Consensus stabilizability and exact consensus controllability of multi-agent linear systems

A goal in engineering systems is to try to control them. Control theory offers mathematical tools for steering engineered systems towards a desired state. Stabilizability and controllability can be studied under different points of view, in particular, we focus on measure of controllability in the sense of the minimum set of controls that need for to steer the multiagent system toward any desired state. In this paper, we study the consensus stabilizability and exact consensus controllability of multi-agent linear systems, in which all agents have a same linear dynamic mode that can be in any orderPostprint (published version

Analyzing controllability of neural networks

In recent years, due to the relation between cognitive control and mathematical concept of control dynamical systems, there has been growing interest in the descriptive analysis of complex networks with linear dynamics, permeating many aspects from everyday life, obtaining considerable advances in the description of their structural and dynamical properties. Nevertheless, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems is of interest to study the exact controllability, this measure is defined as the minimum set of controls that are needed to steer the whole system toward any desired state. In this paper, a revision of controllability concepts is presented and provides conditions for exact controllability for the multiagent systemsPostprint (author's final draft

Wind profile prediction using linear Markov chains: A linear algebra approach

To predict the future wind speed and wind direction is of relevance to the wind industry to maximize the power generation. In this regards, this article describes a methodology for the construction of predictive models based on linear Markov chains under linear algebra point of view. The model analyzes the direction and speed of the wind obtained from a meteorological station. This Model allows making a precise study of wind direction and speeding data; figure out the stability, the most common direction or speed, its behaviour depending on the hours or seasons.Peer ReviewedPostprint (author's final draft

On stability and controllability of multi-agent linear systems

Recent advances in communication and computing have made the control and coordination of dynamic network agents to become an area of multidisciplinary research at the intersection of the theory of control systems, communication and linear algebra. The advances of the research in multi-agent systems are strongly supported by their critical applications in different areas as for example in consensus problem of communication networks, or formation control of mobile robots. Mainly, the consensus problem has been studied from the point of view of stability. Nevertheless, recently some researchers have started to analyze the controllability problems. The study of controllability is motivated by the fact that the architecture of communication network in engineering multi-agent systems is usually adjustable. Therefore, it is meaningful to analyze how to improve the controllability of a multi-agent system. In this work we analyze the stability and controllability of multiagent systems consisting of k + 1 agents with dynamics x¿i = Aixi + Biui, i = 0, 1, . . . , kPostprint (published version

On simultaneously and approximately simultaneously diagonalizable m-tuples of matrices

In this paper, the problem of simultaneous diagonalization of m-tuples of n-order square complex matrices, is analyzed and some necessary and some necessary and sufficient conditions for this property to be fulfilled are presented. This study has an interest in its applications in different areas as for example in engineering and physical sciences. For example, they appear founding when we must give the instanton solution of Yang-Mills field presented in an octonion form, and it can be represented by triples of traceless matrices. In the case where the m-tuple does not simultaneously diagonalize, the possibility of to find near of the given m-tuple, an m-tuple that diagonalize simultaneously is studiedPeer ReviewedPostprint (author's final draft

Exact consensus controllability of multi-agent linear systems

Inthispaperwestudytheexactcontrollabilityofmulti-agentlinearsystems,inwhichallagentshavean identical linear dynamic mode that can be in any orderIn this paper we study the exact controllability of multi-agent linear systems, in which all agents have an identical linear dynamic mode that can be in any order.Postprint (published version

Structural consensus controllability of singular multi-agent linear dynamic systems

The analysis of control of linear multi-agent systems has recently emerged as an important domain that is receiving a lot of interest from a variety of research communities, and consensus plays a fundamental role in this field of study. We will show how using linear algebra techniques can be analyzed the consensus controllability problem for singular multi-agent systems, in which all agents have an identical linear dynamic mode that can be in any order.Postprint (author's final draft

Exact consensus controllability of multi-agent linear systems

Multi-agent systems, consensus, controllability, exact consensus controllability.In this paper we study the exact controllability of multi-agent linear systems, in which all agents have an identical linear dynamic mode that can be in any order.In this paper we study the exact controllability of multi-agent linear systems, in which all agents have an identical linear dynamic mode that can be in any orderPostprint (published version

Analizing exact controllability of l-order linear ystems

In recent years there has been growing interest in the descriptive analysis of l -order time invariant linear dynamical system x l = A l system x l = A l where A i are square complex matrices and x i denotes the i-th derivative of x. We are interested to mesure the minimum number of controls B that are needed in order to make the systemPeer ReviewedPostprint (published version

Sensivity and stability of singular systems under proportional and derivative feedback

Postprint (published version