Related papers: On parametrization of linear pseudo-differential b…
Let $X$ be a manifold with boundary, and let $L$ be a 0-elliptic operator on X which is semi-Fredholm essentially surjective with infinite-dimensional kernel. Examples include Hodge Laplacians and Dirac operators on conformally compact…
In this paper we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
A pseudodifferential calculus for parameter-dependent operators on smooth manifolds with boundary in the spirit of Boutet de Monvel's algebra is constructed. The calculus contains, in particular, the resolvents of realizations of…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the…
This paper studies the construction of dynamic symbolic abstractions for nonlinear control systems via dynamic quantization. Since computational complexity is a fundamental problem in the use of discrete abstractions, a dynamic quantizer…
We consider abstract second order systems of the form $\ddot{x}(t) + D \dot{x}(t) + Sx(t)=0$, which are typically analyzed via the operator matrix $\mathcal{A}=\left[\begin{smallmatrix} 0 & I \\ -S & -D \end{smallmatrix}\right]$ governing…
Symbolic control is an abstraction-based controller synthesis approach that provides, algorithmically, certifiable-by-construction controllers for cyber-physical systems. Symbolic control approaches usually assume that full-state…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The…
We study topologizability and power boundedness of weigh\-ted composition operators on (certain subspaces of) $\mathscr{D}'(X)$ for an open subset $X$ of $\mathbb{R}^d$. For the former property we derive a characterization in terms of the…
The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
Discrete abstractions of continuous and hybrid systems have recently been the topic of great interest from both the control systems and the computer science communities, because they provide a sound mathematical framework for analysing and…
We study model predictive control for singular differential-algebraic equations with higher index. This is a novelty when compared to the literature where only regular differential-algebraic equations with additional assumptions on the…