Nonlinear Singular Systems Research Articles

Quantized iterative learning control for singular nonlinear fractional-order time-delay multi-agent systems with iteration-varying reference trajectories and switching topologies

This paper addresses the consensus tracking of the leader-following singular nonlinear fractional-order system with state time-delay in face of iteration-varying communication topologies and reference trajectories via an iterative learning control scheme. Firstly, by means of the neighbor information, the closed-loop Dα-type quantized iterative learning protocol is constructed based on output tracking errors. Secondly, sufficient conditions of consensus errors between each follower agent and leader agent are given in a fixed time interval and convergence analysis is also presented under the fixed topology and reference trajectory. Thirdly, the extension to iteration-varying reference trajectory tracking and switching topologies cases are investigated. It is shown that the developed protocol can also effectively work along the iteration axis on a finite time interval, although the communication topologies and reference trajectories vary dynamically with respect to iteration. Finally, numerical examples are shown to verify the effectiveness of the obtained results.

Nonlinear switched singular systems in discrete time: The one-step map and stability under arbitrary switching signals

The solvability of nonlinear nonswitched and switched singular systems in discrete time is studied. We provide necessary and sufficient conditions for solvability. The one-step map that generates equivalent nonlinear (ordinary) systems for solvable nonlinear singular systems under arbitrary switching signals is introduced. Moreover, the stability is studied by utilizing this one-step map. A sufficient condition for stability is provided in terms of (switched) Lyapunov functions.

Further results on the finite-time static output feedback control for nonlinear singular systems

This paper studies the finite-time static output feedback control for a class of nonlinear singular systems. Finite-time stability criterion for the closed singular systems is proposed by static output feedback technique. Based on the properties of structure of the singular system, static output feedback control gain is obtained by using singular value decomposition technique. Meanwhile, different from the existing results of normal systems, the presented scheme reduces the conservatism and complexity during the calculation process. Furthermore, static output feedback H∞ controller is designed and finite time stability criterion is proposed for the nonlinear singular systems with external disturbance. Finally, the applicability and effectiveness of the proposed strategy are illustrated by a circuit system simulation.

Observer-Based Fuzzy Control of Uncertain Nonlinear Singular Systems under Multi-Performance Requirements

This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model that can be analyzed using linear control theories. The proposed control scheme is based on the Parallel Distributed Compensation (PDC) approach and Proportional Derivative (PD) control scheme. The goal is to design an observer-based fuzzy controller that achieves stability of the system and also satisfies the Guarantee Cost Control (GCC) constraint while maintaining a desired passive constraint. The stability analysis is performed using Lyapunov theory, and the sufficient conditions are transformed into a Linear Matrix Inequality (LMI) form using a Shur Complement, free-weighting matrix method and Singular Value Decomposition (SVD) techniques. The LMI conditions are then solved using convex optimization algorithms. Finally, the proposed control method is validated using a bio-economic system to demonstrate its effectiveness.

Mathematical Model for Fault Handling of Singular Nonlinear Time-Varying Delay Systems Based on T-S Fuzzy Model

In this paper, a mathematical model based on the T-S fuzzy model is proposed to solve the fault estimation (FE) and fault-tolerant control (FTC) problem for singular nonlinear time-varying delay (TVD) systems with sensor fault. TVD is is extremely difficult to solve and the Laplace transform is devised to build an equal system free of TVD. Additionally, the sensor fault is changed to actuator fault by the developed coordinate transformation. A fuzzy learning fault estimator is first built to estimate the detailed sensor fault information. Then, a PI FTC scheme is suggested aiming at minimizing the damage caused by the fault. Simulation results from multiple faults reveal that the FE and FTC algorithms are able to estimate the fault and guarantee the system performance properly.

Finite-time dissipative control design for one-sided Lipschitz nonlinear singular Caputo fractional order systems

ABSTRACT This paper presents an efficient analytical approach for solving the problem of dissipative control in one-sided Lipschitz singular Caputo fractional-order systems subject to nonlinear perturbations. The approach is based on mathematical transformations, and fractional calculus. A state feedback controller is designed to ensure that the closed-loop system is regular, impulse-free, and finite-time bounded with a dissipativity performance index. The results are established using tractable strict linear matrix inequalities (LMIs) without any equality constraint. Two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Existence of Positive Solutions for a Population Model Involving Nonlocal Operator

By using the method of sub- and supersolutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operators.

An algorithm based on homotopy perturbation theory and its mathematical analysis for singular nonlinear system of boundary value problems

In this paper, a promising technique based on the homotopy perturbation method for solving singular nonlinear system of boundary value problems (BVPs) is employed. The original singular system of BVPs is transformed into an equivalent system of integral equations to overcome the singular behavior at , and then, the recursive series for the solution is established. The mathematical formulation is further supported by conducting the convergence analysis of the recursive schemes. The accuracy of the proposed method is tested by comparing against the current variational iteration method using many standard examples. It is shown that the proposed method is more accurate and efficient than the existing method such as Chebyshev operational matrix method and variational iteration method.

Reduced-Complexity LMI Conditions for Admissibility Analysis and Control Design of Singular Nonlinear Systems

We present a reduced-complexity control approach for a class of descriptor nonlinear systems with a nonlinear derivative matrix, possibly singular. To this end, a systematic approach is proposed to obtain an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equivalent</i> polytopic representation of a given nonlinear system within a compact set of the state-space. This modeling approach has two particular features compared to the related Takagi–Sugeno (T–S) fuzzy model-based framework. First, the model complexity only grows <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proportionally</i> , rather than exponentially, with the number of premise variables. Second, the vertices of the proposed polytopic models can admit an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infinite</i> number of representations for the same predefined set of premise variables. This <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nonuniqueness</i> feature allows introducing some specific slack variables at the modeling step to reduce the control design conservatism. Based on the proposed polytopic representation and Lyapunov stability theory, we derive reduced-complexity admissibility analysis and design conditions, expressed in terms of linear matrix inequalities, for the considered class of descriptor systems. In particular, a new nonlinear control law is proposed for regular descriptor systems to avoid using the extended redundancy form, which may yield numerically complex and conservative results due to the imposed special control structure. Both numerical and physically motivated examples are given to demonstrate the interests of the new control approach with respect to existing T–S fuzzy model-based control results.

Non-fragile sliding mode observer based fault estimation for interval type-2 fuzzy singular fractional order systems

In this paper, an interval type-2 fuzzy model is presented to describe the nonlinear singular fractional order systems (SFOSs) with . The problem of actuator and sensor fault estimation is addressed by designing a non-fragile sliding mode observer (SMO). Firstly, a new criterion is provided to analyse the admissibility of SFOSs, which does not need to divide the fractional order interval into interval and interval to study them separately. Then, by expanding the dimension of the SFOS, the non-fragile SMO and the sliding surface are constructed and the accurate estimations of faults and the SFOS state simultaneously are achieved. A new reaching law is designed, which can divide the process of the system moving to the sliding surface into three stages. Further the control law is constructed to guarantee the observation error reaches the sliding surface in finite time. Finally, three examples show the effectiveness of the proposed scheme.

Observer-Based Robust Fuzzy Controller Design for Uncertain Singular Fuzzy Systems Subject to Passivity Criterion

This paper discusses an observer-based control problem for uncertain Takagi–Sugeno Fuzzy Singular Systems (T-SFSS) subject to passivity performance constraints. Through the Parallel Distributed Compensation (PDC) approach and the Proportional Derivative (PD) control scheme, an observer-based fuzzy controller is constructed to achieve the stability of the considered system. An unlimited positive definite matrix is utilized to construct the Lyapunov function and derive sufficient stability conditions to develop a relaxed design method. Moreover, some technologies, such as the Schur complement, projection lemma, and Singular Value Decomposition (SVD), are applied to convert the conditions to Linear Matrix Inequality (LMI) form. Therefore, the convex optimization algorithm is used to solve the LMI conditions to find feasible solutions. The observer-based fuzzy controller is established with the obtained solutions to guarantee stability and passivity performance for the uncertain nonlinear singular systems. Finally, two examples are provided to verify the availability of the proposed fuzzy control approach.

A Nonlinear Singular Differential System with Perturbed Integral Boundary Conditions

A Nonlinear Singular Differential System with Perturbed Integral Boundary Conditions

Admissible Control for Non-Linear Singular Systems Subject to Time-Varying Delay and Actuator Saturation: An Interval Type-2 Fuzzy Approach

Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when uncertainty also simultaneously affects the system under consideration. To address this issue, this paper investigated a feasible control strategy for nonlinear singular systems with time-varying delay that are subject to uncertainty and actuator saturation. The IT-2 fuzzy model was adopted to describe the dynamic of the non-linear delayed systems using lower and upper membership functions to deal with the uncertainty. Moreover, the polyhedron model was applied to characterize the saturation function. The goal of the control approach was to design a relevant IT2 fuzzy state feedback controller with mismatched membership functions so that the closed-loop system is admissible. On the basis of an appropriate Lyapunov–Krasovskii functional, sufficient delay-dependent conditions were established and an optimization problem was formulated in terms of linear matrix inequality constraints to optimize the attraction domain. Simulation examples are provided to verify the effectiveness of the proposed method.

Sliding-Mode-Based Admissible Consensus Tracking of Nonlinear Singular Multiagent Systems Under Jointly Connected Topologies.

The admissible consensus tracking problem of nonlinear singular multiagent systems (SMASs) with time-varying delay, uncertainties, and external disturbances under jointly connected topologies is investigated in this article. First, the sliding-mode control (SMC) is applied to effectively reduce the adverse effects of uncertainties and nonlinearities of systems. Then, by the combination of admissible analysis, the Cauchy convergence criterion, and SMC, the sufficient conditions for the admissible consensus tracking and disturbance rejection of SMASs under jointly connected topologies are provided. Furthermore, a distributed SMC law is designed such that the sliding-mode dynamics trajectories reach the sliding surface in finite time. Finally, the simulation results are utilized to indicate the effectiveness of the presented methods.

Finite-Time Peak-To-Peak Filtering for Nonlinear Singular System

In this brief, the finite-time peak-to-peak filter design problem is investigated for discrete-time nonlinear singular system. The T-S fuzzy model is introduced to represent the considered nonlinear system. First, a useful analysis method is proposed to detect whether the resulting filtering error system is singular finite-time bounded and guarantees the peak-to-peak performance. Further, in order to cope with the difficulty caused by the special form of filtering error system, we propose a novel filter form which facilitates the elimination of the coupling items in the filter design. And based on this, the sufficient design scheme for finite-time peak-to-peak filter is formulated by means of standard linear matrix inequality technique. Finally, a tunnel diode circuit is used to illustrate the feasibility and effectiveness of the developed algorithm.

Sampled-Data Control for a Class of Singular Takagi-Sugeno Fuzzy Systems with Application in Truck-Trailer System

In order to solve the admissibility problem for a class of nonlinear singular systems with sampling, nonlinearity, and external disturbances, a sample-data control algorithm based on input delay methodology is proposed in this paper. Firstly, the system is converted to a time-delay system based on Takagi–Sugeno fuzzy models via an input delay approach, with many novel time-delay methods being used to deal with the sampled-data control problem. Secondly, both the upper and lower bounds of the sampling period are considered, which has a wider application scope. Thirdly, to obtain less conservative results, an appropriate Lyapunov–Krasovskii function, which involves several symmetric positive definite matrices, is established, and a relaxation variable is introduced by the method of reciprocally convex inequality. Then the conditions of admissibility are given, and the design method of the sampled-data controller is introduced. Finally, a truck-trailer example and two numerical examples are given to prove that the proposed approaches are valid and applicable.

Non-fragile consensus control for nonlinear singular multi-agent systems: An event-triggered sampling scheme

This paper is devoted to the problem of non-fragile consensus control for a class of nonlinear singular multi-agent systems based on an event-triggered control strategy. To reduce the resource occupancy, a decentralized event-triggered sampling consensus control protocol for each agent is proposed, which does not require continuous communication among agents. Analysis of non-fragile consensus problem in the multi-agent systems is transformed into asymptotical stability issues of some lower dimensional subsystems via nonsingular transformation. Using the Lyapunov theory, sufficient conditions are obtained such that for all possible norm-bounded parameter variations in the protocol gains, the designed protocol can bring all agents’ states to a point of agreement. Furthermore, the corresponding protocol design method is also given. Numerical examples are included to illustrate the effectiveness of the derived results.

Robust Finite-time H∞ Control for Discrete-time Nonlinear Uncertain Singular Systems with Time-delay

This paper deals with the problems of finite-time H∞ control for a class of discrete-time nonlinear singular systems subject to uncertainties and external disturbance. Firstly, the finite-time stability problem is discussed for discrete-time nonlinear uncertain singular systems with time-delay. The sufficient conditions of finite-time stability of discrete-time nonlinear singular systems are established. Then, by using the Lyapunov functional method, a criterion is established to ensure that the closed-loop system with external disturbance is finite-time bounded. We design the controller gain matrix. Finally, we provide a numerical example to illustrate the effectiveness of the proposed results.

Finite‐time stability of singular multi‐agent systems with input time‐varying delay and non‐linear dynamics via non‐fragile controller

This paper deals with the finite-time stability problem of non-linear singular multi-agent systems subject to controller gain disturbance via a distributed non-fragile controller. The existing literature on this problem only applies to normal multi-agent systems, or ignores the possible change of control gain in the practical application of the controller, or requires that there is no time-varying delay in the control input. How to tackle the finite-time stability problem of singular multi-agent systems by considering input time-varying delay, Lipschitz non-linear dynamics and controller gain perturbation simultaneously is an open issue. In order to solve this problem, a distributed non-fragile controller is proposed for each agent to make the finite-time stability problem solved for any connected undirected connection topology. With the help of a Linear matrix inequality and a Lyapunov integral appropriate expression, the difficulty caused by the irreversibility of singular system matrices is solved. Then, a sufficient condition to ensure the finite-time stability of the closed-loop system is obtained for the singular multi-agent system including controller disturbance, input–output delay and non-linear dynamics. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method.

A New Adaptive Robust Sliding Mode Control Approach for Nonlinear Singular Fractional-Order Systems

This article focuses on designing an adaptive sliding mode controller via state and output feedback for nonlinear singular fractional-order systems (SFOSs) with mismatched uncertainties. Firstly, on the basis of extending the dimension of the SFOS, a new integral sliding mode surface is constructed. Through this special sliding surface, the sliding mode of the descriptor system does not contain a singular matrix E. Then, the sufficient conditions that ensure the stability of sliding mode motion are given by using linear matrix inequality. Finally, the control law based on an adaptive mechanism that is used to update the nonlinear terms is designed to ensure the SFOS satisfies the reaching condition. The applicability of the proposed method is illustrated by a practical example of a fractional-order circuit system and two numerical examples.