The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform

Xiaomiao Li - One of the best experts on this subject based on the ideXlab platform.

  • Membership-dependent stability analysis of discrete-time positive polynomial fuzzy-model-based control systems with time delay
    IET Control Theory & Applications, 2020
    Co-Authors: Kamyar Mehran, Xiaomiao Li
    Abstract:

    This study proposes a novel, relaxed, Lyapunov-based and membership-function dependent stabilisation analysis of discrete-time polynomial-fuzzy-model-based (PFMB) control systems with time delay under Positivity Constraint. The discrete-time non-linear system with time delay is represented by a polynomial fuzzy model, and corresponding PFMB controller is designed using imperfect premise matching technique which does not require its fuzzy rule and shape of membership functions be matched with those of the model. The authors take advantage of this property to relax the conservativeness of the obtained stability results by introducing the information of membership functions, i.e. the relationship Constraint information of membership functions between the model and the controller and boundary information of membership functions, into the stability and Positivity conditions. A numerical example is given to demonstrate the effectiveness of the proposed approach.

  • Stability analysis of discrete-time positive polynomial-fuzzy-model-based control systems through fuzzy co-positive Lyapunov function with bounded control
    IET Control Theory & Applications, 2020
    Co-Authors: Xiaomiao Li, Kamyar Mehran, Bo Xiao
    Abstract:

    This study employs a novel fuzzy co-positive Lyapunov function to investigate the stability of discrete-time polynomial-fuzzy-model-based control systems under Positivity Constraint. The fuzzy co-positive Lyapunov function consists of a number of local sub-Lyapunov function candidates which includes the Positivity property of a non-linear system and the contribution of each sub-Lyapunov function candidates depends on the corresponding membership functions. Imperfect premise matching design concept is used for the design of a closed-loop polynomial fuzzy controller based on the constructed polynomial fuzzy model. The bounded control signal conditions (upper and lower boundary demands on control signal) are included in the Lyapunov stability and Positivity conditions, in which all are formulated in the form of sum-of-squares conditions. A numerical example is given to validate the proposed approach.

  • Model-Based Control and Stability Analysis of Discrete-Time Polynomial Fuzzy Systems With Time Delay and Positivity Constraints
    IEEE Transactions on Fuzzy Systems, 2019
    Co-Authors: Xiaomiao Li, Kamyar Mehran
    Abstract:

    This paper proposes a novel Lyapunov stabilization analysis of discrete-time polynomial-fuzzy-model-based control systems with time delay under Positivity Constraint. The polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete-time system with time delay. A model-based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the Positivity Constraints. The Lyapunov stability and Positivity conditions are formulated as sum-of squares. To relax the conservativeness of the obtained stability results, two main methods are proposed in this paper: first, the piecewise linear membership functions (PLMFs) are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis; and second, introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information. A numerical example is given to demonstrate the effectiveness of the proposed approach.

Kamyar Mehran - One of the best experts on this subject based on the ideXlab platform.

  • Membership-dependent stability analysis of discrete-time positive polynomial fuzzy-model-based control systems with time delay
    IET Control Theory & Applications, 2020
    Co-Authors: Kamyar Mehran, Xiaomiao Li
    Abstract:

    This study proposes a novel, relaxed, Lyapunov-based and membership-function dependent stabilisation analysis of discrete-time polynomial-fuzzy-model-based (PFMB) control systems with time delay under Positivity Constraint. The discrete-time non-linear system with time delay is represented by a polynomial fuzzy model, and corresponding PFMB controller is designed using imperfect premise matching technique which does not require its fuzzy rule and shape of membership functions be matched with those of the model. The authors take advantage of this property to relax the conservativeness of the obtained stability results by introducing the information of membership functions, i.e. the relationship Constraint information of membership functions between the model and the controller and boundary information of membership functions, into the stability and Positivity conditions. A numerical example is given to demonstrate the effectiveness of the proposed approach.

  • Stability analysis of discrete-time positive polynomial-fuzzy-model-based control systems through fuzzy co-positive Lyapunov function with bounded control
    IET Control Theory & Applications, 2020
    Co-Authors: Xiaomiao Li, Kamyar Mehran, Bo Xiao
    Abstract:

    This study employs a novel fuzzy co-positive Lyapunov function to investigate the stability of discrete-time polynomial-fuzzy-model-based control systems under Positivity Constraint. The fuzzy co-positive Lyapunov function consists of a number of local sub-Lyapunov function candidates which includes the Positivity property of a non-linear system and the contribution of each sub-Lyapunov function candidates depends on the corresponding membership functions. Imperfect premise matching design concept is used for the design of a closed-loop polynomial fuzzy controller based on the constructed polynomial fuzzy model. The bounded control signal conditions (upper and lower boundary demands on control signal) are included in the Lyapunov stability and Positivity conditions, in which all are formulated in the form of sum-of-squares conditions. A numerical example is given to validate the proposed approach.

  • Model-Based Control and Stability Analysis of Discrete-Time Polynomial Fuzzy Systems With Time Delay and Positivity Constraints
    IEEE Transactions on Fuzzy Systems, 2019
    Co-Authors: Xiaomiao Li, Kamyar Mehran
    Abstract:

    This paper proposes a novel Lyapunov stabilization analysis of discrete-time polynomial-fuzzy-model-based control systems with time delay under Positivity Constraint. The polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete-time system with time delay. A model-based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the Positivity Constraints. The Lyapunov stability and Positivity conditions are formulated as sum-of squares. To relax the conservativeness of the obtained stability results, two main methods are proposed in this paper: first, the piecewise linear membership functions (PLMFs) are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis; and second, introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information. A numerical example is given to demonstrate the effectiveness of the proposed approach.

Ahmed Hajjaji - One of the best experts on this subject based on the ideXlab platform.

  • Conditions of Stabilization of Positive Continuous Takagi–Sugeno Fuzzy Systems with Delay
    International Journal of Fuzzy Systems, 2018
    Co-Authors: Abdellah Benzaouia, Ahmed Hajjaji
    Abstract:

    This paper deals with the problem of stability and stabilization of positive Takagi–Sugeno (T–S) fuzzy systems with fixed delays. The obtained conditions are given under the linear programming technique while imposing Positivity Constraint for the closed-loop system. New delay-independent stabilization conditions are derived by using a well-appropriated Lyapunov–Krasovskii functional. A real plant model is studied to show the applicability of the design procedure, while a numerical example is used to compare with LMI-based techniques.

  • Conditions of stabilization of positive continuous Takagi-Sugeno fuzzy systems with delay
    2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016
    Co-Authors: Abdellah Benzaouia, Ahmed Hajjaji
    Abstract:

    This paper deals with the problem of stability and stabilization of Takagi-Sugeno (T-S) fuzzy systems with fixed delay. Using linear programming (LP) technique and by imposing Positivity Constraint for the closed-loop system. new delay-independent stabilization conditions are derived. using a new single Lyapunov-Krasovskii Functional (LKF). A real plant model is studied to show the applicability of the design procedure, while a numerical example is used to compare with LMI based techniques.

  • Stabilization of LPV positive systems
    53rd IEEE Conference on Decision and Control, 2014
    Co-Authors: Ait M. Rami, Ahmed Hajjaji, B. Boulkroune, O. Pagès
    Abstract:

    This paper considers the stabilization issue for continuous-time linear parameter varying (LPV) positive systems. The time varying parameters are known and are modeled as belonging to the simplex set. The proposed stabilization approach relies on a parameter dependent Lyapunov function combined with a subtle choice of a slack variable that is not necessary diagonal. In fact, due to the Positivity Constraint on the closed-loop system the slack variable is chosen to be a Metzler matrix. Indeed, the particular case when the slack matrix is diagonal may work but the resulting stabilization conditions can be conservative. This fact is illustrated by a comparison example.

Yoshio Ebihara - One of the best experts on this subject based on the ideXlab platform.

  • $H_{2}$ State-Feedback Control for Continuous-Time Systems under Positivity Constraint
    2019 18th European Control Conference (ECC), 2019
    Co-Authors: Yoshio Ebihara, Patrizio Colaneri, José C. Geromel
    Abstract:

    This study is concerned with the H2 state-feedback controller synthesis problem under Positivity Constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous- and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable H2 performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains.

  • h_ 2 state feedback control for continuous time systems under Positivity Constraint
    European Control Conference, 2019
    Co-Authors: Yoshio Ebihara, Patrizio Colaneri, José C. Geromel
    Abstract:

    This study is concerned with the $H_{2}$ state-feedback controller synthesis problem under Positivity Constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous- and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable $H_{2}$ performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains.

  • H2 State-Feedback Synthesis under Positivity Constraint: Upper and Lower Bounds Computation of the Achievable Performance
    2018 European Control Conference (ECC), 2018
    Co-Authors: Yoshio Ebihara
    Abstract:

    This paper is concerned with the H2 state- feedback synthesis problem under Positivity Constraint on the closed-loop system. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive several semidefinite programs (SDPs) for the computation of the upper bounds of the achievable performance as well as suboptimal gains. However, if we rely only on the upper bound computation, we cannot say anything quantitatively on the quality of the computed suboptimal gains. For such quantitative evaluation, we next derive an SDP for the lower bound computation of the achievable performance. The key idea in deriving such an SDP is that, if the closed-loop system is positive, then the Lya- punov variable in the standard SDP for the H2 state-feedback synthesis should be (elementwise) nonnegative. By numerical examples, we illustrate the effectiveness and limitation of the proposed strategy with upper and lower bounds computation.

  • h 2 state feedback synthesis under Positivity Constraint upper and lower bounds computation of the achievable performance
    European Control Conference, 2018
    Co-Authors: Yoshio Ebihara
    Abstract:

    This paper is concerned with the $H_{2}$ state- feedback synthesis problem under Positivity Constraint on the closed-loop system. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive several semidefinite programs (SDPs) for the computation of the upper bounds of the achievable performance as well as suboptimal gains. However, if we rely only on the upper bound computation, we cannot say anything quantitatively on the quality of the computed suboptimal gains. For such quantitative evaluation, we next derive an SDP for the lower bound computation of the achievable performance. The key idea in deriving such an SDP is that, if the closed-loop system is positive, then the Lya- punov variable in the standard SDP for the $H_{2}$ state-feedback synthesis should be (elementwise) nonnegative. By numerical examples, we illustrate the effectiveness and limitation of the proposed strategy with upper and lower bounds computation. Keywords: $H_{2}$ state-Feedback synthesis, Positivity Constraint, upper and lower bound computation.

  • ECC - H 2 State-Feedback Synthesis under Positivity Constraint: Upper and Lower Bounds Computation of the Achievable Performance
    2018 European Control Conference (ECC), 2018
    Co-Authors: Yoshio Ebihara
    Abstract:

    This paper is concerned with the $H_{2}$ state- feedback synthesis problem under Positivity Constraint on the closed-loop system. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive several semidefinite programs (SDPs) for the computation of the upper bounds of the achievable performance as well as suboptimal gains. However, if we rely only on the upper bound computation, we cannot say anything quantitatively on the quality of the computed suboptimal gains. For such quantitative evaluation, we next derive an SDP for the lower bound computation of the achievable performance. The key idea in deriving such an SDP is that, if the closed-loop system is positive, then the Lya- punov variable in the standard SDP for the $H_{2}$ state-feedback synthesis should be (elementwise) nonnegative. By numerical examples, we illustrate the effectiveness and limitation of the proposed strategy with upper and lower bounds computation. Keywords: $H_{2}$ state-Feedback synthesis, Positivity Constraint, upper and lower bound computation.

A. Oghbaee - One of the best experts on this subject based on the ideXlab platform.

  • Positive stabilization with maximum stability radius for linear time-delay systems
    53rd IEEE Conference on Decision and Control, 2014
    Co-Authors: B. Shafai, A. Oghbaee, T. Tanaka
    Abstract:

    This paper considers the problem of positive stabilization of uncertain linear time-delay systems by state feedback such that the resulting closed-loop system attains maximum stability radius with Positivity Constraint. First, we focus on the class of linear continuous-time positive delay systems (Metzlerian delay systems) and outline its interesting properties. Using the stability properties associated with this class, we formulate a constrained stabilization problem for the linear time delay system and provide conditions for the existence of controllers satisfying the stability and Metzlerian Constraints. The Metzlerian stabilization is solved using Linear Matrix Inequality (LMI) or Linear Programming (LP). Next, we characterize the uncertainties associated with the positive delay systems and define the stability radius associated with this class which can be expressed in a closed form. Finally, we combine Metzlerian stabilization with maximum stability radius with the aid of bounded real lemma (BRL) and provide a complete solution using LMI. Examples are included for the purpose of illustration.

  • Constrained stabilization with maximum stability radius for linear continuous-time systems
    52nd IEEE Conference on Decision and Control, 2013
    Co-Authors: B. Shafai, R. Ghadami, A. Oghbaee
    Abstract:

    This Paper considers the problem of constrained stabilization of linear continuous-time systems by state feedback control law. The goal is to solve this problem under Positivity Constraint which means that the resulting closed-loop systems are not only stable, but also positive. We focus on the class of linear continuous-time positive systems (Metzlerian systems) and use the interesting properties of Metzler matrix to provide the necessary ingredients for the main results of the paper. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the Metzlerian Constraint, and the constrained stabilization is solved using linear programming (LP) or linear matrix inequality (LMI). A major objective is to formulate the constrained stabilization problem with the aim of maximizing the stability radius. We show how to solve this problem with an additional LMI formulation.