skip to main content


Title: Sparse Linear Ensemble Systems and Structural Controllability
The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern. Controllability of an ensemble system is, by convention, the capability of using a common control input to simultaneously steer every individual systems in it. A sparsity pattern is structurally controllable if it admits a controllable linear ensemble system. A main contribution of the paper is to provide a graphical condition that is necessary and sufficient for a sparsity pattern to be structurally controllable. Like other structural problems, the property of being structural controllable is monotone. We provide a complete characterization of minimal sparsity patterns as well.  more » « less
Award ID(s):
2042360
NSF-PAR ID:
10319635
Author(s) / Creator(s):
Date Published:
Journal Name:
IEEE Transactions on Automatic Control
ISSN:
0018-9286
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Mathematical theories and empirical evidence suggest that several complex natural and man-made systems are fragile: as their size increases, arbitrarily small and localized alterations of the system parameters may trigger system-wide failures. Examples are abundant, from perturbation of the population densities leading to extinction of species in ecological networks [1], to structural changes in metabolic networks preventing reactions [2], cascading failures in power networks [3], and the onset of epileptic seizures following alterations of structural connectivity among populations of neurons [4]. While fragility of these systems has long been recognized [5], convincing theories of why natural evolution or technological advance has failed, or avoided, to enhance robustness in complex systems are still lacking. In this paper we propose a mechanistic explanation of this phenomenon. We show that a fundamental tradeoff exists between fragility of a complex network and its controllability degree, that is, the control energy needed to drive the network state to a desirable state. We provide analytical and numerical evidence that easily controllable networks are fragile, suggesting that natural and man-made systems can either be resilient to parameters perturbation or efficient to adapt their state in response to external excitations and controls. 
    more » « less
  2. Systems composed of large ensembles of isolated or interacted dynamic units are prevalent in nature and engineered infrastructures. Linear ensemble systems are inarguably the simplest class of ensemble systems and have attracted intensive attention to control theorists and practionars in the past years. Comprehensive understanding of dynamic properties of such systems yet remains far-fetched and requires considerable knowledge and techniques beyond the reach of modern control theory. In this paper, we explore the classes of linear ensemble systems with system matrices that are not globally diagonalizable. In particular, we focus on analyzing their controllability properties under a Sobolev space setting and develop conditions under which uniform controllability of such ensemble systems is equivalent to that of their diagonalizable counterparts. This development significantly facilitates controllability analysis for linear ensemble systems through examining diagonalized linear systems. 
    more » « less
  3. Abstract Powder bed fusion (PBF) is an additive manufacturing (AM) process that builds parts in a layer-by-layer fashion out of a bed of metal powder via the selective melting action of a laser or electron beam heat source. Despite its transformational manufacturing capabilities, PBF is currently controlled in the open loop and there is significant demand to apply closed-loop process monitoring and control to the thermal management problem. This paper introduces a controls theoretic analysis of the controllability and observability of temperature states in PBF. The main contributions of the paper are proofs that certain configurations of PBF are classically controllable and observable, but that these configurations are not strongly structurally controllable and observable. These results are complemented by case studies, demonstrating the energy requirement of state estimation under various, industry relevant PBF configurations. These fundamental characterizations of controllability and observability provide a basis for realizing closed-loop PBF temperature estimation. 
    more » « less
  4. Photonic molecules can realize complex optical energy modes that simulate states of matter and have application to quantum, linear, and nonlinear optical systems. To achieve their full potential, it is critical to scale the photonic molecule energy state complexity and provide flexible, controllable, stable, high-resolution energy state engineering with low power tuning mechanisms. In this work, we demonstrate a controllable, silicon nitride integrated photonic molecule, with three high-quality factor ring resonators strongly coupled to each other and individually actuated using ultralow-power thin-film lead zirconate titanate (PZT) tuning. The resulting six tunable supermodes can be fully controlled, including their degeneracy, location, and degree of splitting, and the PZT actuator design yields narrow PM energy state linewidths below 58 MHz without degradation as the resonance shifts, with over an order of magnitude improvement in resonance splitting-to-width ratio of 58, and power consumption of 90 nW per actuator, with a 1-dB photonic molecule loss. The strongly coupled PZT-controlled resonator design provides a high-degree of resolution and controllability in accessing the supermodes. Given the low loss of the silicon nitride platform from the visible to infrared and the three individual bus, six-port design, these results open the door to novel device designs and a wide range of applications including tunable lasers, high-order suppression ultranarrow-linewidth lasers, dispersion engineering, optical parametric oscillators, physics simulations, and atomic and quantum photonics.

     
    more » « less
  5. In this paper, we investigate the problem of actuator selection for linear dynamical systems. We develop a framework to design a sparse actuator schedule for a given large-scale linear system with guaranteed performance bounds using deterministic polynomial-time and randomized approximately linear-time algorithms. First, we introduce systemic controllability metrics for linear dynamical systems that are monotone and homogeneous with respect to the controllability Gramian. We show that several popular and widely used optimization criteria in the literature belong to this class of controllability metrics. Our main result is to provide a polynomial-time actuator schedule that on average selects only a constant number of actuators at each time step, independent of the dimension, to furnish a guaranteed approximation of the controllability metrics in comparison to when all actuators are in use. Our results naturally apply to the dual problem of sensor selection, in which we provide a guaranteed approximation to the observability Gramian. We illustrate the effectiveness of our theoretical findings via several numerical simulations using benchmark examples. 
    more » « less