Uncertain Singular Systems Research Articles

Optimistic value-based optimal control problems with uncertain discrete-time noncausal systems

Uncertain discrete-time noncausal systems are uncertain singular systems that are supposed to be regular along. This study examines optimal control problems (OCPs) using the optimistic value criterion in the context of uncertain discrete-time noncausal systems. Recurrence equations for tackling these OCPs are provided in terms of uncertainty theory. These equations have effectively addressed OCPs involving uncertain noncausal systems with linear, quadratic, and cubic controls, resulting in analytical expressions for their optimal solutions. For illustration, an example is offered to highlight the usefulness of our results.

Robust $$H_\infty $$ asynchronous fault detection for uncertain singular hybrid systems based on Hmm strategy

Robust $$H_\infty $$ asynchronous fault detection for uncertain singular hybrid systems based on Hmm strategy

Adaptive sliding mode control for semi‐Markov jump uncertain discrete‐time singular systems

AbstractThis note is devoted to the analysis of adaptive sliding mode control of H/passivity of semi‐Markov jump discrete‐time uncertain singular systems. We consider the constraints of parameter uncertainties, unknown nonlinear functions, and external disturbances throughout the model. Firstly, a novel mode‐independent sliding mode surface is constructed, then the sliding mode dynamic equation under the equivalent controller is obtained. Secondly, by introducing virtual points, several sufficiency criteria are derived for the sliding mode dynamic ensuring H/passive performance and stochastic admissibility with linear matrix inequalities form. Thirdly, the state trajectory can be driven into a switching band containing the origin by adaptive sliding mode control techniques. Finally, the effectiveness of our findings is demonstrated by comparing existing strategies with three simulation examples.

Robust and minimum norm stabilization for uncertain singular second-order vibration systems

Robust and minimum norm stabilization for uncertain singular second-order vibration systems

Robust Stability Analysis and Feedback Control for Uncertain Systems With Time-Delay and External Disturbance

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

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.

Singular H∞ Finite-time Boundedness for a Class of Uncertain Singular Systems

This paper is concerned with the problem of observer-based finite-time H∞ control for a class of uncertain singular systems with norm-bounded uncertainties. We design a suitable observer and a controller to guarantee that the closed-loop is singular H∞ finite-time bounded. By constructing an appropriate Lyapunov function, and using matrix inequality technique, a sufficient condition for the singular H∞ finite-time boundedness of the closed-loop system is established. The observer and controller gains are designed based on matrix inequality. Two numerical examples are given to demonstrate the effectiveness of the proposed methods.

Robust Stability Analysis and Feedback Control for Uncertain Systems with Time-Delay and External Disturbance

This paper addresses the delay-dependent Takagi-Sugeno (T-S) fuzzy state feedback control and exponential admissibility analysis for a class of T-S fuzzy singular uncertain systems. Firstly, the T-S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input and unmatched disturbance. Secondly, the delay-dependent T-S fuzzy state feedback controller is designed by employing the T-S fuzzy model. Thirdly, the free-weighting matrices and delay-dependent Lyapunov-Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T-S fuzzy state feedback controller is designed for the T-S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

An Observer-Based Composite Nonlinear Feedback Controller for Robust Tracking of Uncertain Nonlinear Singular Systems With Input Saturation

This study proposes an observer-based Composite Nonlinear Feedback (CNF) controller for the robust tracking of uncertain singular systems with input saturation, nonlinear function, time-delay, and disturbances. The suggested control law is designed based states reconstructed using a singular observer so as to increase steady-state accuracy and improve robustness. The CNF controller is developed based on Generalized Riccati Equations (GRE) and Lyapunov–Krasovskii functional. Additionally, the proposed theorem verifies the stability conditions of the system in the presence of uncertainties and disturbances. Among the advantages of this method, are its fewer restrictive assumptions, transient and high-speed performance improvement and steady-state precision. The uniform boundedness of the tracking error in the presence of the input saturation and external disturbances is also a prominent feature of this method. The performance of the proposed approach is assessed using a simulation study.

Optimal control and zero-sum differential game for Hurwicz model considering singular systems with multifactor and uncertainty

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. Based on the concept of uncertain theory, this paper considers optimal control and zero-sum differential game for multi-factor uncertain continuous-time singular systems with Hurwicz criterion, where dynamic systems are modelled by a type of uncertain differential equation driven by canonical Liu process. Using the approach of dynamic programming, the principle of optimality is proposed and then the equation of optimality is derived to resolve an uncertain control model. A two-player zero-sum uncertain differential game is further investigated based on the optimality equation above, and an equilibrium equation is presented to locate a saddle-point in the game. Finally, an example is discussed to illuminate the effectiveness of the results.

A variable memory state feedback and its application to robust control of uncertain singular time-delay systems

A variable memory state feedback and its application to robust control of uncertain singular time-delay systems

Sliding mode observer-based adaptive control of uncertain singular systems with unknown time-varying delay and nonlinear input

A novel adaptive sliding mode observer-based control strategy is put forward for a type of uncertain singular systems subject to unknown state delay, input nonlinearity and uncertain perturbation in this article. Firstly, the unmeasured state is reconstructed by a particular observer without any inputs, from which a novel linear switching surface is provided. Subsequently, performance analysis of the resultant system on the switching surface is ensured under a new admissibility criterion. An associated adaptive control signal is synthesized to ensure that the established switching surface can be attained in finite moment. Finally, three numerical simulations are conducted to confirm the validity and superiority of the specified method.

Adaptive controller design for uncertain singular systems with actuator failure

In this paper, the problem of model reference adaptive controller design with actuator failure is solved for a series of uncertain singular systems. The research on partial actuator failure is relatively mature and it is necessary to solve the problem of how to guarantee the system performance when the actuator fails completely. For this reason, we treat the system with actuator failure as a switching system with two subsystems and then solve the stability analysis problem of the error switching system. The emphasis is to design the adaptive controller by some sufficient linear matrices inequalities (LMIs) conditions and obtain the global stability criterion of the error switching system through the resident time method. Finally, the proposed method is applied to HiMAT aircraft to illustrate the feasibility and effectiveness of this kind of problem.

Robust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance

Robust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance

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.

Robust Finite-Time H∞ Control for the Uncertain Singular System

This paper addresses the robust finite-time $H_\infty $ control problem for the uncertain singular system by using the stability theory of dynamical systems. Firstly, a lemma is provided to show that the singular system is finite-time stability by using the state space decomposition approach. Similar with the proof method of this Lemma, the singular system is divided into a differential system and an algebra one. Then, some conditions are derived to ensure the singular system being finite-time $H_\infty $ stability based on the obtained lemma, and the state feedback control law is designed. These conditions are provided in the form of the linear matrix inequalities and can be easily solved. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

Robust Control for Singular Systems Based on the Uncertainty and Disturbance Estimator

This paper is devoted to investigating the robust control problem for a class of singular systems with model structure uncertainty and external disturbance. Firstly, the uncertainty and disturbance estimator (UDE)-based robust control law is established for uncertain singular systems. Secondly, the two-degree-of-freedom (2DOF) nature of singular systems under the UDE-based robust controller is revealed, which shows that asymptotic reference tracking and disturbance rejection are decoupled. Additionally, on the basis of the small-gain theorem, sufficient conditions are established to ensure robust stability of the closed-loop system and to achieve asymptotic reference tracking and disturbance rejection. Finally, three numerical examples and a practical application to the multi-agent supporting systems are provided to illustrate the validity of the methods proposed.

Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties

This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.

Optimal control for uncertain discrete-time singular systems under expected value criterion

Optimal control problems governed by two different types of uncertain discrete-time singular systems are investigated under expected value criterion. The objective function including uncertain variables is optimized with the help of expected value method provided that the singular systems are both regular and impulse-free. At first, based on the principle of dynamic programming, a recurrence equation is derived to simplify an optimal control model for a class of uncertain discrete-time singular systems. After that, according to uncertainty theory and the recurrence equation, two kinds of optimal control problems subject to an uncertain linear singular system and an uncertain singular system with quadratic input variables are considered in order, and the optimal solutions are both presented by accurate expressions. A numerical example and a dynamic input-output model are settled to illustrate the effectiveness of the results obtained.

Admissible consensus of uncertain fractional-order singular multiagent systems with actuator fault

Consensus of fractional-order singular multiagent systems is considered in this article. The model of uncertain systems with actuator fault is established, and its admissible consensus in the field of fractional-order systems is studied. First, the uncertain singular multiagent systems with actuator fault are proposed. Then, a state feedback controller and a state consensus protocol with an observer based on output information are designed. Then, new consensus criteria of uncertain fractional-order singular multiagent systems are proposed. Finally, for the sake of demonstrating the validity of proposed results, some relevant numerical examples are provided.