Related papers: Existence, uniqueness, and stabilization results f…
Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of…
Falling liquid films are complex physical processes modelled by infinite-dimensional dynamical systems. The interfacial behaviour is characterised by the Reynolds number, a nondimensional parameter, and above a critical value the uniform…
We establish the existence, uniqueness, and $W^{1,2,p}$-regularity of solutions to fully-nonlinear, parabolic obstacle problems when the obstacle is the pointwise supremum of functions in $W^{1,2,p}$ and the nonlinear operator is required…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
This paper develops a robust safety-critical control method for nonlinear strictfeedback systems with mismatched disturbances. Using a state transformation and a linear time-varying disturbance observer, the system is converted into a form…
Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the…
We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting contains the purely nonlocal, as well as the purely local…
Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this paper. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional…
We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for…
In this paper, we study the output feedback stabilization for a scalar conservation law with a nonlocal velocity, that models a highly re-entrant manufacturing system as encountered in semi-conductor production. By spectral analysis, we…
We study an axial dispersion tubular reactor model governed by a nonlinear parabolic equation with Robin-type boundary conditions and boundary feedback control. We derive sufficient conditions for the exponential stability of the…
This paper is devoted to the stabilization problem for nonlinear driftless control systems by means of a time-varying feedback control. It is assumed that the vector fields of the system together with their first order Lie brackets span the…
We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs by two methods: one by time discretisation through elliptic…
We consider the $F$-equivalence problem for parabolic systems: under which conditions a control system, governed by a parabolic operator $A$ and a control operator $B$, can be made equivalent to an exponentially stable system with…
Here we deal with the stabilization problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into…
Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear…
In this article we study the local stabilization of the non-homogeneous Navier- Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that…
This paper examines the impulse controllability of degenerate singular parabolic equations through a modern framework focused on finite-time stabilization. Furthermore, we provide an explicit estimate for the exponential decay of the…
This paper addresses optimal feedback stabilizing control for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations, affected by state and process noise. Instead of directly stabilizing the uncertain system, we…
In this paper, we discuss the feedback stabilization of bilinear systems under weak observation properties. In this case, the uniform stability is not guaranteed. Thus we provide an explicit weak decay rate for all regular initial data.…