Control For Singular Systems Research Articles

Advanced Control for Singular Systems with Applications

Advanced Control for Singular Systems with Applications

Continuous sliding‐mode control for singular systems

SummarySingular systems with matched Lipschitz perturbations and uncertainties are considered in this paper. Since continuous solutions of an impulse‐free singular system require continuous input signals, a two‐step continuous sliding‐mode control strategy to compensate matched Lipschitz perturbations and uncertainties in singular systems is proposed. Our suggested methodology is tested in a singular representation of a DC motor pendulum of relative degree two. The performance of the proposed strategy is assessed by comparing the accuracy, in both cases, with and without considering small noise in the output, obtained through other continuous sliding‐mode control, and reconstruction/compensation of perturbations and uncertainties techniques.

COMPENSATORS FOR SINGULAR CONTROL SYSTEMS WITH DELAYS IN OUTPUTS

In this paper we study the design of dynamic compensators for linear singular control systems described by the equation Ex' ( t) = Ax(t) + Bu(t) with time delayed observed output y(t) = Cx(t- r).The proposed compensators are applied to solve the regulator problema for the mentioned systems with controlled output z(t) = Dx(t). We also establish a result of existence of exponentially bounded solutions of the retarded singular differential equation Ex' ( t) = Ax(t) + Rx(t-r) + f(t), t > 0, with initial condition x(θ) = ᵩ(θ), - r ≤ θ ≤ 0.

H∞ Control of Network Control System for Singular Plant

This paper investigates H∞ control method for a class of singular network control systems (SNCS) based on singular plant. Considering the network delay, external disturbance, impulse behavior and structural instability of singular plant, the H∞ control of SNCS with state feedback and dynamic output feedback are investigated respectively by approach of linear matrix inequality (LMI). The existence H∞ control law, the solving H∞ control law and disturbance degree are presented respectively. Simulation results illustrate the effectiveness and feasibility of the given approach. KEYWORDS: singular networked controls; H∞ control; linear matrix inequality; network delay DOI: http://dx.doi.org/10.5755/j01.itc.47.1.19982

Solution of Singular Fuzzy Fraction order Control Systems via Drazin inverse

In this paper , we investigate solution for singular fuzzy fractional order control system , which in turn gives us two subsystem by drazin inverse . One of these subsystems contain fuzzy fractional order control system used fuzzy laplace transform as well as lower function and upper function in order to get the solution .

Exponential H ∞ control for singular systems with time-varying delay

This paper studies the exponential admissibility and H ∞ control problems for a class of singular systems with time-varying delay in state. Firstly, an exponential admissibility criterion is obtained based on linear matrix inequalities (LMIs). It is worth mentioning that the derivative of the time-varying delay does not need to be smaller than one. Based on the proposed condition, a new delay-dependent H ∞ controller is also given, which guarantees the admissibility and the H ∞ performance γ. Numerical examples are given to illustrate the effectiveness of the proposed method.

Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach

AbstractSingular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Pole assignment for a singular distributed parameter system coupled with a singular lumped parameter system}{Pole assignment for a singular distributed parameter system coupled with a singular lumped parameter system

The pole assignment for a first order singular distributed parameter control system coupled with a first order singular lumped parameter control system is discussed via functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expressions of the solutions are given by the bounded inner inverse of the bounded linear operator. This research is theoretically important for studying the pole assignment and stabilizability of singular distributed parameter control systems.

Comments on “network-based H∞ control for singular systems with event-triggered sampling scheme [Information Sciences 329 (2016) 540–551

This note addresses that the stability conditions given in Theorem 1 of [1] are incorrect, so the proposed design method for networked singular systems is impracticable.

Numerical Solution of the Optimal Control for Fractional Order Singular Systems

This paper presents a method to solve numerically the linear quadratic optimal control problems (LQOCPs) of the fractional singular control systems with Caputo fractional derivatives. Under certain conditions on the singular fractional control systems, the problems under consideration are transformed into LQOCPs of the standard normal fractional control systems. Based on the Grunwald–Letnikov approximation (GLA) of the fractional derivatives (FDs), a numerical technique is used to solve the LQOCPs of the standard normal fractional control systems. An illustrative example is introduced to demonstrate the applicability of the proposed technique.

Minimum entropy fault‐tolerant control for non‐Gaussian singular stochastic distribution systems

This study presents a new fault diagnosis (FD) and fault-tolerant control (FTC) algorithm for a discrete-time non-Gaussian singular stochastic distribution control (SDC) system. An adaptive observer is used to diagnose the fault of the singular stochastic distribution system. Furthermore, the gain of the observer and adaptive updated law can be formulated by solving the corresponding linear matrix inequality. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the entropy subjected to mean constraint. The reconfigured controller can make the output of the post-fault SDC system still have the minimum uncertainty, leading to the minimum entropy FTC of the non-Gaussian singular SDC system. Computer simulations are given to demonstrate the validity of the FD and minimum entropy FTC algorithms.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called "singular estimate control systems" (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

Advanced Control of Complex Dynamical Systems with Applications

There are many practical systems which can be modelled by dynamical equations. Increasing requirements on system performance mean that within control system analysis and design it is necessary to deal with the increasingly complex dynamical systems that are used to model reality. The complexity stems from nonlinearity, uncertainty, time delay, system singularity, stochastic effects, the presence of interconnections, and so forth. Advances in both technology and control theory have provided the potential to investigate complex dynamical systems. Study on complex systems is becoming increasingly important and this has provided renewed impetus for the development of novel techniques and skills for complex control systems. This provides the motivation for this special issue. The purpose of this special issue is to provide an opportunity for scientists and control engineers to publish their latest, novel, and original contributions to the development of complex control systems. The special issue focusses on recent achievements and applications in the field of control and analysis for complex systems with a special emphasis on how to solve various control design and/or observer design problems for nonlinear systems and interconnected systems. The considered systems typically involve at least two features such as nonlinearity, disturbances/uncertainty, faults, time delay, interconnections between subsystems, system singularity, stochastic processes, and comparison between simulation and experiments. The special issue focuses on results in theoretical research and practical applications with emphasis on novel methodologies for analysis, design, synthesis, and/or applications. The topics within the special issue include interconnected/networked systems, variable structure control, singular system control, time delay systems, fuzzy control and impulsive control, robust observer design and parameter identification, fault detection and fault tolerant control, analysis and control of stochastic systems, and applications of advanced control systems. A total of 109 papers were submitted to the special issue for possible publication and 38 of them were accepted and published following a fair and rigorous review process organised by the guest editorial team with the help of the editorial office. The acceptance rate is less than 35%. The accepted papers have been grouped in the following six clusters.

Fault Diagnosis and Fault Tolerant Control for Non-Gaussian Singular Time-Delayed Stochastic Distribution Systems with Disturbance Based on the Rational Square-Root Model

For the non-Gaussian singular time-delayed stochastic distribution control (SDC) system with unknown external disturbance where the output probability density function (PDF) is approximated by the rational square-root B-spline basis function, a robust fault diagnosis and fault tolerant control algorithm is presented. A full-order observer is constructed to estimate the exogenous disturbance and an adaptive observer is used to estimate the fault size. A fault tolerant tracking controller is designed using the feedback of distribution tracking error, fault, and disturbance estimation to let the postfault output PDF still track desired distribution. Finally, a simulation example is included to illustrate the effectiveness of the proposed algorithms and encouraging results have been obtained.

Fault diagnosis and fault tolerant tracking control for the non-Gaussian singular time-delayed stochastic distribution system with PDF approximation error

In this paper, fault diagnosis and fault tolerant tracking control algorithms are proposed for the non-Gaussian singular time-delayed stochastic distribution control system. The square root B-spline model is used to approximate the output probability density function (PDF), and the PDF approximation error is taken into consideration. A fault diagnosis approach based on the adaptive observer is constructed to diagnose the size of fault in the singular stochastic distribution control (SDC) system. When fault occurs, in order to track the expected PDF, a distribution tracking error dynamic system is established. The purpose of fault tolerant tracking control is transformed into making the distribution tracking error at each time instant satisfy a certain upper bound beyond a limited time. Then the fault tolerant controller is designed using the fault diagnosis information and other measurable information. A simulation example is included to illustrate the effectiveness of the proposed algorithms and encouraging results have been obtained.

Network-based H∞ control for singular systems with event-triggered sampling scheme

In this paper, the problem of event-triggered H∞ control is investigated for networked singular systems. To make full use of the characteristics of networked control system, a discrete event-triggered communication scheme, which only needs to supervise the system state in discrete instants, is proposed. The sampling-interval is employed to unify the networked singular system and the event-triggered condition into a new time-delay system. Based on this model, sufficient criteria are derived to guarantee the networked singular system regular, impulse-free and stable with an H∞ norm bound. The corresponding state feedback controller is designed. A practical example is given to show that the proposed event-triggered scheme is more effective and useful than some existing works.

H ∞ control of singular systems via delta operator method

This paper studies the problem of state feedback H ∞ control for singular systems through delta operator approach. A necessary and sufficient condition is presented such that a singular delta operator system is admissible with a prescribed H ∞ performance, which can provide a unified framework of the existing H ∞ performance analysis results for both continuous case and discrete case. The existence condition and explicit expression of a desirable H ∞ controller are also obtained for singular delta operator systems. The proposed design method can be used for both singular continuous systems and singular discrete systems directly. The corresponding design procedures, which simplify the classical approaches, are discussed and presented. All obtained conditions in this paper are in the form of strict linear matrix inequalities whose feasible solutions can be found by standard linear programming method. Numerical examples are provided to illustrate the effectiveness of the theoretical results obtained in this paper.

Fault diagnosis and minimum entropy fault tolerant control for non-Gaussian singular stochastic distribution systems using square-root approximation

The fault diagnosis (FD) and minimum entropy fault tolerant control (FTC) algorithms are proposed for non-Gaussian singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weight vector and the control input is expressed by a singular state space model, which increases the difficulty in the design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An iterative learning observer (ILO) is designed for fault estimation. The concept of entropy is introduced to fault tolerant control of the non-Gaussian stochastic distribution system when the target probability density function (PDF) is not known in advance. Based on the estimated fault information, the controller is reconfigured by minimising the performance function with regard to the entropy subjected to mean constraint. The reconfigured controller can make the output of the post-fault SDC system still have minimum uncertainty, leading to minimum entropy FTC of the non-Gaussian singular SDC system. Computer simulations are given to demonstrate the validity of the fault diagnosis and minimum entropy FTC algorithms.