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We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
Assembling lattices from discrete building blocks enables the composition of large, heterogeneous, and easily reconfigurable objects with desirable mass-to-stiffness ratios. This type of building system may also be referred to as a digital…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A…
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the…
We propose a novel framework for stabilization, with an estimate of the region of attraction, of quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow-up phenomena when null boundary inputs are imposed.…
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…
We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial dimensions. We show optimal global regularity estimates on…
We consider a simply-supported Euler-Bernoulli beam with viscous and Kelvin--Voigt damping. Our objective is to attenuate the effect of an unknown distributed disturbance using one piezoelectric actuator. We show how to design a suitable…
This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the…
In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the…
The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. Here we show that local control…
We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear…
In recently proposed stabilisation techniques for parabolic equations, a crucial role is played by a suitable sequence of oblique projections in Hilbert spaces, onto the linear span of a suitable set of M actuators, and along the subspace…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS…
We construct a Lipschitz metric for conservative solutions of the Cauchy problem on the line for the two-component Camassa--Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, and $\rho_t+(u\rho)_x=0$ with given initial data…
We present a framework to design nonlinear robust output feedback model predictive control (MPC) schemes that ensure constraint satisfaction under noisy output measurements and disturbances. We provide novel estimation methods to bound the…