Related papers: Backstepping for Partial Differential Equations:A …
This work studies the problem of controlling the mean-field density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
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…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
This paper considers the backstepping design of state feedback controllers for coupled linear parabolic partial integro-differential equations (PIDEs) of Volterra-type with distinct diffusion coefficients, spatially-varying parameters and…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of $m$ leftward transporting PDEs. The…
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
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…
Despite the extensive body of work on backstepping for one-dimensional PDEs, results in higher dimensions remain comparatively limited. Most available methods either exploit particular symmetries of the PDE or address problems posed on…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging,…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
The paper is concerned with the strict-feedback form of hyperbolic distributed-parameter systems. Such a system structure is well known to be the basis for the recursive backstepping control design for nonlinear ODEs and is also reflected…