Feedback control of time-delay systems with bounded control and state.
Feedback controller stabilizing vibrations of a flexible cable related to an overhead crane.
Feedback linearization of control for nonlinear systems with uncertainties
Feedback stabilization of a boundary layer equation
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 a boundary layer equation
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
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 control problem associated with the linearized equation.
Feedback stabilization of Navier–Stokes equations
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 parabolic systems with bilinear controls.
Feedback stabilization of semilinear heat equations.
Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system
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
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 settling time stabilisation of a family of discrete-time systems
Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions
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
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
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
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
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
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
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
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...