Related papers: Control Energy of Lattice Graphs
The Directed Power Graph of a group is a graph whose vertex set is the elements of the group, with an edge from $x$ to $y$ if $y$ is a power of $x$. The \textit{Power Graph} of a group can be obtained from the directed power graph by…
We consider the problem of making a set of states invariant for a network of controlled systems. We assume that the subsystems, initially uncoupled, must be interconnected through controllers to be designed with a constraint on the data…
We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the $L^2$ norm and an energy space seminorm. We prove well-posedness and…
In recent times adaptive regulation of sampling rates has gained significant attention in research community and researchers has demonstrated it's effectiveness in embedded control applications from different perspectives. In low power…
The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy either via strategic placement of driver nodes, or by decreasing the cardinality of nodes…
As the scale of networked control systems increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks increase in importance. The need to redefine classical system and…
The power graph of a group $G$ is the graph whose vertex set is $G$ and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power graphs of finite groups. For power…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Pinning control on complex dynamical networks has emerged as a very important topic in recent trends of control theory due to the extensive study of collective coupled behaviors and their role in physics, engineering and biology. In…
Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e.g., sparsity, delay, or spatial…
In this paper, we quantify the resilience of nonlinear dynamical systems by studying the increased energy used by all inputs of a system that suffers a partial loss of control authority, either through actuator malfunctions or through…
Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The…
The control of ensembles of dynamical systems is an intriguing and challenging problem, arising for example in quantum control. We initiate the investigation of optimal control of ensembles of discrete-time systems, focusing on minimising…
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two…
As the energy transition transforms power grids across the globe, it poses several challenges regarding grid design and control. In particular, high levels of intermittent renewable generation complicate the task of continuously balancing…
The aim of this work is to study the controllability of the bilinear Schr\"odinger equation on compact graphs. In particular, we consider the equation (BSE) $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space…
In this paper we introduce the optimal control of a kinetic model describing agents who migrate on a graph and interact within its nodes exchanging a physical quantity. As a prototype model, we consider the spread of an infectious disease…
In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We…
Application of IDA-PBC to mechanical systems has received much attention in recent decades, but its application is still limited by the solvability of the so-called matching conditions. In this work, it is shown that total energy-shaping…
We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among…