Uncertain Delay Research Articles

Role of Integral Control for Enlarging Second-Order Delay Consensus Margin Under PID Protocols: None.

Proportional, integral, and derivative (PID) feedback control, as a popular control law, plays a central role in industrial processes and traditional control applications. In the context of multiagent systems, one may also wonder what the fundamental capability and limitation of PID control may be. This article attempts to provide an answer from the viewpoint of consensus robustness against uncertain delay. We consider robust consensus of second-order unstable agents under PID feedback protocols, subject to a constant but unknown time delay over an undirected graph. The issue concerns the so-called delay consensus margin (DCM), which is the largest delay range within which robust consensus can be achieved. The specific problem under study investigates the role of integral control on the robust consensus, seeking to understand whether integral control can be employed to enhance consensus robustness. Our result shows that there is none; that is, in a PID protocol, the integral control action has no improving effect on the DCM, and that PID and proportional-derivative (PD) protocols achieve the same DCM. As a byproduct of this finding, the DCM under PID and PD protocols is found to be computable by solving a quasiconcave, albeit nonsmooth, unimodal optimization problem.

Delay robustness-constrained control of integrating processes with optimal tracking and quantified disturbance rejection

Regarding a general class of integrating processes subject to uncertain delays, this paper investigates a two-degree-of-freedom (2-Dof) control scheme with a proportional–derivative (PD) controller and disturbance observer (DOB). Relative delay margin is introduced as a paramount metric to evaluate the delay robustness, with which a set of novel and explicit tuning formulae for PD controller is analytically derived under the single external loop. In this individual frame, the stability boundaries associated with the governing parameters are first studied, indicating the nominal stability conditions for the 2-Dof control system. Then the optimal tracking problem is formulated and addressed with such delay robustness constraints. For the design of the internal loop, the performance of DOB will be quantified by the trade-off between the external relative delay margin and the disturbance rejection, thus retaining the original PD controller design. Besides, the stability in the nominal delay range is primarily concerned when demarcating the low-pass filter in DOB, based on which a critical time constant is obtained through exhaustive testing. Following the route of combining analytical design with quantitative adjustment, the synthetic tuning rules can provide prescribed robustness against delay uncertainty for integrating processes. Through conducting illustrative simulations and a water tank experiment, the efficiency and merit of the proposed scheme are demonstrated.

Attack-resilient Fusion of Sensor Data with Uncertain Delays

Malicious attackers may disrupt the safety of autonomous systems through compromising sensors to feed wrong measurements to the controller. This article proposes attack-resilient sensor fusion that combines local sensor readings and shared sensing information from multiple sources. The method results in higher resilience against sensor attacks through jointly considering sensing noise and uncertain communication delay. To be specific, we first identify the considerable impact of the delay on determining attacked sensors. Second, we present a novel two-dimensional abstract sensor model, where each measurement is augmented as a probabilistic interval based on the convolution of the noise and delay. Third, we propose a fusion algorithm that admits the fused value with highest joint probability distribution of the intervals to tolerate corrupted measurements. Finally, we demonstrate the effectiveness of our method in a vehicle-platoon case study using extensive simulations and testbed experiments.

Data-Driven Control for Linear Discrete-Time Delay Systems

The increasing ease of obtaining and processing data together with the growth in system complexity has sparked the interest in moving from conventional model-based control design toward data-driven concepts. Since in many engineering applications time delays naturally arise and are often a source of instability, we contribute to the data-driven control field by introducing data-based formulas for state feedback control design in linear discrete-time time-delay systems with uncertain delays. With the proposed approach, the problems of system stabilization as well as of guaranteed cost and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control design are treated in a unified manner. Extensions to determine the system delays and to ensure robustness in the event of noisy data are also provided.

Parameter estimation in uncertain delay differential equations via the method of moments

Uncertain delay differential equations model time-delayed automatic control systems in which noises are described by Liu process. Parameter estimation plays a pivotal part in the applications of uncertain delay differential equations. In this paper, we first obtain a difference equation of uncertain delay differential equations by the forward Euler’s method. A function of the parameter is given by the difference equation, which is verified to obey the standard normal uncertainty distribution. By using the method of moments, we employ the observed data to obtain the empirical moments that equal the moments given by the standard normal uncertainty distribution, the estimated value of parameters are derived. Moreover, some examples are investigated to demonstrate that the method of moments is effective. Finally, we provide an uncertain delay logistic model to describe the population dynamics of American by using the method of parameter estimation proposed in this paper.

New sufficient conditions for p-th moment stability of uncertain delay differential equation

Uncertain delay differential system is an important mathematical model. Stability is a basic problem of uncertain delay differential system. Delay and uncertain interference often lead to changes in the stability of the system. Establishing the judgment of the stability of uncertain delay differential system conditions is very important. Based on the strong Lipschitz condition, the judgment of p-th moment stability for uncertain delay differential equations (UDDEs) has been investigated. Actually, the strong Lipschitz condition is assumed that it only relates to the current state, it is difficult to be employed to determine the stability in p-th moment for the UDDEs. In this paper, we consider two kinds of new Lipschitz conditions containing the current state and the past state, which are more weaker than the strong Lipschitz condition. Meanwhile, new sufficient theorems and corollaries under the new Lipschitz conditions as the tools to judge the p-th moment stability for the UDDEs are proved. Some examples explain the rationality of the corresponding theorems and corollaries.

Stability in distribution for uncertain delay differential equations based on new Lipschitz condition.

Stability in distribution for uncertain delay differential equations based on the strong Lipschitz condition only involving the current state has been successfully investigated. In reality, the uncertain delay differential equation is not only relate to the current state, but also relate to the past state, so it is very hard to obtain the strong Lipschitz condition. In this paper, the new Lipschitz condition concerning the current state and the past state is provided, if the uncertain delay differential equation satisfies the strong Lipschitz condition, it must satisfy the new Lipschitz condition, conversely, it may not be established. By means of the new Lipschitz condition, a sufficient theorem for the uncertain delay differential equation being stable in distribution is proved. Meanwhile, a class of uncertain delay differential equation is certified to be stable in distribution without any limited condition. Besides, the effectiveness of the above sufficient theorem is verified by two numerical examples.

Robust CACC in the Presence of Uncertain Delays

Cooperative adaptive cruise control employs inter-vehicle wireless communication to safely drive at short inter-vehicle distances, which improves road throughput. The underlying technical requirement to achieve this benefit is formulated by the notion of string stability, requiring the attenuation of the effects of disturbances in upstream direction. However, wireless communication delays significantly compromise string stability. In addition, the time delay is uncertain due to the inherent characteristics of wireless communication. Therefore, a controller design method is desired for a string-stable cooperative adaptive cruise control system, which considers uncertain communication delays. To this end, the string stability requirement is integrated into a μ synthesis approach. Being different from only considering the upper bound of the time delay, the whole range of time delays is taken into account in the controller design. Therefore, the proposed method allows for CACC system behaviour predictable, and rigorously guarantee string stability for all possible uncertain delays. The results are validated with simulations.

From quasilinear structures to population dynamics: Global stability analysis of an uncertain nonlinear delay system with interval approach

In this paper, we analyze a new continuous-time epidemic model including nonlinear delay differential equations by using parameters and functions selected from a class of intervals whose algebraic basis is based on quasilinear spaces. The main idea in the model’s generic structure is based on uncertainties in the values of parameters and functions forming the model. Therefore, using an interval coefficient approach rather than the exact value of parameters and functions that define transmissions between the compartments in the population dynamics will better represent the reality. Furthermore, preferring such an approach provides more realistic scenarios for temporal and stability dynamics of a population exposed to a disease. In this study, the quasilinear space is defined to explain the mathematical background of the interval approach in the fictional chain of the model. Next, descriptions belonging to the introduced model are included. After this compartmental system is presented as two systems formed by the lower and upper endpoints of the intervals determining parameters and functions, local and global dynamics related to stabilities of the models are analyzed separately for each. Then, using some interval analysis and functional analysis methods, these results are combined, and a conclusion about the stability of the proposed epidemic model has been reached. Alongside, the performance of the proposed approach is demonstrated by a visual simulation.

Hyperpath Searching Algorithm considering Delay at Intersection and Its Application in CVIS for Vehicle Navigation

The periodic change of intersection signals in urban road systems is the leading cause of uncertain delays. Therefore, aiming to minimize the travel time on the road segments and the expected delay at the intersections, a hyperpath search method based on intersection signal timing is proposed. The expanded network representation is used to capture the different turning delays at intersections. According to the intersection signal timing, the maximum waiting time of each turn and the turning movement ratio is obtained. A “recommendation priority passable phase” guidance strategy is proposed for the cooperative vehicle-infrastructure system (CVIS) based on the optimal hyperpath. The simulation experiments show that the vehicles can shift the driving route in the hyperpath set according to the guidance strategy, which effectively reduces the actual delay at intersections, and further realize an optimized distribution of traffic flows in the road network.

The almost sure stability for uncertain delay differential equations based on normal lipschitz conditions

Uncertain delay differential equations (UDDEs) can be applied to model the feedback control systems concerning both the present and the past states, such as the engineer system, the pharmacokinetic system, and the microbial batch fermentation system. The almost sure stability of its solution plays a significant role in the applications. By means of the strong Lipschitz condition, which relates to the present state, the almost sure stability of UDDEs is successfully explored. In this paper, the normal Lipschitz conditions concerning both the present and the past states are proposed. In other words, if the UDDEs satisfy the strong Lipschitz condition, it must satisfy the normal Lipschitz conditions. Conversely, it may not be established. Based on the normal Lipschitz conditions, two theorems for the almost sure stability of UDDEs and their equivalence relations are proved. Finally, a class of UDDEs being the almost sure stability is verified without any limited condition.

IEEE 1588-Based Timing and Triggering Prototype for Distributed Power Supplies in HIAF

In High-Intensity Heavy Ion Accelerator Facility (HIAF), a high precision timing system is necessary because highly synchronous triggering of distributed power supply is essential for the facility operation. To obtain a cost-effective local area timing system, a nanosecond-accuracy private synchronization approach based on IEEE 1588 protocol is proposed. Instead of Ethernet protocol usually used, universal asynchronous transceiver protocol over dedicated optical fiber is applied in the method to avoid the uncertain delay in Ethernet architecture. Besides, the timing system simplifies the communication message formats and increases synchronization frequency to 1 kHz to reduce the timing deviation due to oscillator frequency deviation. The test results show that the implementation ensures a synchronization accuracy of better than &#x00B1;10 nanoseconds with 2ppm temperature-compensation crystal oscillator for dozens of distributed power supply controllers.

A GEVP formulation for robust predictor feedback controller design of linear systems with uncertain input delay

Predictor feedback controllers are irreplaceable and widely used for systems with long input delays. However, it is also known to be sensitive to mismatch between the nominal input delay and the true unknown one. In this paper, we propose a robust predictor feedback controller design to enlarge the admissible delay mismatch, while keeping the convergence rate within a prescribed level. It is shown that the controller synthesis problem can be cast into a generalised eigenvalue problem (GEVP).

Stable Neural Adaptive Filters for Teleoperations With Uncertain Delays

Uncertainties in communication networks negatively affect the performance and usability of teleoperation systems, specially, in time-critical applications such as telesurgery. There already exist different methods to tackle this problem using filtering and learning approaches to smoothly estimate perturbed reference signals. Despite these efforts, the instability issue remains unsolved for such systems under random time-delay perturbations. This study employs and extends one of the best filtering techniques and proposes a new strategy based on learning capabilities of artificial neural networks to adaptively filter out delay-related disturbances and provides the most stable yet accurate estimations. To achieve this goal, an adaptive learning mechanism is proposed based on a Lyapunov-Krasovskii functional to not only analyse and guarantee the stability of the overall system, but also preventing the learning algorithm to get stuck in local optima. The proposed method is experimentally evaluated and compared with other closely similar methods in the recent literature. The results demonstrate the outstanding performance of the proposed solution in this study.

Delay compensated state estimation for Telepresence robot navigation

Telepresence robots empower human operators to navigate remote environments. However, operating and navigating the robot in an unknown environment is challenging due to delay in the communication network (e.g., distance, bandwidth, communication drop-outs etc.), processing delays and slow dynamics of the mobile robots resulting in time-lagged in the system. Also, erroneous sensor data measurement which is important to estimate the robot’s true state (positional information) in the remote environment, often create complications and make it harder for the system to control the robot. In this paper, we propose a new approach for state estimation assuming uncertain delayed sensor measurements of a Telepresence robot during navigation. A new real world experimental model, based on Augmented State Extended Kalman Filter (AS-EKF), is proposed to estimate the true position of the Telepresence robot. The uncertainty of the delayed sensor measurements have been modelled using probabilistic density functions (PDF). The proposed model was successfully verified in our proposed experimental framework which consists of a state-of-the-art differential-drive Telepresence robot and a motion tracking multi-camera system. The results show significant improvements compared to the traditional EKF that does not consider uncertain delays in sensor measurements. The proposed model will be beneficial to build a real time predictive display by reducing the effect of visual delay to navigate the robot under the operator’s control command, without waiting for delayed sensor measurements.

Stability in measure for uncertain delay differential equations based on new Lipschitz conditions

Uncertain delay differential equations (UDDEs) charactered by Liu process can be employed to model an uncertain control system with a delay time. The stability of its solution always be a significant matter. At present, the stability in measure for UDDEs has been proposed and investigated based on the strong Lipschitz condition. In reality, the strong Lipschitz condition is so strictly and hardly applied to judge the stability in measure for UDDEs. For the sake of solving the above issue, the stability in measure based on new Lipschitz condition as a larger scale of applications is verified in this paper. In other words, if it satisfies the strong Lipschitz condition, it must satisfy the new Lipschitz conditions. Conversely, it may not be established. An example is provided to show that it is stable in measure based on the new Lipschitz conditions, but it becomes invalid based on the strong Lipschitz condition. Moreover, a special class of UDDEs is verified to be stable in measure without any limited condition. Besides, some examples are investigated in this paper.

Rendezvous Under Temporal Uncertainty.

Three experiments sought to understand performance limitations in controlling a ship attempting to meet another moving ship that approached from various trajectories. The influence of uncertainty, resulting from occasional unpredictable delays in one's own movement, was examined. Cognitive elements of rendezvous have been little studied. Related work such as the planning fallacy and bias toward underestimating time-to-contact imply a tendency toward late arrival at a rendezvous. In a simplified simulation, participants controlled the speed and/or heading of their own ship once per scenario to try to rendezvous with another ship. Forty-five scenarios of approximately 30 s were conducted with different starting geometries and, in two of three experiments, with different frequencies and lengths of the unexpected delays. Perfect rendezvous were hard to obtain, with a general tendency to arrive late and pass behind the target vessel, although this was dependent on the angle of approach and relative speed. When occasional delays were introduced, less frequent but longer delays disrupted performance more than shorter but more frequent delays. Where delays were possible, but no delay occurred, there was no longer evidence of a general tendency to more frequently pass behind the target ship. Additionally, people did not wait to see if the unpredictable delays would occur before executing a course of action. Different control strategies were deployed and dual axis control was preferred. The tendency to arrive late and the influence of the possibility of uncertain delays are discussed in relationship to control strategies.

Robustness to delay mismatch in extremum seeking

In this paper, we generalize our previous results of Newton-based extremum seeking of higher derivatives via predictors with averaging-based estimates for uncertain delays. We show necessary conditions for the robustness to small delay uncertainties of the proposed extremum seeking controller with predictor feedback. Local stability and exponential convergence to a small neighborhood of the unknown extremum can still be guaranteed. A numerical simulation example is presented to illustrate the performance of the predictor-based control scheme for uncertain time-delay compensation.

PRUDENT DISCOUNTING: EXPERIMENTAL EVIDENCE ON HIGHER ORDER TIME RISK PREFERENCES

AbstractWe report results from an experiment that contrasts preferences toward the risk of what may happen (outcome risk preferences) with preferences toward the risk of when something may happen (time or delay risk preferences). Just as choices over monetary risks identify utility independently from discounting, choices over uncertain delays of a fixed reward identify discounting independently from utility. We replicate the widespread finding of outcome risk aversion, but—in a perfectly symmetric design—find substantial heterogeneity in delay risk aversion. Going beyond the second order of risk aversion, on the other hand, yields pervasive evidence for delay prudence and outcome prudence alike. This first empirical support for prudent discounting speaks to recent theoretical arguments that prudence may be a more important trait than previously realized.

Unbiased FIR, Kalman, and game theory [formula omitted] filtering under bernoulli distributed random delays and packet dropouts

It is known that due to uncertain delays and missing data wireless sensor networks (WSNs) may incur a significant loss in performance. In this work, we solve the problem in discrete-time state-space by developing the unbiased finite impulse response (UFIR) filter, Kalman filter (KF), and game theory H∞ filter for systems with randomly delayed data and packet dropouts. The binary Bernoulli distribution is adopted for WSN channels to model the arrival data with supposedly known delay-time probability. The effectiveness of the UFIR filter, KF, and H∞ filter is compared experimentally in terms of accuracy and robustness employing the GPS-measured vehicle coordinates transmitted with latency over WSN.