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Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…
A magnetizable piezoelectric beam model, free at both ends, is considered. Piezoelectric materials have a strong interaction of electromagnetic and acoustic waves, whose wave propagation speeds differ substantially. The corresponding…
Deep neural network approximation of nonlinear operators, commonly referred to as DeepONet, has proven capable of approximating PDE backstepping designs in which a single Goursat-form PDE governs a single feedback gain function. In boundary…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into…
We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different…
We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and…
Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…
This paper investigates the decentralized stabilization problem for a class of interconnected systems in the presence of non-triangular structural uncertainties and time-varying parameters, where each subsystem exchanges information only…
In this paper, we consider the feedback stabilization problem for N-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the…
Backstepping is a mature and powerful Lyapunov-based design approach for a specific set of systems. Throughout the development over three decades, innovative theories and practices have extended backstepping to stabilization and tracking…
These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…
This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both state and output feedback Lagrange stabilization…
We consider closed-loop control of a two-dimensional supersonic boundary layer at M = 4.5 that aims at reducing the linear growth of second Mack mode instabilities. These instabilities are first characterized with local spatial and global…
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
This survey paper deals with the stabilization of nonlinear systems by analyzing the controlling method in terms of state feedback and output feedback. A brief overview of some literature on how the feedback controller of some dynamic…
This study investigates a strongly-coupled system of partial differential equations (PDE) governing heat transfer in a copper rod, longitudinal vibrations, and total charge accumulation at electrodes within a magnetizable piezoelectric…
This work concerns the internal stabilization of underactuated linear systems of $m$ heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the…