Multiple Delays Research Articles

Stability and Hopf bifurcation analysis of a fractional-order p53 multiple time delays model under PD$$^\alpha $$ control

Stability and Hopf bifurcation analysis of a fractional-order p53 multiple time delays model under PD$$^\alpha $$ control

Delay-dependent set-invariance for linear difference equations with multiple delays: a polyhedral approach

This paper revisits the set-invariance for linear delay-difference equations and proposes novel delay-dependent notions in contrast with the existing delay-independent constructions available in the literature. The main tool in this endeavour is the model transformation by means of a matrix parametrization, which opens the way to the elaboration of delay-dependent conditions for set invariance. For the class of polyhedral sets, it will be shown how these transformed models enable particularly structured invariance conditions. Aside from the mathematical developments, a discussion of the delay-dependent conditions with respect to the confinement of the state trajectories of the original system will be presented. The relationship will be established by means of constraints involving the initial states for the time-delay systems. The characterization of this set of admissible initial conditions can be analysed in terms of complexity and conservativeness with respect to the classical delay-independent set-invariance. An illustrative example is provided to underline that confinement of state trajectories in a set can be achieved even though this is not invariant according to the classical definition.

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

Digitally Diagnosing Multiple Developmental Delays Using Crowdsourcing Fused With Machine Learning: Protocol for a Human-in-the-Loop Machine Learning Study.

A considerable number of minors in the United States are diagnosed with developmental or psychiatric conditions, potentially influenced by underdiagnosis factors such as cost, distance, and clinician availability. Despite the potential of digital phenotyping tools with machine learning (ML) approaches to expedite diagnoses and enhance diagnostic services for pediatric psychiatric conditions, existing methods face limitations because they use a limited set of social features for prediction tasks and focus on a single binary prediction, resulting in uncertain accuracies. This study aims to propose the development of a gamified web system for data collection, followed by a fusion of novel crowdsourcing algorithms with ML behavioral feature extraction approaches to simultaneously predict diagnoses of autism spectrum disorder and attention-deficit/hyperactivity disorder in a precise and specific manner. The proposed pipeline will consist of (1) gamified web applications to curate videos of social interactions adaptively based on the needs of the diagnostic system, (2) behavioral feature extraction techniques consisting of automated ML methods and novel crowdsourcing algorithms, and (3) the development of ML models that classify several conditions simultaneously and that adaptively request additional information based on uncertainties about the data. A preliminary version of the web interface has been implemented, and a prior feature selection method has highlighted a core set of behavioral features that can be targeted through the proposed gamified approach. The prospect for high reward stems from the possibility of creating the first artificial intelligence-powered tool that can identify complex social behaviors well enough to distinguish conditions with nuanced differentiators such as autism spectrum disorder and attention-deficit/hyperactivity disorder. PRR1-10.2196/52205.

Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay, where the system dynamics rely on the conditional expectations of future states. The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model. In particular, we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case. The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

Abstract TP139: Revascularization Improves Vascular Hemodynamics in Pediatric Moyamoya Patients

Introduction: Cerebrovascular reactivity (CVR) reflects the change in cerebral blood flow (CBF) in response to vasodilation. Studies have demonstrated that impaired CVR was associated with a higher risk of acute stroke in patients with intracranial vasculopathy and that bypass surgeries can reduce the risk of strokes. Moyamoya disease is a progress cerebrovascular disorder that begins during childhood. Arterial spin labeling (ASL) is a quantitative MRI technique for non-invasive CBF and CVR measurement; ASL with multiple delays can also measure arterial transit time (ATT). Here, we compare the CBF, CVR, and ATT in pediatric Moyamoya patients before and after bypass using multi-delay ASL. Hypothesis: CVR will increase significantly after bypass surgeries. Methods: Imaging data were acquired from 22 Moyamoya patients (11 months - 18 years, 14 females) using a 3T MRI system. All patients had unilateral or bilateral occlusion at ACA, MCA and/or PCA. Multi-delay ASL data (7 delays) were acquired at baseline and 15 minutes after acetazolamide administration. CBF and ATT were computed using the general kinetic model. CVR was computed as the percentage of CBF change compared with baseline CBF. Flow territories (right and left ACA, MCA, and PCA) were defined using the Harvard-Oxford atlases. Paired t-tests were conducted to compare the mean CVR, CBF, and ATT changes before and after bypass surgeries. Results: The figure shows the hemodynamic maps of an example patients. Overall, CVR and CBF in the affected regions increased after bypass; ATT in these regions decreased after bypass. For this cohort, our analysis showed that CVR of the affected regions increased significantly by 68% and ATT reduced significantly by 10.7% measured by multi-delay ASL, implying improved circulation and lower risk for strokes. Discussion: Multi-delay ASL was effective to detect improved CVR and reduced ATT in pediatric Moyamoya patients after bypass surgeries.

Stability and bifurcation analysis of fractional‐order tumor–macrophages interaction model with multi‐delays

In the realm of modeling biological systems with memory, particularly those involving intricate interactions like tumor‐immune responses, the utilization of multiple time delays and Caputo‐type fractional‐order derivatives represents a cutting‐edge approach. In this research paper, we introduce a novel fractional‐order model to investigate the dynamic interplay between tumors and macrophages, a key component of the immune system, while incorporating multiple time delays into our framework. Our proposed model comprises a system of three Caputo‐type fractional‐order differential equations, each representing distinct cell populations: tumor cells, anti‐tumor cells (specifically ‐type macrophages with pro‐inflammatory properties), and pro‐tumor cells ( ‐type macrophages with immune‐suppressive characteristics). The stability of equilibria is discussed by analyzing the characteristic equations for each case, and the existence conditions for the Hopf bifurcation are obtained according to the critical values of delay parameters. Furthermore, numerical simulations are presented in order to verify the analytical results obtained for stability and Hopf‐bifurcation with respect to the two‐time delay parameters and . The analysis shows the rich dynamics of the model according to the fractional‐order parameter and the time delay parameters.

Global inverse optimality for a class of recurrent neural networks with multiple proportional delays

This paper formulates two novel theoretical designs of input-to-state stabilizing control for a class of recurrent neural networks with multiple proportional delays. The analysis tool developed in this paper is based on Lyapunov function and inverse optimality method, which does not require solving Hamilton-Jacobi-Bellman equations. Two inverse optimal feedback laws are constructed via the dimensions of state and input, which ensure the input-state stability for the considered system. When the dimensions of state and input are different, we establish a scalar function and give one of the control laws by Sontag's formula. Furthermore, the designs of inverse optimal control reach both global inverse optimality and global asymptotic stability of the system for some meaningful cost functional. Four numerical examples are provided to show the effectiveness of the inverse optimal control.

Delay‐difference approximations of PD‐controllers. Improperly‐posed systems in multiple delays case

SummaryIn this paper, we study the behavior of characteristic roots of a class of strictly proper LTI SISO systems that are subject to a PD controller for which the derivative action has been implemented by means of a delay‐difference approximation scheme that uses multiple delays. To such an end, the improperly‐posed case is discussed in depth, that is, the situations where “small delays” induce instability in the closed‐loop system. The effect of adding more delays on the improperly‐posed case is analyzed and a methodology for determining the set of parameters that produces such a situation for a given number of delays is derived. Some illustrative examples complete the presentation.

Delayed resonator with multiple distributed delays – Considering and optimizing the inherent loop delay

We generalize the distributed delayed resonator (DDR) concept by incorporating the previously unutilized but inevitable feedback loop delay, thus creating a so-called multiple-delay distributed delayed resonator (MD-DDR) for complete vibration suppression. The necessary parameter tuning and control stability analysis become more involved but remain analytically solvable. Particularly, we take the operability of control parameters imposed by hardware as an explicit condition for parameter tuning and show that the loop delay (even if it is small) can lead to incomplete vibration suppression and, counter-intuitively, even no suppression if the excitation frequency exceeds a threshold value. On the other hand, such negative effects are neutralized by correcting control parameters. The loop delay is then intentionally augmented to seek enhanced performance, yielding a considerably extended operable frequency band for the desired complete vibration suppression. Furthermore, it is optimized to expedite response speed by achieving the leftmost placement of the dominant (i.e., the rightmost) characteristic root. Instead of applying a brute-force sweeping procedure as in the previous works, we analyze the dominant root locus and seek if the jump phenomenon occurs to conduct exact optimization at a low computational cost. Finally, extensive comparisons using actual experimental parameters are performed to explore various effects of the loop delay on vibration suppression and the benefits of the proposed MD-DDR in handling such issues over the conventional DDR that treats a single delay. This study fully exploits the strength of the distributed delayed control logic, moving the DDR concept closer to real applications and aiming to establish a broader design and analysis framework for the delayed resonator from a multiple-delay perspective.

Optimized robust control for improving frequency response of delay dependent AC microgrid with uncertainties

Converter-interface-based renewable energy incorporated into modern power systems causes deterioration in power system stability and it is proving to be a main challenge for operators using sluggish traditional generation with a growing share of converter-interface generation, and there is a need for an alternative means to deliver rapid frequency control. This paper proposes two control loops as secondary frequency control, first is an improved optimized delay-dependent frequency control to ensure robust frequency control under daily changes in system parameters that may occur in prospective, renewable-rich future AC microgrids. For a variety of operating conditions, the design process employs a mixed H2/H∞ robust control based on linear matrix inequality (LMI). In second, a speedy-acting improved power stability control loop is utilized as the proposed secondary frequency control, because demand response aggregators can be beneficial for frequency control. Robustness is evaluated against several perturbations and communication delay attacks through dynamic simulation and stability is evaluated by small-signal analysis. Different case studies subject to generation\\load loss, multiple time delay and parameter uncertainties are demonstrated on an interconnected AC microgrid system to verify the performance of the proposed control technique.

Robust cascade observer for a disturbance unmanned aerial vehicle carrying a load under multiple time-varying delays and uncertainties

In this article, a novel approach of a robust flight observer for a disturbance quadrotor transporting a payload in the presence of multiple time-varying delays is proposed. The developed algorithm is not only pertinent to a vehicle output signal with multiple small time-varying delays but also to long time-varying delays that are common for a quadrotor transporting a hanging load because a cascade structure is also employed to achieve outstanding performance, and the delay can be removed. The multiple time-varying delays and disturbances are compensated in the system with the proposed observer. The stability of the proposed methodology is proved using the Lyapunov–Krasovskii functional associated with an H ∞ criterion. Numerical simulations are shown to assess and validate the observer's performance and robustness under multiple time-varying delays and disturbances.

Topology property analysis and application of stable time‐delay regions for linear multiple time‐delay systems

AbstractThis study examines the relationship between the topology of stable time‐delay regions and the stability analysis of an linear multiple time delay system. To analyze the topology of stable time‐delay regions, we construct a function with a value equal to zero for the time‐delay points on the boundaries of stable time‐delay regions. The function is continuous and differentiable in the whole defining field with a global minimum of zero so that we can locate the boundaries by minimizing the value of the function. Based on the topology analysis, we proposed a performance validation approach for controllers that are designed to stabilize the system using feedback signals with time delays. The method based on the topology analysis is simple and reliable so that can deal with a linear time‐invariant system with high order and multiple time delays (more than 3). The example case study shows that the above method is reliable and enables ultra‐low latency coordination and control for the future power grid with ubiquitous power electronics.

Stability for multiple delays machining system with variable pitch tools considering nonlinear cutting force coefficients

Stability for multiple delays machining system with variable pitch tools considering nonlinear cutting force coefficients

Retracted: Single-Input Single-Output System with Multiple Time Delay PID Control Methods for UAV Cluster Multiagent Systems

Retracted: Single-Input Single-Output System with Multiple Time Delay PID Control Methods for UAV Cluster Multiagent Systems

Exploration on bifurcation for an incommensurate five-neuron fractional-order BAM neural network involving multiple delays

Some qualitative analyses of bifurcations for an incommensurate fractional-order neural network with delays are considered. At first, we display an incommensurate five-neuron fractional-order bidirectional associative memory neural network (FOBAMNN) with four delays. Next, the existence and uniqueness of the solution are analyzed. Afterward, from the perspective of the two different cases of delays inducing bifurcations, some sufficient criteria of the stability and the occurrence of Hopf bifurcation are established. Some numerical simulations are designed to verify the feasibility and validity of the obtained theorems. In addition, the effects of the delays on the stability and bifurcation of the integer-order neural network and the fractional-order neural network are discussed and some meaningful results are presented in the end.

Controllability of nonlinear fractional integrodifferential systems involving multiple delays in control

This work studies the existence of solutions and approximate controllability of fractional integrodifferential systems with Riemann-Liouville derivatives and with multiple delays in control. We establish suitable assumptions to prove the existence of solutions. Controllability of the system is shown by assuming a range condition on control operators and Lipschitz condition on non-linear functions. We use the concepts of strongly continuous semigroup rather than resolvent operators. Finally, an example is give to illustrate the theory.

On the [formula omitted]-exponential stability of linear positive singular systems with multiple time-varying delays

This paper deals with α-exponential stability analysis of the continuous-time linear positive singular systems with multiple time-varying delays. First, α-exponential stability problem of the single delay case is addressed. For this purpose, delay-range dependent sufficient conditions for such systems, which are regular and impulse-free, are stated in the paper. Then, α-exponential stability conditions for systems with multiple constant delays are addressed, and after that, we extend our idea for stability to multiple delays. To show the usefulness of the proposed conditions, two numerical and practical examples are given.

Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions

In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated by the fixed point method using progressive contractions, which are due to T.A. Burton. We prove four new theorems including sufficient conditions with regard to GEU of solutions of the equations. The results generalize and improve some related published results of the relevant literature.

Global Robust Exponential Synchronization of Interval BAM Neural Networks with Multiple Time-Varying Delays

Global Robust Exponential Synchronization of Interval BAM Neural Networks with Multiple Time-Varying Delays