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Feedback stabilization of a boundary layer equation

Jean-Marie Buchot, Jean-Pierre Raymond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminar-to-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate linear parabolic equation. Because of the degenerate character of the state equation, the classical existence...

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2003)

ESAIM: Control, Optimisation and Calculus of Variations

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a L Q control problem associated with the linearized equation.

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation.

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended...

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended...

Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions

Antonios Armaou, Panagiotis Christofides (2001)

International Journal of Applied Mathematics and Computer Science

This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initial conditions and input perturbations) ensemble of solutions of the resulting time-varying PDE system is...

Finite-time boundedness and stabilization of switched linear systems

Haibo Du, Xiangze Lin, Shihua Li (2010)

Kybernetika

In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem,...

Finite-time consensus problem for multiple non-holonomic mobile agents

Jiankui Wang, Zhihui Qiu, Guoshan Zhang (2012)

Kybernetika

In this paper, the problem of finite time consensus is discussed for multiple non-holonomic mobile agents. The objective is to design a distributed finite time control law such that the controlled multiple non-holonomic mobile agents can reach consensus within any given finite settling time. We propose a novel switching control strategy with the help of time-rescalling technique and graph theory. The numerical simulations are presented to show the effectiveness of the method.

Finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems

Haibo Du, Yigang He, Yingying Cheng (2013)

Kybernetika

The problem of finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems is studied in this paper. The agent dynamic is described by a second-order nonlinear system with uncertain time-varying control coefficients and unknown nonlinear perturbations. Based on the finite-time control technique and graph theory, a class of distributed finite-time control laws are proposed which are only based on the neighbors' information. Under the proposed controller, it...

Finite-time output feedback stabilization and control for a quadrotor mini-aircraft

Chuanlin Zhang, Shihua Li, Shihong Ding (2012)

Kybernetika

This paper focuses on the finite-time output feedback control problem for a quad-rotor mini-aircraft system. First, a finite-time state feedback controller is designed by utilizing the finite-time control theory. Then, considering the case that the velocity states are not measurable, a finite-time stable observer is developed to estimate the unmeasurable states. Thus a finite-time output feedback controller is obtained and the stability analysis is provided to ensure the finite-time stability of...

Finite-time tracking control of multiple nonholonomic mobile robots with external disturbances

Meiying Ou, Shengwei Gu, Xianbing Wang, Kexiu Dong (2015)

Kybernetika

This paper investigates finite-time tracking control problem of multiple nonholonomic mobile robots in dynamic model with external disturbances, where a kind of finite-time disturbance observer (FTDO) is introduced to estimate the external disturbances for each mobile robot. First of all, the resulting tracking error dynamic is transformed into two subsystems, i. e., a third-order subsystem and a second-order subsystem for each mobile robot. Then, the two subsystem are discussed respectively, continuous...

Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

Chaoqun Guo, Jiangping Hu, Jiasheng Hao, Sergej Čelikovský, Xiaoming Hu (2023)

Kybernetika

In this paper, a fixed-time safe control problem is investigated for an uncertain high-order nonlinear pure-feedback system with state constraints. A new nonlinear transformation function is firstly proposed to handle both the constrained and unconstrained cases in a unified way. Further, a radial basis function neural network is constructed to approximate the unknown dynamics in the system and a fixed-time dynamic surface control (FDSC) technique is developed to facilitate the fixed-time control...

Fixed-time tracking control for nonholonomic mobile robot

Ou Meiying, Sun Haibin, Zhang Zhenxing, Li Lingchun, Wang Xiang-ao (2021)

Kybernetika

This paper investigates the fixed-time trajectory tracking control problem for a nonholonomic mobile robot. Firstly, the tracking error system is derived for the mobile robot by the aid of a global invertible transformation. Then, based on the unified error dynamics and by using the fixed-time control method, continuous fixed-time tracking controllers are developed for the mobile robot such that the robot can track the desired trajectory in a fixed time. Moreover, the settling time is independent...

Flocking analysis for a generalized Motsch-Tadmor model with piecewise interaction functions and processing delays

Yipeng Chen, Yicheng Liu, Xiao Wang (2023)

Applications of Mathematics

In this paper, a generalized Motsch-Tadmor model with piecewise interaction functions and fixed processing delays is investigated. According to functional differential equation theory and correlation properties of the stochastic matrix, we obtained sufficient conditions for the system achieving flocking, including an upper bound of the time delay parameter. When the parameter is less than the upper bound, the system achieves asymptotic flocking under appropriate assumptions.

Functional observers design for nonlinear discrete-time systems with interval time-varying delays

Yali Dong, Laijun Chen, Shengwei Mei (2019)

Kybernetika

This paper is concerned with the functional observer design for a class of Multi-Input Multi-Output discrete-time systems with mixed time-varying delays. Firstly, using the Lyapunov-Krasovskii functional approach, we design the parameters of the delay-dependent observer. We establish the sufficient conditions to guarantee the exponential stability of functional observer error system. In addition, for design purposes, delay-dependent sufficient conditions are proposed in terms of matrix inequalities...

Further results on robust fuzzy dynamic systems with LMI 𝓓-stability constraints

Wudhichai Assawinchaichote (2014)

International Journal of Applied Mathematics and Computer Science

This paper examines the problem of designing a robust ∞ fuzzy controller with -stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust ∞ fuzzy controller that guarantees (i) the ₂-gain of the mapping from the exogenous input noise to the...

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