Time-varying Measurement Delays Research Articles

Nonsingular Terminal Sliding Mode Control for Vehicular Platoon Systems with Measurement Delays and Noise

Platooning of vehicular systems has been considered an effective solution for alleviating traffic congestion and reducing energy consumption. Because of limitations in onboard sensors, the measurement system inevitably suffers from measurement delays and noise, yet it receives insufficient attention. In this article, to deal with the measurement delays and noise while improving convergence performance, the platoon control problem of vehicular systems is studied under the nonsingular terminal sliding mode control (NTSMC) framework. A sliding mode observer (SMO) is proposed to estimate the states affected by measurement delays and noise. A distributed NTSMC scheme is developed for the platooning of the vehicular systems and ensures the convergence of the sliding mode surface affected by measurement delays and noise. One salient feature of the proposed SMO is that it can handle time-varying measurement delays rather than constant ones. Moreover, the control law is free of initial spacing error conditions under the employed coupled spacing policy. Numerical simulations are finally provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

VB-Based Gaussian Sum Cubature Kalman Filter for Adaptive Estimation of Unknown Delay and Loss Probability

The traditional Kalman filter assumes that all measurements can be obtained in real time, which is invalid in practical engineering. Therefore, a variational Bayesian- (VB-) based Gaussian sum cubature Kalman filter is proposed to solve the nonlinear tracking problem of multistep random measurement delay and loss (MRMDL) with unknown probability. First, the measurement model with MRMDL is modified by Bernoulli random variables. Then, the expression of the likelihood function is reformulated as a mixture of multiple Gaussian distributions, and the cubature rule is used to improve the estimation accuracy under the framework of Gaussian sum filter in the process of time update. Finally, by constructing a hierarchical Gaussian model, the unknown and time-varying measurement delay and loss probability are estimated in real time with the state jointly using the VB method in the measurement update stage. The algorithm does not need to calculate the equivalent noise covariance matrix so as to avoid the possible division by zero operation, which improves the stability of the algorithm. Simulation results for a target tracking problem show that the proposed algorithm has a better performance in the presence of MRMDL and can estimate the unknown measurement delay and loss probability accurately.

Sampled-Data Output Feedback Control for Nonlinear Uncertain Systems Using Predictor-Based Continuous-Discrete Observer.

In this article, we investigate the problem of sampled-data robust output feedback control for a class of nonlinear uncertain systems with time-varying disturbance and measurement delay based on continuous-discrete observer. An augmented system that includes the nonlinear uncertain system and disturbance model is first found, and by using the delayed sampled-data output, we then propose a novel predictor-based continuous-discrete observer to estimate the unknown state and disturbance information. After that, in order to attenuate the undesirable influences of nonlinear uncertainties and disturbance, a sampled-data robust output feedback controller is developed based on disturbance/uncertainty estimation and attenuation technique. It shows that under the proposed control method, the states of overall hybrid nonlinear system can converge to a bounded region centered at the origin. The main benefit of the proposed control method is that in the presence of measurement delay, the influences of time-varying disturbance and nonlinear uncertainties can be effectively attenuated with the help of feedback domination method and prediction technique. Finally, the effectiveness of the proposed control method is demonstrated via the simulation results of a numerical example and a practical example.

A time-delay approach to stabilization by extremum seeking controller via simplified ISS analysis

We study stabilization of linear uncertain systems under unknown control directions using a bounded extremum seeking controller with a small parameter. We consider a small time-varying measurement delay. By using the recently proposed time-delay approach to Lie-Brackets-based averaging, we transform the closed-loop system to a time-delay (neutral type) one, which has a form of perturbed Lie brackets system. The input-to-state stability (ISS) of the time-delay system guarantees the same for the original one. Differently from the existing analysis via Lyapunov-Krasovskii (L-K) method, we transform the neutral system to an ordinary differential equation (ODE) with delayed perturbations and employ variation of constants formula that greatly simplifies the analysis and leads to simpler stability conditions. Two numerical examples illustrate that the proposed method allows essentially larger parameter uncertainties with bounds on the small parameter and time-delay that are not too small.

A Method for Maintaining Virtually Coupled States of Train Convoys

Virtual coupling, which provides great advantages in operational flexibility and line capacity, is an advanced signaling concept for the railway industry. The dynamic disturbances caused by line conditions might change the coupled movements of the train convoy into abnormal states, which means the speed difference and separation distance of the adjacent trains exceed the given thresholds. This paper proposes a method to maintain the coupled states using terminal sliding mode control (SMC) based on second-order nonlinear train dynamics, with a nonlinear observer eliminating the estimation error due to time-varying measurement delay. The controller calculates the optimal unit effective tractive force for the following train in real-time, taking the leader velocity and desired separation as control targets. The simulation of a two-train convoy on a high-speed railway is conducted including different abnormal scenarios. The results demonstrate that the proposed method eliminates the observation errors and achieves synchronous convergence of the tracking errors while guaranteeing passenger comfort, and that it outperforms traditional SMC.

Filtering linear systems with large time-varying measurement delays

In this paper we consider the estimation problem for linear stochastic systems affected by multiple known and time-varying delays on all the output signals. Based on a modification of a previous proposal we prove for the first time the result that a filter based on simple eigenvalue assignment of the closed-loop error system may achieve uniform performance, with respect to the delay bound and estimation variance, in presence of both constant and time-varying delays that are differentiable. A new and simple demonstration technique provides non conservative delay bounds for time-varying delays. A cascaded version of the filter can cope with arbitrarily large delays.

Observer based sliding mode control for subsonic piezo-composite plate involving time varying measurement delay

In this study, an observer based sliding mode control (SMC) scheme is proposed for vibration suppression of subsonic piezo-composite plate in the presence of time varying measurement delay by using the piezoelectric patch (PZT) actuator. Firstly, the state space form of the subsonic piezo-composite plate model is derived by Hamilton’s principle with the assumed mode method. Then an state observer involving time varying delay is constructed and the sufficient condition of the asymptotic stability is derived by using the Lyapunov-Krasovskii function, descriptor method and linear matrix inequalities (LMIs) for the state estimation error dynamical system. Subsequently, a sliding manifold is constructed on the estimation space. Then an observer-based controller is synthesized by using the SMC theory. The proposed SMC strategy ensures the reachability of the sliding manifold in the state estimate space. Finally, the simulation results are presented to demonstrate that the proposed observer-based controller strategy is effective in active aeroelastic control of subsonic piezo-composite plate involving time varying measurement delay.

An Enhanced Observer for Nonlinear Systems With Time-Varying Measurement Delays

In this article, we propose an observer for a class of Lipschitz nonlinear systems affected by time-varying and known measurement delays, which is an improvement of the one presented by Cacace <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> ., 2014. Under the assumption that the delay function is piecewise continuous and differentiable, we prove that exponential convergence to zero of the observation error can be achieved with any desired decay rate, by suitably tuning a gain vector. The delay bound achieved with the observer proposed here is less conservative than the one obtained by Cacace <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2014, as confirmed by numerical tests. For the sake of brevity, in this article, only one-step observers are considered. However, a cascade observer can be arranged to cope with arbitrarily long delays.

Sequential predictors for delay compensation for discrete time systems with time-varying delays

We study time-varying linear discrete time systems with uncertainties and time-varying measurement delays, whose outputs are perturbed by uncertainty. We build sequential predictors, which ensure input-to-state stability with respect to the uncertainties and which can be constructed using output values under arbitrarily long delays. The number of required sequential predictors is any upper bound for the delay in our feedback stabilized closed loop systems. We illustrate our work in a digital control problem for a continuous time system that is discretized through sampling.

A Stability Criterion for Networked Control Systems With Packetized Transmissions

A stability criterion for networked feedback loops with time-varying measurement delays is proposed. It allows to check stability under the presence of different packetized network transmission policies where, e.g., newer packets may arrive at the same time or before older packets. The criterion is based on the small gain theorem and explicitly takes into account a packet selection and hold mechanism at the receiver side. It can easily be checked in frequency domain and does not involve any computationally expensive optimization algorithms.

Sampled-data output feedback controllers for nonlinear systems with time-varying measurement and control delays

In this paper, we propose sampled-data output feedback controllers for nonlinear systems with time-varying measurement and input delays. A state prediction is generated by chains of saturated high-gain observers with switching error-correction terms and the state prediction is used to stabilize the system with saturated controls. The observers reconstruct the unmeasurable states at different delayed time-instants, which partition the maximal variation interval of the time-varying delays. The density of these delayed time instant depend both on the magnitude of the delays and the growth rate of the nonlinearities. Our sampled-data feedback controllers are obtained as zero-order discretizations of continuous time controllers.

Sequential Predictors Under Time-Varying Feedback and Measurement Delays and Sampling

We build sequential predictors for time-varying linear systems with time-varying input delays, outputs, sampling in the control, and time-varying measurement delays. We prove global exponential stability and robustness properties. We allow the sup norm of the input delay to be arbitrarily large and aperiodic sampling. We use a new set of dynamical extensions that contain output measurements, and whose advantages over existing methods include their lack of distributed terms.

Continuous-Time and Sampled-Data Stabilizers for Nonlinear Systems With Input and Measurement Delays

In this paper, we propose continuous-time and sampled-data output feedback controllers for nonlinear multi-input multi-output systems with time-varying measurement and input delays, with no restriction on the bound or serious limitations on the growth of the nonlinearities. A state prediction is generated by chains of saturated high-gain observers with switching error-correction terms and the state prediction is used to stabilize the system with saturated controls. The observers reconstruct the unmeasurable states at different delayed time-instants, which partition the maximal variation interval of the time-varying delays. These delayed time instant depend both on the magnitude of the delays and the growth rate of the nonlinearities. We also design sampled-data stabilizers as zero-order discretization of a hybrid modification (with continuous-time states and discrete-time control and innovations) of the continuous-time stabilizers.

Predictor-based control of stochastic systems with nonlinear diffusions and input delay

We consider the problem of state-feedback control of linear continuous-time stochastic systems with nonlinear diffusion terms affected by time-varying input delays or, equivalently, by time-varying state measurement delays. We propose a finite-dimensional control law based on closed-loop predictors and derive sufficient delay bounds for the exponential stability in mean and exponential mean square stability with prescribed rate.

Observation and stabilization of LTV systems with time-varying measurement delay

This work deals with observer-based output-feedback stabilization of linear time-varying (LTV) systems with time-varying measurement delay. The delay is modeled by a first-order hyperbolic partial differential equation (PDE), whose boundary condition evolves according to an ordinary differential equation (ODE), namely, the plant. The overall system is thus represented by an ODE–PDE cascade, which is also the structure of the proposed observer. The exponential stability of the estimation error is established for arbitrarily large time-varying delays. An observer-based controller is also introduced and the closed-loop stability is proved. The separation principle holds and the design of both the observer and controller gains can be done as if there was no delay. Some simulations illustrate the feasibility of this approach.

Multilayer State Predictors for Nonlinear Systems with Time-Varying Measurement Delays

In this paper, we propose state predictors for stable genuinely nonlinear systems with time-varying measurement delay, with no restriction on its bound or serious limitations on the growth of the n...

Torsional vibration control of drill-string systems with time-varying measurement delays

This paper is concerned with torsional vibration control of drill-string systems. The objective is to develop a delay-dependent control scheme such that the downhole vibrations can be minimized by using ground measurement output with time-varying measurement delays. By regarding a drill-string as a series of lumped masses, a state space model is derived from a generic multi-degree-of-freedom model of the drill-string through a variable transformation. This provides the foundation of an observer-based output feedback control system, in which an internal model is inserted to represent the drill rig for improving the tracking performance, and a state observer is combined with a low-pass filter to estimate an equivalent effect of the downhole bit-rock interaction in the control input channel. To calculate the parameters of this control system, some sufficient conditions are derived in terms of linear-matrix-inequalities by taking into account a refined allowable delay set. It is shown through a numerical example that (i) the measurement of rotary table’s angular displacement helps to produce less conservative results and (ii) a small measurement delay is beneficial for designing a controller with a smaller gain in the sense of Euclidean norm, however it may also result in a larger control torque by enhancing the bit-rock interaction.

Robust Controller Design for Attitude Dynamics Subjected to Time-Delayed State Measurements

Attitude control and time-delay systems are well-developed fields in the control theory, but only a modicum of papers have explored control systems that fall within the intersection of the two. Indeed, combining kinematics and dynamics nonlinearities with sensor and actuator delays reinvigorates the original attitude control problem, typically leading to involved stability arguments based on nonlinear analysis techniques. This paper instead proposes solving the attitude stabilizer design problem by formulating it as a linear matrix inequality feasibility problem. The proposed approach simplifies the stability arguments, without loosing generality; the obtained conditions cope with the general case of rigid bodies that suffer from unknown, heterogeneous, time-varying state measurement delays, and have inertia uncertainties. This methodology is particularly well suited to resource-limited applications, because controllers can be designed offline using computationally efficient tools. Although simple, numerical evidence shows the stability criterion derived in this paper largely outperforms previous results.

State and unknown input observers for nonlinear systems with delayed measurements

The use of connected devices or humans-in-the-loop for measuring outputs of dynamical systems inevitably produces time-varying measurement delays. These delays can lead to instability or severe degradation of system performance. In this paper, linear matrix inequality-based sufficient conditions are proposed for the design of state and unknown input observers based on delayed measurements for a class of nonlinear systems, where the nonlinearities are characterized by incremental multiplier matrices. The proposed observer is guaranteed to perform at specified operational levels in the presence of unknown exogenous inputs acting on the states and measurement outputs. Sufficient conditions are also provided for the estimation of these unknown inputs to a specified degree of accuracy. The potential of the proposed approach is illustrated via estimation of enzyme kinetics.

Dynamic consensus of double‐integrator multi‐agent systems with aperiodic impulsive protocol and time‐varying delays

This study involves an examination of the dynamic consensus problem for networks of double-integrator agents with aperiodic impulsive protocol and fixed topology. With respect to each agent, the control law is designed based on relative state measurements (i.e. position and velocity) between the agent and the neighbouring agents at a few discrete times. Additionally, these state measurements can include time-varying measurement delays. The theory of impulsive differential equations is used to prove that the dynamic consensus can be achieved under the condition of a graph with a spanning tree and to provide the consensus state finally reached by all agents. Furthermore, the study establishes algebraic inequalities that should be satisfied by the control gains, the bounds of impulsive interval lengths, and the upper bound of delays. Two numerical examples are illustrated to validate the main results.