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M. Kanat Camlibel

Publications and source records attributed to M. Kanat Camlibel.

48 records · Page 3Linked to original sources
arXiv2020

Data informativity: a new perspective on data-driven analysis and control

The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.

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arXiv2019

Necessary and Sufficient Topological Conditions for Identifiability of Dynamical Networks

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions for identifiability of such dynamical networks, where we assume that only a subset of nodes is measured but the underlying graph structure of the network is known. This problem has recently been investigated from a generic viewpoint. Roughly speaking, generic identifiability means that the transfer functions in the network can be identified for "almost all" network matrices associated with the graph. In this paper, we investigate the stronger notion of identifiability for all network matrices. To this end, we introduce a new graph-theoretic concept called the graph simplification process. Based on this process, we provide necessary and sufficient topological conditions for identifiability. Notably, we also show that these conditions can be verified by polynomial time algorithms. Finally, we explain how our results generalize existing sufficient conditions for identifiability.

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arXiv2019

Distributed Linear Quadratic Tracking Control for Leader-Follower Multi-Agent Systems: A Suboptimality Approach

In this paper, we extend the results from Jiao et al. (2019) on distributed linear quadratic control for leaderless multi-agent systems to the case of distributed linear quadratic tracking control for leader-follower multi-agent systems. Given one autonomous leader and a number of homogeneous followers, we introduce an associated global quadratic cost functional. We assume that the leader shares its state information with at least one of the followers and the communication between the followers is represented by a connected simple undirected graph. Our objective is to design distributed control laws such that the controlled network reaches tracking consensus and, moreover, the associated cost is smaller than a given tolerance for all initial states bounded in norm by a given radius. We establish a centralized design method for computing such suboptimal control laws, involving the solution of a single Riccati inequality of dimension equal to the dimension of the local agent dynamics, and the smallest and the largest eigenvalue of a given positive definite matrix involving the underlying graph. The proposed design method is illustrated by a simulation example.

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arXiv2019

Distributed Linear Quadratic Optimal Control: Compute Locally and Act Globally

In this paper we consider the distributed linear quadratic control problem for networks of agents with single integrator dynamics. We first establish a general formulation of the distributed LQ problem and show that the optimal control gain depends on global information on the network. Thus, the optimal protocol can only be computed in a centralized fashion. In order to overcome this drawback, we propose the design of protocols that are computed in a decentralized way. We will write the global cost functional as a sum of local cost functionals, each associated with one of the agents. In order to achieve 'good' performance of the controlled network, each agent then computes its own local gain, using sampled information of its neighboring agents. This decentralized computation will only lead to suboptimal global network behavior. However, we will show that the resulting network will reach consensus. A simulation example is provided to illustrate the performance of the proposed protocol.

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arXiv2019

A Unifying Framework for Strong Structural Controllability

This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. This graph theoretic condition makes use of a new color change rule that is introduced in this paper. Based on these two results, we then establish a necessary and sufficient graph theoretic condition for strong structural controllability. Moreover, we relate our results to those that exists in the literature, and explain how our results generalize previous work.

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arXiv2018

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.

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arXiv2018

Identifiability of Undirected Dynamical Networks: a Graph-Theoretic Approach

This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state matrix of the network can be uniquely identified. As our main contribution, we present a graph coloring condition that ensures identifiability of the network's state matrix. Additionally, we show how the framework can be used to assess identifiability of dynamical networks with general, higher-order node dynamics. As an interesting corollary of our results, we find that excitation and measurement of all network nodes is not required. In fact, for many network structures, identification is possible with only small fractions of measured and excited nodes.

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arXiv2018

Topological Conditions for Identifiability of Dynamical Networks with Partial Node Measurements

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in graph-theoretic conditions for identifiability of such dynamical networks, where we assume that only a subset of nodes is measured but the underlying graph structure of the network is known. This problem has recently been investigated in the case of generic identifiability. In this paper, we investigate a stronger notion of identifiability for all network matrices associated with a given graph. For this, we introduce a new graph-theoretic concept called constrained vertex-disjoint paths. As our main result, we state conditions for identifiability based on these constrained vertex-disjoint paths.

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arXiv2018

A Suboptimality Approach to Distributed $\mathcal{H}_2$ Optimal Control

This paper deals with the distributed $\mathcal{H}_2$ optimal control problem for linear multi-agent systems. In particular, we consider a suboptimal version of the distributed $\mathcal{H}_2$ optimal control problem. Given a linear multi-agent system with identical agent dynamics and an associated $\mathcal{H}_2$ cost functional, our aim is to design a distributed diffusive static protocol such that the protocol achieves state synchronization for the controlled network and such that the associated cost is smaller than an a priori given upper bound. We first analyze the $\mathcal{H}_2$ performance of linear systems and then apply the results to linear multi-agent systems. Two design methods are provided to compute such a suboptimal distributed protocol. For each method, the expression for the local control gain involves a solution of a single Riccati inequality of dimension equal to the dimension of the individual agent dynamics, and the smallest nonzero and the largest eigenvalue of the graph Laplacian.

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arXiv2018

A Suboptimality Approach to Distributed Linear Quadratic Optimal Control

This paper is concerned with the distributed linear quadratic optimal control problem. In particular, we consider a suboptimal version of the distributed optimal control problem for undirected multi-agent networks. Given a multi-agent system with identical agent dynamics and an associated global quadratic cost functional, our objective is to design suboptimal distributed control laws that guarantee the controlled network to reach consensus and the associated cost to be smaller than an a priori given upper bound. We first analyze the suboptimality for a given linear system and then apply the results to linear multiagent systems. Two design methods are then provided to compute such suboptimal distributed controllers, involving the solution of a single Riccati inequality of dimension equal to the dimension of the agent dynamics, and the smallest nonzero and the largest eigenvalue of the graph Laplacian. Furthermore, we relax the requirement of exact knowledge of the smallest nonzero and largest eigenvalue of the graph Laplacian by using only lower and upper bounds on these eigenvalues. Finally, a simulation example is provided to illustrate our design method.

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arXiv2016

A Distance-Based Approach to Strong Target Control of Dynamical Networks

This paper deals with controllability of dynamical networks. It is often unfeasible or unnecessary to fully control large-scale networks, which motivates the control of a prescribed subset of agents of the network. This specific form of output control is known under the name target control. We consider target control of a family of linear control systems associated with a network, and provide both a necessary and a sufficient topological condition under which the network is strongly targeted controllable. Furthermore, a leader selection algorithm is presented to compute leader sets achieving target control.

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