Sergio Daniel Pequito

A Framework for Structural Input/Output and Control Configuration Selection in Large-Scale Systems

This paper addresses problems on the structural design of large-scale control systems. An efficient and unified framework is proposed to select the minimum number of manipulated/measured variables to achieve structural controllability/observability of the system, and to select the minimum number of feedback interconnections between measured and manipulated variables such that the closed-loop system has no structural fixed modes. Global solutions are computed using polynomial complexity algorithms in the number of the state variables of the system. Finally, graph-theoretic characterizations are proposed, which allow a characterization of all possible solutions.

A structured systems approach for optimal actuator-sensor placement in linear time-invariant systems

In this paper we address the actuator/sensor allocation problem for linear time invariant (LTI) systems. Given the structure of an autonomous linear dynamical system, the goal is to design the structure of the input matrix (commonly denoted by B) such that the system is structurally controllable with the restriction that each input be dedicated, i.e., it can only control directly a single state variable. We provide a methodology to determine the minimum number of dedicated inputs required to ensure structural controllability, and characterize all (when not unique) possible configurations of the minimal input matrix B. Furthermore, we show that the proposed solution incurs polynomial complexity in the number of state variables. By duality, the solution methodology may be readily extended to the structural design of the corresponding minimal output matrix (commonly denoted by C) that ensures structural observability.

On the complexity of the constrained input selection problem for structural linear systems

This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures systems structural controllability. We refer to this problem as the minimum constrained input selection (minCIS) problem, since the selection has to be performed on an initial given set of possible inputs. We prove that the minCIS problem is NP-hard, which addresses a recent open question of whether there exist polynomial algorithms (in the size of the system plant matrices) that solve the minCIS problem. To this end, we show that the associated decision problem, to be referred to as the CIS, of determining whether a subset (of a given collection of inputs) with a prescribed cardinality exists that ensures structural controllability, is NP-complete. Further, we explore in detail practically important subclasses of the minCIS obtained by introducing more specific assumptions either on the system dynamics or the input set instances for which systematic solution methods are provided by constructing explicit reductions to well known computational problems. The analytical findings are illustrated through examples in multi-agent leader-follower type control problems.

Minimum cost input/output design for large-scale linear structural systems

In this paper, we provide optimal solutions to two different (but related) input/output design problems involving large-scale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take different values, but is independent of the input/output performing the task. Under these conditions, we first aim to determine and characterize the input/output placement that incurs in the minimum cost while ensuring that the resulting placement achieves structural controllability/observability. Further, we address a constrained variant of the above problem, in which we seek to determine the minimum cost placement configuration, among all possible input/output placement configurations that ensures structural controllability/observability, with the lowest number of directly actuated/measured state variables. We develop new graph-theoretical characterizations of cost-constrained input selections for structural controllability and properties that enable us to address both problems by reduction to a weighted maximum matching problem - efficiently addressed by algorithms with polynomial time complexity (in the number of state variables). Finally, we illustrate the obtained results with an example.

Design of communication networks for distributed computation with privacy guarantees

In this paper we address a communication network design problem for distributed computation with privacy guarantees. More precisely, given a possible communication graph between different agents in a network, the objective is to design a protocol, by proper selection of the weights in the dynamics induced by the communication graph, such that 1) weighted average consensus of the initial states of all the agents will be reached; and 2) there are privacy guarantees, where each agent is not able to retrieve the initial states of non-neighbor agents, with the exception of a small subset of agents (that will be precisely characterized). In this paper, we assume that the network is cooperative, i.e., each agent is passive in the sense that it executes the protocol correctly and does not provide incorrect information to its neighbors, but may try to retrieve the initial states of non-neighbor agents. Furthermore, we assume that each agent knows the communication protocol.

Minimum Robust Sensor Placement for Large Scale Linear Time-Invariant Systems: A Structured Systems Approach

Abstract The paper addresses the problem of robust sensor placement for large scale linear time-invariant systems. Two different concepts of robustness are analyzed: 1) the robustness with respect to one sensor failure, and 2) the robustness with respect to one link failure. We show that both aforementioned problems can be posed as certain set cover problems, a classical problem for which many solutions exist. In addition we formulate and partially solve the minimum robust sensor placement, a much harder problem. By relating robust sensor placement to spanning trees associated with the dynamical system structure, readily computable upper and lower bounds are provided on the size of such robust placement configurations. Finally, some illustrative examples are presented.

Minimum number of information gatherers to ensure full observability of a dynamic social network: A structural systems approach

This paper studies the problem of identifying the minimum number of entities (agents), referred to as information gatherers, that are able to infer all the states in a dynamical social network. The information gatherers can be, for instance, service providers and the remaining agents the clients, each comprising several dynamic states associated with the services and personal information. The problem of identifying the minimum number of information gatherers can constitute a way to create coalitions to oversee the entire state of the system, and consequently the behavior of the agents in the social network. The dynamical social network is assumed to be modelled as a linear time-invariant system, and we will make use of the structural systems concept, i.e., by considering only the sparsity pattern (location of zeroes/non-zeroes) of the system coupling matrix. As a consequence, the design guarantees derived hold for almost all numerical parametric realizations of the system. In this paper, we show that this problem is NP-hard: in addition, we provide a reduction of the coalition problem to a minimum set covering problem that, in practice, leads to efficient (polynomial complexity) approximation schemes for solving the coalition problem with guaranteed optimality gaps. Finally, an example is provided which illustrates the analytical findings.

Minimum cost input-output and control configuration selection: A structural systems approach

In this paper we provide solutions to two different (but related) design problems involving large-scale linear dynamical systems: 1) the optimal input/output structural design ensuring structural controllability/observability and incurring in the minimal cost under generic assumptions; and 2) the optimal structural control configuration design for decentralized control, i.e., the sparsest information pattern or the minimal communication between outputs and inputs, such that the closed-loop system has no structurally fixed modes and incurring in the minimal cost under the assumption that the communication devices have the same cost. We show that the proposed solution can be implemented efficiently, i.e., using an algorithm with polynomial time complexity in the number of the state variables. We illustrate the obtained results with an example.

A model checking framework for linear time invariant switching systems using structural systems analysis

This paper introduces the concept of structural hybrid systems to address, as a particular case, the model checking problem of switching (possible large scale) linear time invariant systems. Within the proposed setup, we provide necessary conditions to ensure properties such as controllability, at each time. We show that such model checking controllability properties can be implemented using efficient algorithms (with polynomial complexity). An example, based on the IEEE 5-bus power system, is presented which illustrates our model checking and design methodologies.

Optimal design of observable multi-agent networks: A structural system approach

This paper introduces a method to design observable directed multi-agent networks, that are: 1) either minimal with respect to a communications-related cost function, or 2) idem, under possible failure of direct communication between two agents. An observable multi-agent network is characterized by agents that update their states using a neighboring rule based on directed communication graph topology in order to share information about their states; furthermore, each agent can infer the initial information shared by all the agents. Sufficient conditions to ensure that 1) is satisfied are obtained by reducing the original problem to the travelling salesman problem (TSP). For the case described in 2), sufficient conditions for the existence of a minimal network are shown to be equivalent to the existence of two disjoint solutions to the TSP. The results obtained are illustrated with an example from the area of cooperative path following of multiple networked vehicles by resorting to an approximate solution to the TSP.