Unknown Time Delay Research Articles

Fuzzy-Based Tracking Control for a Class of Fractional-Order Systems with Time Delays

This paper focuses on the tracking control problem for a family of fractional-order systems with unknown drift functions and unknown time delays. By employing fuzzy logic systems (FLSs), the unknown functions are approximated and compensated. Meanwhile, with the help of a hyperbolic tangent function and a sign function, the adverse effects of time-varying delays and FLSs approximation error are mitigated simultaneously. It should be stressed that the proposed method eliminates the assumption that the time delay is bounded by a known function. The stability analysis shows that the tracking error can converge to a small neighborhood of the origin. Finally, simulation is conducted to confirm the effectiveness of the presented control strategy.

Dual ML-ADHDP method for heterogeneous discrete-time nonlinear multi-agent systems with unknown dynamics and time delay

This paper develops a new dual ML-ADHDP method to solve the optimal consensus problem (OCP) of a class of heterogeneous discrete-time nonlinear multi-agent systems (MASs) with unknown dynamics and time delay. A hierarchical and distributed control strategy is used to transform the original problem into nonlinear model reference adaptive control (MRAC) problems and an OCP of virtual linear MASs. For the nonlinear MRAC problems, a new multi-layer action-dependent heuristic dynamic programming (ML-ADHDP) method is developed to overcome the unknown dynamics and neural network estimation errors, which has higher control accuracy. In order to solve the OCP of virtual linear MASs and improve the convergence speed, a new multi-layer performance index is proposed. Then the ML-ADHDP method is used to solve the coupled Hamiltonian–Jacobi–Bellman equation and obtain the optimal virtual control. Theoretical analysis proves that the original MASs can achieve Nash equilibrium, and simulation results show that the developed dual ML-ADHDP method ensures better convergence speed and higher control accuracy of original MASs.

Robust Multi-Mode Synchronization of Chaotic Fractional Order Systems in the Presence of Disturbance, Time Delay and Uncertainty with Application in Secure Communications

This paper investigates the robust adaptive synchronization of multi-mode fractional-order chaotic systems (MMFOCS). To that end, synchronization was performed with unknown parameters, unknown time delays, the presence of disturbance, and uncertainty with the unknown boundary. The convergence of the synchronization error to zero was guaranteed using the Lyapunov function. Additionally, the control rules were extracted as explicit continuous functions. An image encryption approach was proposed based on maps with time-dependent coding for secure communication. The simulations indicated the effectiveness of the proposed design regarding the suitability of the parameters, the convergence of errors, and robustness. Subsequently, the presented method was applied to fractional-order Chen systems and was encrypted using the chaotic masking of different benchmark images. The results indicated the desirable performance of the proposed method in encrypting the benchmark images.

A novel robust finite time control approach for a nonlinear disturbed quarter-vehicle suspension system with time delay actuation

This paper presents a novel robust control approach for a nonlinear uncertain vehicle suspension system with time-delayed actuation and bounded disturbances. Three factors affect the stability and performance of the suspension system: (1) Uncertainty that arises from the difference between the model and the real system. (2) The disturbances that enter mostly from the side of the road to the suspension system. (3) Input delay that occurs by actuator performance. In this study, all three components are considered simultaneously, and sliding mode and backstepping methods have been used to overcome them. A nonlinear model is considered to more accurately describe the behaviour of the suspension and controller design. The Lyapunov function is inspired by the backstepping algorithm, and stability in the Lyapunov concept is obtained for the closed-loop system under the proposed robust finite time control. To demonstrate the capabilities of the proposed controller, simulation scenarios are considered in the MATLAB environment. Simulation results verify good active suspension performance regardless of the presence of unknown time delay and disturbances in the nonlinear model.

Data‐driven consensus control for a class of unknown nonlinear multiagent systems with time delays

In this paper, the distributed output consensus tracking problem for a class of unknown heterogeneous discrete-time single-input single-output nonlinear multiagent systems (MASs) with time delays is considered. For this problem, a distributed data-driven consensus control strategy is proposed by using improved model-free adaptive control with a time delay. First, the unknown nonlinear multiagent time delay system is transformed into a virtual data model with time-varying parameters by using a partial form dynamic linearisation method. Then, a controller with model-free adaptive control and a tracking differentiator are designed. The proposed method uses only the input/output data of neighbouring agents during the control process without mathematically modelling multiple agents. For the time delay system, the boundedness of the closed-loop tracking error is theoretically proven for both the tracking problem and the regulation problem. Furthermore, this result can be generalised to switching topology structures by a rigorous mathematical proof. Numerical simulations verify the effectiveness of the proposed algorithm.

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.

Adaptive consensus control for a class of nonlinear multi-agent systems with unknown time delays and external disturbances

This paper investigates a class of unknown nonlinear multi-agent systems with unknown time delays and external disturbances. The external disturbance considered in this paper is completely unknown, and the accurate mathematical expression cannot be obtained. To eliminate the external disturbance, a disturbance observer is constructed by the Disturbance-Observer-Based-Control (DOBC) method. By utilizing Young’s inequality scaling technique, the problem of time delay is solved. By assuming that the communication graph among the agents is directed and connected, a novel distributed adaptive consensus control protocol is established based on the relative output information to achieve the goal of consensus control. Furthermore, the stability of the multi-agent system is analyzed by selecting an appropriate Lyapunov function; it is certified that with the proposed control protocol, all signals are guaranteed to be globally uniformly bounded, and the considered multi-agent systems can reach consensus even in the presence of time delay and external disturbance. Finally, two simulation examples are given to support the proposed control strategy.

Indirect output-error modeling scheme for continuous processes with unknown time delay using iterative instrument variable approach

Indirect output-error modeling scheme for continuous processes with unknown time delay using iterative instrument variable approach

Identification of fractional-order systems with both nonzero initial conditions and unknown time delays based on block pulse functions

In this paper, we present an effective method for the identification of fractional order system (FOS) with both nonzero initial conditions and unknown time delays based on a construction of suitable separable nonlinear least squares problem including both. The separable nonlinear least squares problem is first projected into the least squares problem only with respect to nonlinear parameters, time delays. Next, a bias compensated recursive least squares identification method is used to estimate the remaining linear parameters involving initial conditions of FOS. The effectiveness of the proposed method is illustrated by several simulations.

Simultaneous Fault and Input Time Delay Estimation for an Actuator System: Theory and Flight Data Validation

This letter proposes a first order sliding mode observer for the purpose of simultaneously estimating the unknown input time delay and reconstructing the loss of effectiveness in a model of an actuator. The adaptive algorithm is driven by the `equivalent output error injection' signal associated with the sliding motion. Sufficient conditions are given to ensure finite time convergence of the state estimation error system, ensuring both the time delay estimation error and the estimation error associated with the actuator fault converge to a small region around zero. The efficacy of the approach has been evaluated via both a numerical simulation and flight data validation.

Ziv-Zakai Bound for Compressive Time Delay Estimation

Compressive radar receiver can keep a good balance between sub-Nyquist sampling and high resolution. To evaluate the performance of compressive time delay estimators, Cram&#x00E9;r-Rao bound (CRB) has been derived for lower bounding the mean square error (MSE), which, unfortunately, is a local bound being tight in the asymptotic region only. In this paper, we use the Ziv-Zakai bound (ZZB) methodology to develop a Bayesian MSE bound on compressive time delay estimation by incorporating the <i>a priori</i> information of the unknown time delay. Specifically, we respectively derive deterministic ZZB and stochastic ZZB as functions of compressive sensing (CS) kernel, where there is no restriction on CS kernels and Gaussian noise colors. Simulation results demonstrate that compared with Bayesian CRB, ZZB provides a better performance prediction for minimum MSE estimator of compressive time delay estimation over a wide range of signal-to-noise ratios, where different CS kernels, compression ratios, <i>a priori</i> distributions and Gaussian noise colors are tested.

An Improved Model Predictive Fast Frequency Control for Power System Stability Against Unknown Time-Delay Switch Attack

A modern power grid is a cyber-physical system, which are vulnerable to cyber attacks. A recently found attack, the time-delay switch attack (TDSA), is made by inserting time delays into communication channels. A TDSA can be highly destructive to a power system as it can lead to instability. This paper presents a novel model predictive control (MPC) for fast frequency controller in a power system which can effectively mitigate the unknown TDSA. The MPC recently has received great attentions to be applied as FFC in a power system. Most of the MPC design are based on discrete-time model, whose future plant behaviour is calculated through iteration, rather than convolution. Nevertheless, one crucial step in the derivation of discrete-time MPC (DTMPC) is to capture the control trajectory over a finite prediction horizon. This imposes a challenge in designing a DTMPC to counteract the time-delay with unknown time length. Thus, a continuous-time MPC (CTMPC) is proposed to deal with TDSA. To overcome the unknown time delay, we synthesize an accurate time-delay estimator and sequential state predictor (SSP), are designed to accurately estimate and effectively counteract the unknown and random TDSA. All presented case studies are based on a real Taipower system and justification of the effectiveness of the proposed method was verified.

A Hybrid Predictive Type-3 Fuzzy Control for Time-Delay Multi-Agent Systems

In this paper, the consensus problem is addressed for multi-agent systems. The dynamics of each agent contain unknown uncertain/nonlinear terms and unknown time delays. A type-3 fuzzy logic system is developed to tackle the effect of unknown dynamics and design a hybrid controller. The policy scheme involves two control signals for the stabilization of the approximation and consensus error of each agent dynamic. To this end, based on the concept of the model predictive control approach, the constrained control laws are designed and updated at each time step. The simulations results portray the error signals. Feasibility, appropriate convergence, and proper transient response are the main merits of the suggested method.

All state constrained decentralized adaptive implicit inversion control for a class of large scale nonlinear hysteretic systems with time-delays

This paper proposes an all state constrained decentralized adaptive implicit inversion control scheme for a class of large scale nonlinear systems with unknown time delays and asymmetric saturated hysteresis. First, to address the states constrained problem, the asymmetric barrier Lyapunov function is introduced to keep the error surface within an appropriate range from the view of engineering practice to ensure the performance and safety, such as for attitude tracking of rigid spacecraft, for spacecraft approach and intersection. Second, the transmission delays between different subsystems are considered and approximated through the incorporation of the neural-network approximators and the finite coverage lemma. Third, a new hysteresis implicit inverse algorithm is designed to effectively mitigate asymmetric and saturated hysteresis nonlinearities. It should be noted that the implicit inverse implies that the analytical inverse of the asymmetric and saturated hysteresis is not required. Instead, the decoupling algorithms are designed to extract the actual control signal from the temporarily hysteretic control signal , which reduces the preliminary work of the control algorithm. Finally, all of the signals in the closed-loop system are proved to be semi-globally ultimately uniformly bounded and the tracking errors converge to an arbitrarily small residual set. The experimental results on two-machine excitation power systems in the hardware-in-loop system are presented to illustrate the effectiveness of the proposed scheme.

Finite-time tracking control for nonstrict-feedback nonlinear systems with unknown time delays and input saturation

In this article, the problem of adaptive finite-time control is studied for a category of nonstrict-feedback nonlinear time-delay systems with input saturation and full state constraints. The fuzzy logic systems are applied to model the unknown nonlinear terms in the systems. Then, a novel tan-type barrier Lyapunov function is adopted to overcome the problem of full state constraints. By utilizing the finite-time control theory and the backstepping technique, a finite-time fuzzy adaptive controller is designed. The controller can guarantee that the tracking error is adjusted around zero with a small neighborhood in a finite time and all the signals in the closed-loop system are bounded. Finally, two simulation examples are included to verify the validity and feasibility of the control scheme.

Robust finite-time consensus subject to unknown communication time delays based on delay-dependent criteria

In this paper, robust finite-time consensus of a group of nonlinear multi-agent systems in the presence of communication time delays is considered. In particular, appropriate delay-dependent strategies which are less conservative are suggested. Sufficient conditions for finite-time consensus in the presence of deterministic and stochastic disturbances are presented. The communication delays don’t need to be time invariant, uniform, symmetric, or even known. The only required condition is that all delays satisfy a known upper bound. The consensus algorithm is appropriate for agents with partial access to neighbor agents’ signals. The Lyapunov–Razumikhin theorem for finite-time convergence is used to prove the results. Simulation results on a group of mobile robot manipulators as the agents of the system are presented.

Limit cycle oscillator in nonlinear systems with multiple time delays

This paper concerns with the problem of generation stable limit cycles in a class of nonlinear time-delay systems with multiple time delays. With the help of the Lyapunov–Krasovskii functional approach, a state-feedback controller is constructed based on the backstepping technique. According to the recursive procedure of the backstepping technique, at first, the desired limit cycle is generated in the second-order subsystem by utilizing the Lyapunov theorem analysis of the positive limit sets. Then, this method is expanded for higher-order systems. By introducing an appropriate Lyapunov-Krasovskii functional, the complexities raised by unknown time-delays are solved in the control design process. Based on this scheme, a delay-independent controller is explicitly designed which does not need the precise knowledge of time delays. The proposed method rigorously guarantees the practical stability of the closed-loop system and also ensures the convergence of the phase trajectories of the closed-loop system to the target limit cycle. Finally, to prove the theoretical achievement and also to illustrate the effective performance of the proposed approach, the simulation results are provided for several examples.

Adaptive Neural Control and Modeling for Continuous Stirred Tank Reactor with Delays and Full State Constraints

In this paper, an adaptive neural network control method is described to stabilize a continuous stirred tank reactor (CSTR) subject to unknown time-varying delays and full state constraints. The unknown time delay and state constraints problem of the concentration in the reactor seriously affect the input-output ratio and stability of the entire system. Therefore, the design difficulty of this control scheme is how to debar the effect of time delay in CSTR systems. To deal with time-varying delays, Lyapunov–Krasovskii functionals (LKFs) are utilized in the adaptive controller design. The convergence of the tracking error to a small compact set without violating the constraints can be identified by the time-varying logarithm barrier Lyapunov function (LBLF). Finally, the simulation results on CSTR are shown to reveal the validity of the developed control strategy.

Stabilizer design for an under-actuated autonomous underwater vehicle in a descriptor model under unknown time delay and uncertainty

This paper focuses on autonomous underwater vehicle (AUV) stabilization in the nonlinear descriptor model, as well as some AUV limitations such as model uncertainty, singularity, saturation constraint, and time delay. The capability of the descriptor model to show the real model is more reasonable than the standard state-space model. Based on the constructed Lyapunov function method and applying the bilinear matrix inequalities technique, all of the constraints are handled by introducing the new theorem. This theorem aims to design a state feedback with the intent that the closed-loop system be admissible. Here, the results are less conservative than other approaches. This issue has not yet been fully addressed in the literature, especially on AUVs. Theorem achievement is implemented on new AUV descriptor model that is obtained and introduced here. This method covers both neutral and descriptor systems. Also, it can be generalized and applied to conventional AUVs or similar dynamics. Examples and simulation results illustrate the effectiveness of the proposed approach.

FEA-based tracking control of flexible body switching dynamic structure

AbstractIn dynamically switched systems with unknown switching signal, the control system is conventionally designed based on the worst switching scenario to ensure system stability. Such conservative design demands excessive control effort in less critical switching configurations. In the case of continuum mechanics systems, such excessive control inputs result in increased structural deformations and resultant modeling uncertainties. These deformations alter differential equations of motion which cripple the task of control. In this paper, a new approach for tracking control of uncertain continuum mechanics multivariable systems undergoing switching dynamics and unknown time delay has been proposed. Control algorithm is constructed based on the mathematical rigid model of the plant and a Common Lyapunov Function (CLF) is proposed upon sliding hyperplane regarding all switching configurations. Considering the model-based nature of sliding mode control (SMC) and inevitable uncertainties induced from modeling simplifications of continuum system or parameter evaluation errors, Finite Element Analysis (FEA) is utilized to approximate total model uncertainties. To obtain robust stability, instead of conventional switching functions in the construction of control law, the control inputs are selected such that system dynamics reside within stability bounds which are calculated based on the Lyapunov asymptotic stability criterion. Therefore, the unwanted chattering issue caused by continuous switching is not observed in control input signals. Eventually, the accuracy of the proposed method has been verified through the student version of ANSYS® mechanical APDL-based simulations and its effectiveness has been demonstrated in multiple operating conditions.