Related papers: Learning an optimal feedback operator semiglobally…
It is shown that an explicit oblique projection nonlinear feedback controller is able to stabilize semilinear parabolic equations, with time-dependent dynamics and with a polynomial nonlinearity. The actuators are typically modeled by a…
The aim of this work is to design an explicit finite dimensional boundary feedback controller of sampled-data form for locally exponentially stabilizing the equilibrium solutions to semilinear parabolic equations. The feedback controller is…
A learning approach for optimal feedback gains for nonlinear continuous time control systems is proposed and analysed. The goal is to establish a rigorous framework for computing approximating optimal feedback gains using neural networks.…
The feedback exponential stabilization to trajectories for semilinear parabolic equations in a given bounded domain is addressed. The controls take values in a finite-dimensional space and are supported in a small region. Both internal and…
In this article a stabilizing feedback control is computed for a semilinear parabolic partial differential equation utilizing a nonlinear model predictive (NMPC) method. In each level of the NMPC algorithm the finite time horizon open loop…
These notes are issued from a short course given by the author in a summer school in Chamb{\'e}ry in June 2015. We consider general semilinear PDE's and we address the following two questions: 1) How to design an efficient feedback control…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
Predictor feedback designs are critical for delay-compensating controllers in nonlinear systems. However, these designs are limited in practical applications as predictors cannot be directly implemented, but require numerical approximation…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
This note studies the robust output feedback stabilization problem of multi-input multi-output invertible nonlinear systems with output-dependent multipliers. An "ideal" state feedback is first designed under certain mild assumptions. Then,…
The estimation of the full state of a nonautonomous semilinear parabolic equation is achieved by a Luenberger type dynamical observer. The estimation is derived from an output given by a finite number of average measurements of the state on…
The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…
It is shown that an oblique projection based feedback control is able to stabilize the state of the Kuramoto-Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The number of actuators is finite and…
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
In this paper, we present output feedback boundary stabilization for a class of semilinear parabolic PDEs with a boundary measurement and an actuation located at the same place. The method uses backstepping transformations, where the state…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
In the first part of this article, we study feedback stabilization of a parabolic coupled system by using localized interior controls. The system is feedback stabilizable with exponential decay $-\omega<0$ for any $\omega>0$. A stabilizing…