared using a new interpretation of PID controller as an extension of the stabilising PD controller by disturbance observer (DOB). The input disturbances reconstructed by DOB by evaluating the controller output of an integral process model in steady-state, can be estimated by a low-pass filter with a sufficiently long (integral) time constant. All analysed results are in full agreement with the proposed DOB interpretation, which furthermore contributes significantly to the explanation of the problems related to the optimal design of PID controllers. Full article
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Article
Regularity of Fractional Heat Semigroup Associated with Schrödinger Operators
Fractal Fract. 2022, 6(2), 112; https://doi.org/10.3390/fractalfract6020112 - 14 Feb 2022
Abstract
Let L=Δ+V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. By the subordinative formula, we introduce the fractional heat semigroup [...] Read more.
Let L=Δ+V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. By the subordinative formula, we introduce the fractional heat semigroup {etLα}t>0, 0<α<1, associated with L. By the aid of the fundamental solution of the heat equation: tu+Lu=tuΔu+Vu=0, we estimate the gradient and the time-fractional derivatives of the fractional heat kernel Kα,tL(·,·), respectively. This method is independent of the Fourier transform, and can be applied to the second-order differential operators whose heat kernels satisfy the Gaussian upper bounds. As an application, we establish a Carleson measure characterization of the Campanato-type space BMOLγ(Rn) via the fractional heat semigroup {etLα}t>0. Full article
Article
Controller Design for Unstable Time-Delay Systems with Unknown Transfer Functions
Mathematics 2022, 10(3), 431; https://doi.org/10.3390/math10030431 - 29 Jan 2022
Cited by 1
Abstract
This study developed a method for designing parallel two-degree-of-freedom proportional-integral-derivative controllers for unstable time-delay processes with unknown dynamic equations. First, a performance index accounting for both transient response performance and disturbance rejection was developed. To obtain useful data even if the output of [...] Read more.
This study developed a method for designing parallel two-degree-of-freedom proportional-integral-derivative controllers for unstable time-delay processes with unknown dynamic equations. First, a performance index accounting for both transient response performance and disturbance rejection was developed. To obtain useful data even if the output of the system exceeds the allowable range, an effective penalty function was included in the performance index. The N–M simplex method was used to iteratively determine the optimal controller parameters. The proposed approach has the following advantages: (1) it can be used regardless of the stability of the open-loop system; (2) the mathematical model and parameters of the process need not be known in advance; (3) it can be used for processes that include measurement noise; (4) it has good transient response performance and is also robust against external disturbances; and (5) it enables more efficient controller design and reduces costs. Full article
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Article
Finite-Time Boundedness of Linear Uncertain Switched Positive Time-Varying Delay Systems with Finite-Time Unbounded Subsystems and Exogenous Disturbance
Mathematics 2022, 10(1), 65; https://doi.org/10.3390/math10010065 - 25 Dec 2021
Cited by 1
Abstract
The problem of finite-time boundedness for a class of linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance is addressed. This characteristic research is that the studied systems include the finite-time bounded subsystems and finite-time unbounded subsystems. Both a slow [...] Read more.
The problem of finite-time boundedness for a class of linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance is addressed. This characteristic research is that the studied systems include the finite-time bounded subsystems and finite-time unbounded subsystems. Both a slow mode-dependent average dwell time and a fast mode-dependent average dwell time switching techniques are utilized reasonably. And by applying a copositive Lyapunov-Krasovskii functional, novel delay-dependent sufficient criteria are derived to guarantee such systems to be finite-time bounded concerning the given parameters and designed switching signal. Furthermore, new finite-time boundedness criteria of the systems without interval uncertainties are also obtained. Finally, the efficiency of the theoretical results is presented in two illustrative examples. Full article
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Article
Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs
Mathematics 2021, 9(22), 2883; https://doi.org/10.3390/math9222883 - 12 Nov 2021
Abstract
Let G be an infinite connected graph. We introduce two kinds of multilinear fractional maximal operators on G. By assuming that the graph G satisfies certain geometric conditions, we establish the bounds for the above operators on the endpoint Sobolev spaces and [...] Read more.
Let G be an infinite connected graph. We introduce two kinds of multilinear fractional maximal operators on G. By assuming that the graph G satisfies certain geometric conditions, we establish the bounds for the above operators on the endpoint Sobolev spaces and Hajłasz–Sobolev spaces on G. Full article
Article
Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations
Mathematics 2021, 9(21), 2763; https://doi.org/10.3390/math9212763 - 30 Oct 2021
Abstract
In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are [...] Read more.
In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H2/H) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results. Full article
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Article
On a Boundary Value Problem of Hybrid Functional Differential Inclusion with Nonlocal Integral Condition
Mathematics 2021, 9(21), 2667; https://doi.org/10.3390/math9212667 - 21 Oct 2021
Abstract
In this work, we present a boundary value problem of hybrid functional differential inclusion with nonlocal condition. The boundary conditions of integral and infinite points will be deduced. The existence of solutions and its maximal and minimal will be proved. A sufficient condition [...] Read more.
In this work, we present a boundary value problem of hybrid functional differential inclusion with nonlocal condition. The boundary conditions of integral and infinite points will be deduced. The existence of solutions and its maximal and minimal will be proved. A sufficient condition for uniqueness of the solution is given. The continuous dependence of the unique solution will be studied. Full article
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