Uncertain Discrete Systems Research Articles

A randomized algorithm based approach to fault detection for uncertain systems subject to deception attack

This paper presents a fault detection strategy for discrete uncertain systems subject to deception attack based on the probabilistic framework. Probabilistic parameter models are utilized for characterizing model uncertainties, multiplicative faults and additive faults. An observer-based fault detection filter is constructed to generate fault information under deception attack. A randomized algorithm based approach is developed to determine the observer gain and threshold for attaining a trade-off between the false alarm rate (FAR) and fault detection rate (FDR). Simulation of an unmanned surface vehicle (USV) system and comparison against existing work are performed to illustrate the effectiveness of the proposed scheme.

Robust Feedforward Control of Discrete Uncertain Systems Over a Finite Frequency Range

Robust Feedforward Control of Discrete Uncertain Systems Over a Finite Frequency Range

Guaranteed Cost Control for 2-D Uncertain Discrete State-Delayed Systems in Roesser Model Employing Actuator Saturation

Guaranteed Cost Control for 2-D Uncertain Discrete State-Delayed Systems in Roesser Model Employing Actuator Saturation

Robust dynamic output feedback predictive control for discrete uncertain systems with time-varying delays

A robust dynamic output feedback predictive control approach is developed for a discrete system with time-varying delays, unknown external disturbances, and unmeasurable states. First, the discrete system is transformed into an incremental state deviation model. Based on this model, a novel tracking deviation feedback model is established by extending the output tracking error. Then, a robust predictive control law, possessing more degrees of freedom, is designed. The closed-loop model is further given in conjunction with the feedback model. Second, by using the linear matrix inequality (LMI) method, relaxation technique, and variable transformation method, a less conservative stability condition is given in LMI form, which allows the controller to tolerate a greater range of time-varying delays. The gains of the control law are acquired by solving the stability condition, and the control performance can be significantly enhanced. Finally, by utilizing the TTS20 water tank as a simulation case, the viability and effectiveness of the proposed method are demonstrated.

Finite-time stability in measure for nabla uncertain discrete linear fractional order systems

Finite-time stability in measure for nabla uncertain discrete linear fractional order systems

Formula omitted] fusion estimation for uncertain discrete time-delayed Hamiltonian systems with sensor saturations: An event-triggered approach

This paper is concerned with the event-triggered H∞ fusion estimation problem for uncertain discrete-time Hamiltonian systems with time-varying delays and sensor saturations. In order to improve the efficiency of resource utilization, a component-based event-triggered mechanism is implemented on the communication path from sensors to the estimator, where each output is sent only when a prescribed event-triggering condition is satisfied. By considering the structural characteristics of discrete-time Hamiltonian systems and utilizing the Lyapunov–Krasovskii stability, sufficient conditions are established to guarantee the augmented system (i.e., the underlying system combined with the estimation error dynamics) is locally exponentially stable. Meanwhile, the estimator gain is acquired by resorting the approach of certain matrix inequality. Finally, two examples are provided to demonstrate the effectiveness of the proposed scheme.

Robust feedback feed-forward PD-type iterative learning control for uncertain discrete systems over finite frequency ranges

This paper proposes a robust feedback feed-forward proportional-derivative type (PD-type) iterative learning control (ILC) scheme for a class of linear discrete systems with polytopic uncertainty over finite frequency ranges. First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman–Yakubovich–Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. Compared with previously established works, the new algorithm is more effective in delivering higher performance and achieving better tracking effect.

Robust State Estimation for Uncertain Discrete Linear Systems with Delayed Measurements

Measurement delays and model parametric uncertainties are meaningful issues in actual systems. Addressing the simultaneous existence of random model parametric uncertainties and constant measurement delay in the discrete-time linear systems, this study proposes a novel robust estimation method based on the combination of Kalman filter regularized least-squares (RLS) framework and state augmentation. The state augmentation method is elaborately designed, and the cost function is improved by considering the influence of modelling errors. A recursive program similar to the Kalman filter is derived. Meanwhile, the asymptotic stability conditions of the proposed estimator and the boundedness conditions of its error covariance are analyzed theoretically. Numerical simulation results show that the proposed method has a better processing capability for measurement delay and better robustness to model parametric uncertainties than the Kalman filter based on nominal parameters.

Stable learning laws design for long short-term memory identifier for uncertain discrete systems via control Lyapunov functions

This study introduces a method for designing stable learning laws of Long Short-Term Memory (LSTM) networks working as a non-parametric identifier of nonlinear systems with uncertain models. The strategy applies the concept of stability for discrete-time systems in the sense of Lyapunov to prove that origin is a practical stable equilibrium point for the identification error. The laws consider a general class of sigmoidal functions placed at the different gates of a LSTM structure (long and short memory). The design of the learning laws uses a matrix inequality framework to obtain the rate gains associated with the evolution of the weights. Numerical results show the designed learning laws for the non-parametric identifier based on a LSTM approximation tested on two classes of nonlinear systems: the first one describes the ozone-based degradation of organic contaminants, and the second one represents the dynamics of a Van Der Poll oscillator. The LSTM identifier is compared against a classical Lyapunov-based recurrent neural network. This comparison demonstrates how the proposed algorithm approximates the trajectories of both systems with a smaller mean squared error, which serves as an indicator of the benefits obtained with these new learning laws.

Robust ellipsoidal set-membership fault estimation for time-varying systems with uniform quantization effects over sensor networks.

This article is concerned with the robust set-membership fault estimation problem for a class of uncertain discrete time-varying systems over sensor networks. The system measurements are subject to the uniform quantization which results in the unknown-but-bounded noises. Attention is focused on the design of a set-membership fault estimator such that, in the simultaneous presence of uncertain parameters, unknown-but-bounded noises and uniform quantization effects, the estimation errors are confifined to a certain ellipsoidal region. By using the mathematical induction, a suffificient condition is derived for the existence of the desired fault estimator at each time step in terms of a set of recursive matrix inequalities. Moreover, an optimization problem is formulated by minimizing the ellipsoid of the estimation error. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault estimator design scheme.

Robust Sliding Mode Control for Stochastic Uncertain Discrete Systems with Two-Channel Packet Dropouts and Time-Varying Delays.

In this paper, the control problem is investigated for discrete time-varying delayed systems with stochastic uncertainty, external disturbance, and two-channel packet dropouts. Sliding mode functions with packet loss probabilities are proposed for the packet loss problem in the sensor–controller channel and the controller–actuator channel. Furthermore, by employing the Lyapunov–Krasovskii functional, some new stability conditions are established in terms of solvable linear matrix inequalities (LMIs), and H∞ performance is analyzed for the sliding mode motion of the system. Meanwhile, a sliding mode controller is designed to drive the system state to the pre-designed sliding surface. Moreover, the designed controller can be robust for two-channel packet dropouts, time-varying delays, stochastic uncertainty and external disturbance. Finally, two numerical examples are given to demonstrate the feasibility of the proposed theoretical method.

H_infinity Stabilization of Uncertain Discrete Time-Delayed System with Actuator Saturation by using Wirtinger Inequality

H_infinity Stabilization of Uncertain Discrete Time-Delayed System with Actuator Saturation by using Wirtinger Inequality

Event-triggered secure control of discrete systems under cyber-attacks using an observer-based sliding mode strategy

This paper is concentrated on the event-triggered adaptive sliding mode control (SMC) issue for a class of discrete uncertain nonlinear systems subject to false data injection attack (FDIA). The considered control input undergoes the loss of effectiveness (LE) and FDIA in a unified framework. Furthermore, in order to cater the engineering reality, the event-triggered mechanism is introduced in the sensor to observer (S-O) channel and observer to controller (O-C) channel with hope to reduce the communication load. By introducing a novel scheme, sufficient conditions are provided to ensure the asymptotic stability of resultant sliding mode dynamics with prescribed H∞ performance. Subsequently, to reduce the communication burden, an optimal strategy is proposed which can guarantee the stability simultaneously through choosing suitable weighting matrices. Moreover, a projection-based adaptive SMC law is designed to compensate the effects caused by the LE and FDIA, which can force the system state to be attracted into the pre-defined sliding manifold. Finally, some comparison simulations are presented to illustrate the validity of the provided control method.

Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H2/H∞) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results.

Guaranteed cost controller for discrete time-delayed systems with actuator saturation

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

Design and Implementation of Novel LMI-Based Iterative Learning Robust Nonlinear Controller

An iterative learning robust fault-tolerant control algorithm is proposed for a class of uncertain discrete systems with repeated action with nonlinear and actuator faults. First, by defining an actuator fault coefficient matrix, we convert the iterative learning control system into an equivalent unknown nonlinear repetitive process model. Then, based on the mixed Lyapunov function approach, we describe the stability of the nonlinear repetitive mechanism on time and trial indices and have appropriate conditions for the repeated control system’s stability in terms of linear matrix inequality theory. Through LMI techniques, we have obtained satisfactory results and controller stability, and robustness against fault tolerance is also discussed in detail. Finally, the simulation results of the output tracking control of the two exemplary models verify the effectiveness of the proposed algorithm.

LMI based nonlinear Iterative Learning Control for uncertain discrete repetitive system

LMI based nonlinear Iterative Learning Control for uncertain discrete repetitive system

Admissibility Analysis and Controller Design for Discrete Singular Time-Delay Systems Embracing Uncertainties in the Difference and Systems’ Matrices

This paper mainly investigates the admissibility analysis and the admissibilizing controller design for the uncertain discrete singular system with delayed state. Based on Lyapunov–Krasovskii stability theory, an original admissibility condition for the nominal singular delay system is first presented. By involving the uncertainties in both difference and system matrices simultaneously, we devote to analyzing the robust admissibility for the regarded uncertain discrete singular system with delayed state. Furthermore, by hiring the state feedback control law, we further discuss the admissibilizing controller design for the resulting closed-loop system. Since all the derived criteria are expressed in terms of strict linear matrix inequalities (LMIs) or parametric LMIs, we thus can handily verify them via current LMI solvers. Finally, two numerical examples are given to illustrate the effectiveness and validity of the proposed approach.

Observer-based [formula omitted] sliding mode control for networked systems subject to communication channel fading and randomly varying nonlinearities

In this paper, the H∞ sliding mode control (SMC) problem is discussed for a class of uncertain discrete networked systems with channel fading and randomly varying nonlinearities (RVNs) by employing the observer-based approach. Here, the Jth-order Rice fading model is adopted to describe the phenomenon of channel fading, where the channel coefficients are mutually independent random variables that take the values on certain interval. In addition, a sequence of mutually independent Bernoulli distributed random variables is utilized to characterize the phenomenon of the RVNs, where the occurrence probabilities of RVNs consist of the nominal mean and the bound of error. The main objective of the addressed problem is to design the observer-based sliding mode controller such that the closed-loop system is asymptotically stable in mean-square sense and the pre-specified H∞ performance requirement is guaranteed. By employing novel Lyapunov–Krasovskii functional, sufficient criteria are derived to force the system state trajectories onto a pre-specified sliding mode region. Afterwards, the solvability of non-convex problem is discussed by testifying the feasibility of a minimization problem. Finally, an illustrative example is given to demonstrate the effectiveness of aforementioned SMC technique.

Sliding mode prediction fault-tolerant control method for multi-delay uncertain discrete system with sensor fault

In this paper, we design a novel sliding mode prediction fault-tolerant control algorithm for multi-delays discrete uncertain systems with sensor fault. The global sliding surface is designed to replace the traditional linear sliding surface as a predictive model to ensure the global robustness of the system. For sensor fault and sliding mode buffeting, a power-dependent function reference trajectory with fault compensation is designed to attenuate chattering and achieve better stability. In the process of rolling optimization, an improved whale optimization algorithm is developed. On the premise of obtaining good convergence speed and accuracy, the optimization process can avoid falling into the local minimum value and solve the problem of premature convergence. Finally, the comparison experiments on the quad-rotor simulation platform prove the rationality and superiority of the algorithm.