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 that addresses this design question: specifically, we determine the minimum number of dedicated inputs required to ensure such structural controllability, and characterize, and characterizes all (when not unique) possible configurations of the \emph{minimal} input matrix $B$. Furthermore, we show that the proposed solution methodology incurs \emph{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.Comment: 8 pages, submitted for publicatio

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 system's 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

A convoy protection strategy using the moving path following method

This paper considers the problem of convoy protection missions using a fixed-wing Unmanned Aerial Vehicle (UAV) in scenarios where the radius of the circular region of interest around the convoy is smaller than the UAV minimum turning radius. Using the Moving Path Following (MPF) method, we propose a guidance algorithmic strategy where a UAV moving at constant ground speed is required to converge to and follow a desired geometric moving path that is attached to the convoy center. Conditions under which the proposed strategy solves the convoy problem are derived. A performance metric that is proposed together with numerical simulation results demonstrate the effectiveness of the proposed approach.info:eu-repo/semantics/acceptedVersio

Moving path following for unmanned aerial vehicles with applications to single and multiple target tracking problems

This paper introduces the moving path following (MPF) problem, in which a vehicle is required to converge to and follow a desired geometric moving path, without a specific temporal specification, thus generalizing the classical path following that only applies to stationary paths. Possible tasks that can be formulated as an MPF problem include tracking terrain/air vehicles and gas clouds monitoring, where the velocity of the target vehicle or cloud specifies the motion of the desired path. We derive an error space for MPF for the general case of time-varying paths in a two-dimensional space and subsequently an application is described for the problem of tracking single and multiple targets on the ground using an unmanned aerial vehicle (UAV) flying at constant altitude. To this end, a Lyapunov-based MPF control law and a path-generation algorithm are proposed together with convergence and performance metric results. Real-world flight tests results that took place in Ota Air Base, Portugal, with the ANTEX-X02 UAV demonstrate the effectiveness of the proposed method.info:eu-repo/semantics/acceptedVersio