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In this work, we formulate two controllability maximization problems for large-scale networked dynamical systems such as brain networks: The first problem is a sparsity constraint optimization problem with a box constraint. The second…
In this paper the problem of finding the sparsest (i.e., minimum cardinality) critical $k$-tuple including one arbitrarily specified measurement is considered. The solution to this problem can be used to identify weak points in the…
Although modern deep learning often relies on massive over-parameterized models, the fundamental interplay between capacity, sparsity, and robustness in low-capacity networks remains a vital area of study. We introduce a controlled…
In this paper, we consider composite networks formed from the Kronecker product of smaller networks. We find the observability and controllability properties of the product network from those of its constituent smaller networks. The overall…
This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…
This paper discusses the controllability problem of complex networks. It is shown that almost any weighted complex network with noise on the strength of communication links is controllable in the sense of Kalman controllability. The concept…
Given a state transition matrix (STM), we reinvestigate the problem of constructing the sparest input matrix with a fixed number of inputs to guarantee controllability. We give a new and simple graph theoretic characterization for the…
In this paper we consider a control problem for a Partially Observable Piecewise Deterministic Markov Process of the following type: After the jump of the process the controller receives a noisy signal about the state and the aim is to…
In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a…
Liu et al recently proposed a minimum number of driver nodes needed to obtain full structural controllability over a directed network. Driver nodes are unmatched nodes, from which there are directed paths to all matched nodes. Their most…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
In the {\em capacitated} survivable network design problem (Cap-SNDP), we are given an undirected multi-graph where each edge has a capacity and a cost. The goal is to find a minimum cost subset of edges that satisfies a given set of…
We study a novel control problem in the context of network coordination games: the individuation of the smallest set of players capable of driving the system, globally, from one Nash equilibrium to another one. Our main contribution is the…
Controllability maximization problem under sparsity constraints is a node selection problem that selects inputs that are effective for control in order to minimize the energy to control for desired state. In this paper we discuss the…
In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where…
Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization…
In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at…
This paper shows that the optimal policy and value functions of a Markov Decision Process (MDP), either discounted or not, can be captured by a finite-horizon undiscounted Optimal Control Problem (OCP), even if based on an inexact model.…
In this paper we provide a set of stability conditions for linear time-invariant networked control systems with arbitrary topology, using a Lyapunov direct approach. We then use these stability conditions to provide a novel low-complexity…