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Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…
This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…
The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…
We establish that stabilization of a class of linear, hyperbolic partial differential equations (PDEs) with a large (nevertheless finite) number of components, can be achieved via employment of a backstepping-based control law, which is…
In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2…
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…
Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on…
This paper presents a safe output regulation control strategy for a class of systems modeled by a coupled $2\times 2$ hyperbolic PDE-ODE structure, subject to fully distributed disturbances throughout the system. A state-feedback controller…
A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this…
A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling…
This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an actuator at one…
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…
This paper proposes a backstepping boundary control design for robust stabilization of linear first-order coupled hyperbolic partial differential equations (PDEs) with Markov-jumping parameters. The PDE system consists of 4 X 4 coupled…
In this work, it is demonstrated that the usual power system dynamic model exhibits a feedforward-feedback control structure. The distinct properties of the feedforward and feedback subsystems are identified and studied using respective…
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…
Unlike ODEs, whose models involve system matrices and whose controllers involve vector or matrix gains, PDE models involve functions in those roles functional coefficients, dependent on the spatial variables, and gain functions dependent on…
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 presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…
We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be…
This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design…