Control For Singular Systems Research Articles

Disturbance rejection analysis of singular time-delay systems based on state decomposition method

The state decomposition technique (SDT) based on memory state-feedback control (MSFC) is used in this article to provide a new disturbance-rejection (DR) method for singular time-delay systems (STSs). First, under MSFC, a singular time-delay control system with disturbance estimator is constructed. Then, a DR control law, which contains disturbance information and MSFC, is designed. Second, the STS is split into algebraic and differential subsystems based on the SDT. Next, a brand-new enhanced Lyapunov–Krasovskii function (LKF) with fewer state vectors is designed. Additionally, a new delay-dependent admissible criterion with fewer decision variables is obtained based on the LKF by combining a Jensen inequality and two zero equations. Third, the controller is designed according to the decomposition component of the controller gain. Finally, the usefulness and efficiency of the strategy are demonstrated by comparing it to a sliding mode control and a traditional control technique.

Finite frequency H ∞ control for singular systems with application to a 2-machine 6-bus power network

This paper is concerned with the H ∞ control problem for singular systems over finite frequency ranges. The disturbance is assumed to be within low-/middle-/high-frequency ranges. Both the state feedback and static output feedback controllers are designed. First, by combining the Lyapunov function method and the generalized Kalman–Yakubovich–Popov lemma, a new finite frequency bounded real lemma (BRL) is proposed, which ensures the resulting closed-loop system to be regular, impulse free and stable with given finite frequency H ∞ performance bound. It is shown by theoretical analysis and numerical simulation that the proposed BRL has less conservatism than the existing ones in the literature. With the aid of the Finsler's Lemma, two improved finite frequency BRLs are further presented for the design of controllers. Then, by utilizing convexification techniques, sufficient conditions for solving the desired state feedback and static output feedback gains are presented in terms of linear matrix inequalities, respectively. Finally, the applicability and effectiveness of the proposed control methods are verified by a 6-bus power network system.

Reliable stabilization of discrete-time nonlinear singular systems with time-varying delays

The problem of delay-dependent reliable control for uncertain discrete-time nonlinear singular system with time-varying delays is investigated. A new set of delay-dependent sufficient conditions are established for the existence of a reliable controller which ensures the singular system to be regular, causal (absence of impulses) and stable for all admissible parameter uncertainties. First, the controller for singular system in the presence of known actuator fault matrix is designed. Further, the result is extended to study the robust stabilization of singular systems with unknown actuator fault matrix. The sensor failures of actuator are considered by a variable, which is varying in a given interval. The conditions for the existence of proposed controller design are established in the form of linear matrix inequality (LMI), which can be easily solved via standard numerical software. Finally, numerical examples with simulation results are provided to illustrate the usefulness of control design and results are compared with existing results to show the less conservatism of the proposed theory.

Distributed fusion robust filter for multisensor networked singular control system with uncertain variances and missing measurement

AbstractA distributed fusion time‐varying robust filtering algorithm for multisensor networked singular control system is studied in this paper, mainly aiming at the system with missing measurement and uncertain variances in practical application. First, the singular value decomposition (SVD) method and de‐randomization method are used to transform the singular control system into a standard system only with uncertain variances. Based on the new standard system, a minimax robust local Kalman filter is proposed by using the minimax robust estimation principle, which ensures that the actual filtering error variance has the corresponding minimum upper bound for all allowable uncertainties. Further, the robust local and distributed fusion filters for original singular control systems are proposed, and the actual and conservative filtering error variances are obtained. Their robustness is proved by Lyapunov equation method and nonnegative definite matrix decomposition method. A simulation example of two‐loop system verifies the effectiveness of the proposed results.

Stability analysis for singular random impulsive control system: A novel neutral impulsive delay system approach

The paper studies stability analysis for an uncertain singular time varying delay system (USTDS) under random impulsive control (RIC). It also proves the stability results for a singular impulsive time delay system in terms of neutral impulsive time delay system approach. Besides, we derive the new sufficient conditions for stability results like exponential stability (ES) and robust exponential stability (RES) of the proposed system via linear matrix inequality (LMI) by employing the Lyapunov–Krasovskii functional (LKF) approach. In addition, two numerical examples, along with graphical simulations, are provided to illustrate the validity and effectiveness of the proposed results.

Singular fuzzy fractional quadratic regulator problem

This study aims to create a fuzzy optimal control system for a singular fuzzy fractional quadratic regulator problem, which is governed by singular fuzzy fractional differential equations. Additionally, this paper introduces new terms such as fuzzy stability, asymptotic stability, stabilizability, and detectability in the context of singular fractional control systems. Theoretical concepts regarding the stabilizability and detectability of these systems are also outlined, as well as a theorem and related algorithm for determining the fuzzy optimal control and trajectory of the singular fuzzy fractional quadratic regulator problem. The proposed method is tested through simulation on an electrical circuit modeled as a singular fuzzy fractional system, with results demonstrating the efficacy of the approach.

Singular Value Decomposition-Based Saturated Control Scheme for a Multi-DOF Wave Energy Converter

This paper proposes a singular value decomposition-based velocity tracking control system for the multi-degree of freedom wave energy converter (WEC) to address the velocity tracking problem. Compared with our previous work presented at the conference, the detailed hydrodynamics of WEC is analyzed. In order to estimate the wave excitation force and optimal reference velocity, a linear extended state observer is employed in this control scheme. Considering that the output torque of power take-off (PTO) is limited, a novel saturated sliding mode controller is proposed to ensure that the output control torque of PTO will not exceed what the actuators can supply. With the attempt to enhance the performance of LESO, a new fuzzy logic rule is introduced into this control scheme to make the observer achieve self-tune. Based on the proposed control scheme, the power take-off system can generate appropriate control input to drive the WEC's buoy to operate at the specified speed to maximize the performance benefit of the WEC's power generation.

Distributed fusion robust estimators for multisensor networked singular control system with uncertain-variance correlated noises and missing measurement

Distributed fusion robust estimators for multisensor networked singular control system with uncertain-variance correlated noises and missing measurement

Formula omitted] control for singular systems with interval time-varying delays via dynamic feedback controller

The issue of dynamic feedback H∞ control in this paper is carefully revisited for singular systems with interval time-varying delays. A Lyapunov-Krasovskii functional, made up of state decomposition components and relatively few decision variables, is proposed. Further, a delay-dependent admissible criterion (conforming to non–impulsiveness, regularity, and stability) with a given H∞ performance index for the unforced nominal singular systems is founded by some linear matrix inequalities. Subsequently, a dynamic feedback controller for the closed–loop system is designed and the corresponding admissibility conditions are obtained. By means of a state decomposition recombination method, the desired dynamic feedback controller parameters are clearly determined by solving each decomposition component of the dynamic feedback controller. Interestingly, our results can enhance the previous results and the method proposed has greater flexibility. By numerical examples, some comparisons are shown to reveal the superiority and feasibility of our method.

Stabilization of networked singular control systems under double-channel quantization and DoS attacks

This paper is concerned with the asymptotic stabilization of discrete singular systems over a bandwidth limited digital network, when the state measurements are periodically sampled and encoded using a finite alphabet, and the control input signals are subject to finite-alphabet encoding and Denial-of-Service attacks. It is assumed that the attack signals are uniform for all sampling periods and have been identified. A dynamic controller is designed based on a restricted equivalent model of the controlled plant. Two types of finite-level quantizers are designed for encoding: uniform and logarithmic. For both types of quantizers, dynamic encoding-decoding strategies for the plant state and the control input are proposed, which exploit the controller’s state and the origin, respectively, as the quantization centers. Sufficient conditions for asymptotic stabilizability involving the sampling period, the numbers of the state and input quantization levels, the beginning time and corresponding duration of the attack signals are established by propagating reachable sets during sampling interval. Finally, several numerical examples are given to illustrate the design procedures and the efficacy of the theoretical results.

Parameterization technique for solving variational formulation of index three linear time-varying singular control systems

This paper deals with finding an approximate solution to an index three time-varying linear differential algebraic control equations based on the theory of variational formulation. The critical points of the formulated variational functional subject to the differential- algebraic equation with the class of consistent initial conditions are shown to be the solution of the proposed index-three DAEs with control problem (singular control systems) and vise- versa. The given variational problem is also transformed from indirect method into direct method using generalized Ritz bases technique. From the numerical illustrations results, the efficiency and very good accuracy as well as the simplicity of the present approach are obtained.

Observer-Based Event-Triggered H∞ Control for Singular Systems with Unknown Disturbances

Observer-Based Event-Triggered H∞ Control for Singular Systems with Unknown Disturbances

Inverse Optimal Control in State Derivative Space System with Applications in Motor Control

This paper mathematically explains how state derivative space (SDS) system form with state derivative related feedback can supplement standard state space system with state related feedback in control designs. Practically, inverse optimal control is attractive because it can construct a stable closed-loop system while optimal control may not have exact solution. Unlike the previous algorithms which mainly applied state feedback, in this paper inverse optimal control are carried out utilizing state derivative alone in SDS system. The effectiveness of proposed algorithms are verified by design examples of DC motor tracking control without tachometer and very challenging control problem of singular system with impulse mode. Feedback of direct measurement of state derivatives without integrations can simplify implementation and reduce cost. In addition, the proposed design methods in SDS system with state derivative feedback are analogous to those in state space system with state feedback. Furthermore, with state derivative feedback control in SDS system, wider range of problems such as singular system control can be handled effectively. These are main advantages of carrying out control designs in SDS system.

Periodic event‐triggered and self‐triggered control of singular system under stochastic cyber‐attacks

The periodic event-triggered control (PETC) and self-triggered control (STC) for networked singular systems under denial-of-service (DoS) attack and deception attack are studied. Due to the fact that DoS attack is able to prevent the control input from transmitting and deception attack falsifies the control input as a non-linear disturbance, a closed-loop system is constructed with different control inputs based on the switched system method. Next, the attention is focused on the design of PETC and STC schemes. PETC scheme adopts the input delay approach to transform the closed-loop system into a switched singular time-delay system and adjusts the triggering intervals by the frequency and duration of cyber-attacks. STC scheme relies on a reduced-order system derived from the original singular system and utilises the current sampled information to predict the next triggering instant. Then, exponential stability criteria are derived by codesigning the triggering parameter and controller gain. Finally, a small-signal version of the structure-preserving power network model is given to demonstrate the effectiveness of the proposed methods.

Iterative Learning Control for Singular Network Control System with Time-Delay and Data Dropout

Since the object becomes more and more complicated and the existed data dropout and network-introduced time-delay are random and varying in network control system (NCS), the traditional control method is more and more difficult to obtain a good control effect. In this paper, the iterative learning control (ILC) issue for a class of linear continuous singular network control system (SNCS) with time-delay and data dropout is investigated. According to the λ norm and expectation algorithm, the convergence condition of the system is derived. At last, simulation example shows the effectiveness and superiority of the presented method.

A new Solution of the Fractional-order Singular Linear Time-Invariant System

A new solution, the distributional solution of the fractional-order singular linear time-invariant control system (FOSLTIS) is studied in the paper. On the basis of proposing the definition of the Caputo fractional derivatives of Dirac function δ(t), the Laplace transform was obtained, then was derived. With regard to FOSLTIS, the system was decomposed into fast subsystem and slow subsystem by restricted equivalent transformation. Using Laplace transformation and taking into account, distributional solution for the fast subsystem was obtained. Two examples illustrated the correctness of the distributional solution of the FOSLTIS.

Event‐triggered H‐infinity stabilization for singular systems with state delay

AbstractThis paper is concerned with the problems of stability analysis, controller design, and H∞ control for singular systems with state delay and disturbance based on event‐triggered control. Firstly, the corresponding model of this system is proposed, taking into consideration issues of regular, impulse free, and stability. According to the model, the admissible condition is derived in terms of Lyapunov‐Krasovskii stability theory, and the co‐design method of the H∞ controller and event‐triggered scheme is also presented based on the above results. The presented method emphasizes the employment of event‐triggered control to a class of singular systems with time delay. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.

Dynamics and control of singular boolean networks

AbstractConsider a class of singular Boolean networks, which consist of two parts: difference part and algebraic part. Using the truth matrix of the algebraic part, the trajectories of the networks are obtained and certain properties are investigated. Then the results are extended to Boolean control networks and the controllability of singular Boolean control systems is investigated. Necessary and sufficient conditions are obtained.

Fault Tolerant Control for Nonlinear Singular Stochastic Distribution Systems Based on Fuzzy Modeling

When the desired output probability density function (PDF) is unknown, the active fault-tolerant control (FTC) method for the non-Gaussian nonlinear singular stochastic distribution control (SDC) system is investigated in this paper. Algebraic constraints and the nonlinearity in singular systems make the design of fault diagnosis and fault-tolerant control more complex. Different from traditional static modeling methods, the linear fuzzy logic system is served for approximating the output PDF. Takagi-Sugeno (T-S) fuzzy model is used to describe the nonlinear system. Subsequently, a fuzzy descriptor fault diagnosis (FD) observer is used to provide the unknown fault information for the fault-tolerant controller design. Combining minimum entropy control and fault compensation algorithm, the minimum Shannon entropy fault tolerant control strategy is developed to compensate the performance losses caused by the fault. At last, simulation results are applied to demonstrate the effectiveness of the proposed algorithms.

Minimum rational entropy fault tolerant control for non-Gaussian singular stochastic distribution control systems using T-S fuzzy modelling

ABSTRACTIn this paper, a new fault diagnosis (FD) and fault tolerant control (FTC) algorithm for a non-Gaussian nonlinear singular stochastic distribution control (SDC) system is studied. The rational square-root fuzzy logic model is used to approximate the output probability density function of non-Gaussian processes and a Takagi-Sugeno (T-S) fuzzy model is employed to transform the non-Gaussian nonlinear SDC system into a fuzzy SDC system. An adaptive fuzzy fault diagnosis observer is constructed to achieve reconstruction of system state and fault. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the rational entropy subjected to mean constraint. Minimum rational entropy fault tolerant control is introduced to make the output of the past-fault SDC system still have the minimum uncertainty. Simulation results are provided to demonstrate the validity of the FD and minimum rational entropy FTC algorithm.