Input Delay Research Articles

Fully distributed consensus of discrete-time linear multi-agent systems with large input and communication delays

This paper investigates the consensus problem for discrete-time leader-following multi-agent systems subject to large time delays. Building upon two assumptions, a novel fully distributed protocol is devised by utilizing a normalized weighting matrix, depending solely on the relative output measurement. It is shown that, for arbitrarily large yet bounded input and communication delays that are constant and exactly known, the consensus problem can be effectively addressed by both the proposed protocol and its truncated version. Assuming further that followers incorporate solely input delays, then the permitted delays can be time-varying and different. The proposed protocols do not rely on global information of the directed communication topology, thus ensuring robustness against alterations in the communication topology. A numerical example is employed to validate the effectiveness of the suggested approach.

Ground Reaction Forces and Joint Moments Predict Metabolic Cost in Physical Performance: Harnessing the Power of Artificial Neural Networks

Understanding metabolic cost through biomechanical data, including ground reaction forces (GRFs) and joint moments, is vital for health, sports, and rehabilitation. The long stabilization time (2–5 min) of indirect calorimetry poses challenges in prolonged tests. This study investigated using artificial neural networks (ANNs) to predict metabolic costs from the GRF and joint moment time series. Data from 20 participants collected over 270 walking trials, including the GRF and joint moments, formed a detailed dataset. Two ANN models were crafted, netGRF for the GRF and netMoment for joint moments, and both underwent training, validation, and testing to validate their predictive accuracy for metabolic cost. NetGRF (six hidden layers, two input delays) showed significant correlations: 0.963 (training), 0.927 (validation), 0.883 (testing), p < 0.001. NetMoment (three hidden layers, one input delay) had correlations of 0.920 (training), 0.956 (validation), 0.874 (testing), p < 0.001. The models’ low mean squared errors reflect their precision. Using Partial Dependence Plots, we demonstrated how gait cycle phases affect metabolic cost predictions, pinpointing key phases. Our findings show that the GRF and joint moments data can accurately predict metabolic costs via ANN models, with netGRF being notably consistent. This emphasizes ANNs’ role in biomechanics as a crucial method for estimating metabolic costs, impacting sports science, rehabilitation, assistive technology development, and fostering personalized advancements.

Robustness of reaction–diffusion PDEs predictor-feedback to stochastic delay perturbations

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction–diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The stabilization problem under consideration involves random perturbations modeled by a finite-state Markov process that further obstruct the actuation path at the controlled boundary of the infinite-dimension plant. This scenario is useful to describe several actuation failure modes in process control. Employing the recently introduced infinite-dimensional representation of the state of an actuator subject to stochastic input delay for ODEs (Ordinary Differential Equations), we convert the stochastic input delay into r+1 unidirectional advection PDEs, where r corresponds to the number of jump states. Our stability analysis assumes full-state measurement of the spatially distributed plant’s state and relies on a hyperbolic–parabolic PDE-PDE cascade representation of the plant plus actuator dynamics. Integrating the plant and the nominal stabilizing boundary control action, all while considering probabilistic delay disturbances, we establish the proof of mean-square exponential stability as well as the well-posedness of the closed-loop system when random phenomena weaken the nominal actuator compensating effect. Our proof is based on the Lyapunov method, the theory of infinitesimal operator for stability, and C0-semigroup theory for well-posedness. Our stability result refers to the L2-norm of the plant state and the H2-norm of the actuator state. Furthermore, our study presents a qualitative analysis of the maximum deviation of the stochastic disturbance relative to the nominal delay, which is expressed as a function of the severity of the plant instability, namely, the magnitude of the reactivity coefficientand the known upper bound of the transition rate of the underlying stochastic perturbations. Extensive simulation results illustrate the viability of the robustness study.

Robust reinforcement learning control for quadrotor with input delay and uncertainties

In this paper, a new control method is proposed for the control of the quadrotor with time-varying input delay and uncertainties. The controller is primarily composed of two components: the reinforcement learning (RL) component and the robust component. The robust component is designed to ensure basic control performance. The basic control performance can guarantee the tracking characteristics with nonlinear uncertainties. The tracking error can be arbitrarily small by robust component. The RL component further improves the convergence speed and control precision on the basis of the basic control performance. Both components have input delay problems, and each component of the proposed method solves this problem separately. For the robust component, the filter is used to eliminate the uncertainties and restrain the influence of the input delay. It can ensure safety during the initial training period. For the RL component, the extended state method and the extending control period method are used to handle the problem of input delay with lower computational complexity. In addition, the convergence of network weights is proven, and the stability of the whole system is analyzed according to the Lyapunov method. Finally, simulation results are presented to illustrate the effectiveness and superior performance of our method.

A switched system approach to exponential stabilization of interval type-2 fuzzy nonlinear systems with packet dropouts

This paper investigates the exponential stabilization problem for interval type-2 (IT2) fuzzy system with parameter uncertainties and packet dropouts. The sample-and-hold characteristic is simulated by employing an input delay methodology, and we present a model for the packet dropout phenomenon using switched approach. Some novel two-side delay-dependent looped-functionals are proposed by considering state information in the intervals from tr to t and t to tr+1 which relaxes the monotonic constraint of the Lyapunov–Krasovskii functional (LKF) and enhances the utilization of the actual sampling pattern. Additionally, some free-weighting matrices, slack matrices, the bound information in membership functions (MFs) and the signs of the first-order time derivative of fuzzy MFs are used to obtain a novel relaxed sufficient conditions for exponential stabilization of interval type-2 fuzzy systems (IT2 FS). Based on the LKF theory, new relaxed sufficient conditions with linear matrix inequalities (LMIs) constraints are derived. According to the criterion, sampled-data controller is devised to ensure that the closed-loop system is exponential stabilization. Finally, an illustrative example is presented to demonstrate the practicality and effectiveness of the method proposed. Comparative analysis highlights the simplicity and practicality of the suggested algorithm.

Adaptive neural dynamic surface control for nonstrict feedback systems with state delays

AbstractThis article focuses on a class of nonstrict feedback systems with input delay, state delays and time‐varying full‐state constraints by proposing an adaptive neural control scheme. To overcome the problems of all state variables effected by time‐varying constraints, the asymmetric time‐varying barrier Lyapunov functions are constructed. The influence of state delays and input delay is eliminated by employing suitable Lyapunov–Krasovskii functionals. Additionally, the process of controller design is based on backstepping method and the unknown functions can be approximated by radial basis function neural networks. Moreover, the problem of repeated differentiations for nonlinear components during controller design is hugely simplified by taking advantage of the dynamic surface control method. The boundness of all the closed‐loop signals can be ensured by the designed controller. Finally, two numerical simulations illustrate that the proposed adaptive neural control scheme is effective.

Adaptive Fuzzy Control for Fractional-Order Networked Control Systems with Input Time Delay and Data Loss

This paper considers the adaptive fuzzy control of fractional-order nonlinear networked control systems subjected to network-induced input delay and data loss. To approximate unknown functions, fuzzy logic systems are employed. Furthermore, the Pade approximation method and an intermediate variable are introduced to eliminate the impact of input delay, and an adaptive fuzzy controller is designed using backstepping technology. Based on fractional-order Lyapunov stability theory, the proposed method can ensure that all signals are uniformly ultimately bounded, and the tracking error can converge to a small region of the origin. Two simulation examples are provided to verify the viability of the control method.

Adaptive PI event-triggered control for MIMO nonlinear systems with input delay

An adaptive PI event-triggered control method for a class of multi-input and multi-output (MIMO) nonlinear systems with uncertain input delay is proposed. First, a new variable is designed to eliminate the impact of uncertain input delay based on the Pade approximation and Laplace transform. Then, a nonlinear controller with PI structure is developed, it has a linear structure and the ability to deal with uncertainties. Meanwhile, only one parameter is required to be updated online through RBFNN in the system. Moreover, an event-triggered control strategy is established to dynamically allocate the communication resources based on the PI nonlinear controller. With the proposed method, MIMO nonlinear systems are able to handle input delay of different duration dynamically and still maintain superior tracking performance. Finally, the effectiveness of the proposed method is demonstrated through two sets of simulation experiments.

Output-Feedback Regulation of Nonlinear Networked Systems With Input Delay Under Event-Triggered and Quantized Mechanism

Output-Feedback Regulation of Nonlinear Networked Systems With Input Delay Under Event-Triggered and Quantized Mechanism

Distributed Prescribed Performance Fault-Tolerant Control of Multi-UAVs With Input Delays via Dynamic Event-Triggered Observers

Distributed Prescribed Performance Fault-Tolerant Control of Multi-UAVs With Input Delays via Dynamic Event-Triggered Observers

LQR and Stabilization for Discrete-Time Systems With Multiplicative Noises and Input Delays

LQR and Stabilization for Discrete-Time Systems With Multiplicative Noises and Input Delays

Adaptive Input Delay Compensation Under Event-Based Control Signal Implementation

Adaptive Input Delay Compensation Under Event-Based Control Signal Implementation

Backstepping based neural [formula omitted] optimal tracking control for nonlinear state constrained systems with input delay and disturbances

This paper focuses on the problem of H∞ optimal tracking control for a class of nonlinear state constrained systems with input delay and disturbances. With the aid of Pade approximation, an auxiliary variable is devised to eliminate the effects of input delay. Combining barrier Lyapunov functions (BLFs) with backstepping design technique, a feedforward adaptive controller is designed to transform the tracking control problem of nonlinear state constrained system into an equivalent H∞ control problem of input-affine error system without state constraints, wherein neural networks (NNs) are employed to approximate unknown system dynamics. Then based on single-network adaptive dynamic programming (ADP), an H∞ optimal feedback controller is developed by utilizing a single critic network to learn the Nash equilibrium related to Hamilton–Jacobi–Isaacs (HJI) equation. Therefore, the whole tracking controller can be constructed by integrating the feedforward adaptive controller with the optimal feedback controller. Moreover, it is proven by Lyapunov’s theory that all signals within the closed-loop system are uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin without violating any state constraints. Two simulation examples are also presented to validate the effectiveness of the proposed approach.

Adaptive path tracking control for autonomous vehicles with sideslip effects and unknown input delays

This paper presents an adaptive path-tracking control of autonomous ground vehicles with sideslip effects and time-varying input delays. To handle the problem of unknown time-varying input delays, the vehicle kinematic model is transformed into a novel chain model, and a delay-based auxiliary integral term is introduced for the estimation of the unknown terms caused by time-varying delays. To avoid modeling errors caused by existing linear approximation methods, a new adaptive path-tracking control strategy is proposed, such that the optimal tracking performance is achieved by appropriately adjusting certain design parameters. In addition, the inherent complexity explosion issue is avoided with the aid of a boundary estimation strategy. All signals of the closed-loop systems are guaranteed to be bounded. Simulation results illustrate the effectiveness of the method proposed.

Observer-based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay.

This article introduces an observer-based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time-varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose-insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer-based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer-based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed-loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

Stabilization and Optimal Control for Discrete-Time Markov Jump Linear System With Multiplicative Noises and Input Delays: A Complete Solution

Stabilization and Optimal Control for Discrete-Time Markov Jump Linear System With Multiplicative Noises and Input Delays: A Complete Solution

Event-Triggered Practical Fixed-Time Containment Control for Stochastic Multiagent Systems With Input Delay

Event-Triggered Practical Fixed-Time Containment Control for Stochastic Multiagent Systems With Input Delay

Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Tube-based model predictive control for linear systems with bounded disturbances and input delay

This paper proposes a tube-based model predictive control strategy for linear systems with bounded disturbances and input delay to ensure input-to-state stability. Firstly, the actual disturbed system is decomposed into a nominal system without disturbances and an error system. For the nominal system, solving an optimization problem, where the delayed control input is set as an optimization variable, yields a nominal control law that enables the nominal state signal to approach to zero. Then, for the error system, the Razumikhin approach is used to identify a robust control invariant set. Using the set invariance theorem, an ancillary control law is developed to confine the error state signal in the invariant set. Combining the two results, we obtain a control law that enables the state signal to remain within a robustly invariant tube. Finally, the effectiveness of the developed control strategy is validated by simulations.

Event-Triggered Adaptive Neural Network Control for State-Constrained Pure-Feedback Fractional-Order Nonlinear Systems with Input Delay and Saturation

In this research, the adaptive event-triggered neural network controller design problem is investigated for a class of state-constrained pure-feedback fractional-order nonlinear systems (FONSs) with external disturbances, unknown actuator saturation, and input delay. An auxiliary compensation function based on the integral function of the input signal is presented to handle input delay. The barrier Lyapunov function (BLF) is utilized to deal with state constraints, and the event-triggered strategy is applied to overcome the communication burden from the limited communication resources. By the utilization of a backstepping scheme and radial basis function neural network, an adaptive event-triggered neural state-feedback stabilization controller is constructed, in which the fractional-order dynamic surface filters are employed to reduce the computational burden from the recursive procedure. It is proven that with the fractional-order Lyapunov analysis, all the solutions of the closed-loop system are bounded, and the tracking error can converge to a small interval around the zero, while the state constraint is satisfied and the Zeno behavior can be strictly ruled out. Two examples are finally given to show the effectiveness of the proposed control strategy.