Estimation Of Attraction Domain Research Articles

Composite quadratic Lyapunov function event-triggered control of vertical take-off and landing aircraft systems with actuator saturation

This paper deals with the problem of event-triggered control (ETC) for vertical take-off and landing (VTOL) aircraft systems under actuator saturation. By introducing the VTOL system with saturated actuators, a composite quadratic Lyapunov function (CQLF) approach is first proposed to describe the problem of the event triggering mechanism. The proposed transfer mechanism not only further saves communication resources, but also further suppresses the conservatism of the attraction domain estimation. Then, sufficient conditions are established via linear matrix inequality (LMI) by incorporating new event triggering mechanism condition and prescribed passive performance metrics under the closed-loop system that is asymptotically stable and strictly passive, respectively. Finally, the method proposed in this paper can effectively reduce the number of triggers and expand the domain of attraction. The validity and feasibility of the obtained results are demonstrated by two example simulations.

Robust fault-tolerant control of a class of uncertain nonlinear switched systems with actuator saturation

This paper addresses the robust fault-tolerant control problem for a class of uncertain nonlinear switched systems with actuator saturation. Our aim is to design a switching law and a robust fault-tolerant control law for guaranteeing that the closed-loop system is asymptotically stabilizable, while at the same time the attraction domain estimation is as large as possible. By using the multiple Lyapunov functions method, sufficient conditions for robust fault-tolerant stabilisation are proposed for the closed-loop system. Then, when some scalar parameters are given in advance, the problem of fault-tolerant controller design and attraction domain estimation is transformed into a convex optimisation problem with linear matrix inequality (LMI) constraints. Finally the validity of the proposed design method is verified by a numerical example.

Stabilization of discrete-time positive switched T-S fuzzy systems subject to actuator saturation

<abstract><p>The stabilization of discrete-time positive switched Takagi-Sugeno (T-S) fuzzy systems with actuator saturation is investigated in this paper. It is assumed that the switched subsystems are partially stabilizable. Based on the convex hull technique (CHT) and parallel distribution compensation (PDC) algorithm, a saturated fuzzy controller and slow-fast combined mode-dependent average dwell time (MDADT) switching signal are co-designed and sufficient conditions for the positivity and stability of closed-loop positive switched T-S fuzzy systems (PSTSFSs) are developed, which can be reduced to the ones under the case where all switched subsystems are stabilizable. Moreover, the largest attraction domain estimation (ADE) is given for PSTSFSs by formulating an optimization problem. Finally, the designed control scheme is applied to two illustrative examples to verify its availability and superiority.</p></abstract>

Estimation of attraction domain of nonlinear systems with saturated impulses and input disturbances

AbstractIn this article, the estimation of attraction domain of nonlinear systems with saturated impulses and input disturbances is investigated. The sufficient conditions which can ensure the robust convergence of a class of nonlinear dynamical systems for every initial condition in the attraction domain are established. Moreover, some optimization problems are proposed to design the control gain so as to enlarge the size of the estimation of attraction domain as much as possible with a prespecified decay rate. In addition, the exponential stabilization and the estimation of attraction domain for nonlinear dynamical systems under this saturated impulsive control without disturbances are also studied. Finally, simulation results for a chaotic oscillator are displayed to show the effectiveness and feasibility of our results.

A Lyapunov approach for attraction domain estimation of polynomial discrete nonlinear systems with quadratic and cubic terms

In this paper, we propose a Lyapunov method for estimating asymptotic stability domain of polynomial discrete nonlinear systems, drawn from an existing approach for attraction domain estimation of continuous nonlinear systems. Proceeding from two different forms of a parametric equation, we present two development methods with the aim of identifying a sufficient condition to obtain a part of the stability domain for quadratic and cubic n-dimensional polynomial discrete systems. The results consist in solving a polynomial equation and unconstrained nonlinear optimization problems, where in case of quadratic or cubic systems, significant simplifications are obtained. The main notable advantages of this approach are its applicability on high-dimensional systems and obtaining an ellipsoidal stability domain which approaches the exact attraction domain limits. Two application examples are illustrated to validate each development.

On the synthesis of a polynomial controller for enlarging the stability domain for nonlinear discrete system

This paper aims to propose an algebraic method for estimating the stability region for nonlinear discrete systems. The main contribution is the improvement of an existing technique to enlarge the initial stability region in which the asymptotic stability is guaranteed. To deal with the maximization issue, a state feedback controller is proposed to extend the largest estimation of attraction domain of nonlinear polynomial discrete systems. The proposed approach is illustrated and validated on an isothermal stirred tank reactor.

Local stability and stabilization of uncertain nonlinear systems with two additive time-varying delays

This paper investigates the local stability and stabilization problem of nonlinear time-delay systems subject to parameter uncertainties, which are represented by interval type-2(IT2) T-S fuzzy systems with two additive time-varying delays. Because T-S fuzzy models often represent primitive nonlinear systems well only in the region of validity, local stability and stabilization problems are considered. By constructing a novel Lyapunov–Krasovskii functional and using the matrix inequality scaling approach, a new delay-dependent local stability and stabilization criterion is derived in terms of linear matrix inequalities(LMIs). Using Lyapunov level set, the estimation of attraction domain is also developed. Finally, two numerical examples are employed to verify the effectiveness of proposed methods.

The processing of saturation function in saturation control system

This article mainly for linear systems with actuator saturation as the research object, in order to further expand the saturated attraction domain of linear system and the estimate for the main purpose, starting from the process of saturation function, enumerates the convex hull representation and the conditions of local sectors two methods, and then get bigger attraction domain estimation. Finally, an example is given to compare the two methods.

Discretization of a Lyapunov Approach for Attraction Domain Estimation Through a BMI Optimization Problem

This paper proposes a Lyapunov method for estimating the asymptotic stability domain of polynomial discrete nonlinear systems. Based on an existing approach of attraction domain estimation for continuous nonlinear systems, we present an analogous technique focusing on discrete systems. The idea is to reformulate the problem as a bilinear matrix inequalities (BMI) optimization problem where the Lyapunov function is considered as a decision variable. The exploitation of polar coordinates and positive definite matrices properties defines the objective function and the constraint functions. One of the main advantages of this method is that the results are independent of the Lyapunov function. Furthermore, the obtained stability domain approaches the exact domain boundaries. An application example is illustrated to validate found results.

Disturbance Attraction Domain Estimation for Saturated Markov Jump Systems with Truncated Gaussian Process

This paper investigates the disturbance attraction domain estimation of saturated Markov jump systems with truncated Gaussian process. The aim is to estimate the disturbance domain of attraction so that the state is maintained in a neighbour around the origin by a state feedback controller regardless of bounded disturbance. The problem is formulated as parameter-dependent linear matrix inequalities (LMIs). The optimal disturbance attraction domain is obtained through searching for most appropriate auxiliary parameters in the defined domain. A numerical example is presented to show the potential application of the results.

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

SUMMARY This paper considers the problem of observer-based H ∞ controller design for a class of discrete-time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time-varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode-dependent and parameter-dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer-based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H ∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.

On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

This paper investigates the estimation of domain of attraction for nonlinear port-controlled Hamiltonian (PCH) systems with actuator saturation (AS). Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities (LMIs) optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.

A new approach for estimating the attraction domain for Hopfield-type neural networks.

In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.

A New Approach for Estimating the Attraction Domain for Hopfield-Type Neural Networks

In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.

Estimation of Attraction Domain for Linear Systems with Static Feedback Nonlinearities

In this paper will be shown some results for the estimation of the attraction domain for nonlinear control systems consisting of a LTI system and of memoryless nonlinearities in the feedback. For the estimation are used quadratic Lyapunov functions derived from the dissipativity theory. Stability conditions and the search for attraction domain are formulated in terms of LMIs. The usefulness of the approach is illustrated for a fuzzy control system.

Estimation of attraction domain and exponential convergence rate of continuous feedback associative memory

The attraction domain of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated again by using of some analysis techniques and Liapunov method, some new re sults are obtained, that can be used for evaluation of fault-tolerance capability and the syn thesis procedures for continuous feedback associative memory neural networks.

Estimation of attraction domain and exponential convergence rate of continuous feedback associative memory

We revisit the study of the attraction domain of memory patterns and exponential convergence rate of the network trajectory memory patterns for the continuous feedback associative memory by using some analysis techniques and the Lyapunov method. Some new estimation results are obtained and can be used for the evaluation of fault-tolerance capability and synthesis procedures of continuous feedback associative memory networks.

Estimation of attraction domain and exponential convergence rate of continuous feedback associative memory and its applications

The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluation of error-correction capability and the synthesis procedures for continuous-time associative memory neural networks.