相关论文: On the solution of constrained Sylvester-observer …
In this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable Lie group. We show that a linear control system of such kind admits exactly one control set or infinite control…
In this paper we prove an approximate controllability result for the bilinear Schr\"odinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schr\"odinger operator than those…
We consider the convolution equation $F*X=B$, where $F\in\mathbb{R}^{3\times 3}$ and $B\in\mathbb{R}^{m\times n}$ are given, and $X\in\mathbb{R}^{m\times n}$ is to be determined. The convolution equation can be regarded as a linear system…
Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of…
We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…
Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological,…
A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite…
We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential equations and integral equations, commonly used in fluid…
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We study controllability issues for the Navier-Stokes Equation on a two dimensional rectangle with so-called Lions boundary conditions. Rewriting the Equation using a basis of harmonic functions we arrive to an infinite-dimensional system…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
We present our public-domain software for the following tasks in sparse (or toric) elimination theory, given a well-constrained polynomial system. First, C code for computing the mixed volume of the system. Second, Maple code for defining…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…
An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of…
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the…
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…