Bassam Bamieh

Bassam Bamieh, Mihailo R. Jovanović, Partha Mitra et al.

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

Lorenzo Fagiano, Khahn Huynh, Bassam Bamieh et al.

A study on filtering aspects of airborne wind energy generators is presented. This class of renewable energy systems aims to convert the aerodynamic forces generated by tethered wings, flying in closed paths transverse to the wind flow, into electricity. The accurate reconstruction of the wing's position, velocity and heading is of fundamental importance for the automatic control of these kinds of systems. The difficulty of the estimation problem arises from the nonlinear dynamics, wide speed range, large accelerations and fast changes of direction that the wing experiences during operation. It is shown that the overall nonlinear system has a specific structure allowing its partitioning into sub-systems, hence leading to a series of simpler filtering problems. Different sensor setups are then considered, and the related sensor fusion algorithms are presented. The results of experimental tests carried out with a small-scale prototype and wings of different sizes are discussed. The designed filtering algorithms rely purely on kinematic laws, hence they are independent from features like wing area, aerodynamic efficiency, mass, etc. Therefore, the presented results are representative also of systems with larger size and different wing design, different number of tethers and/or rigid wings.

Maurice Filo, Bassam Bamieh

We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a purely input-output approach, i.e. without having to resort to state space realizations. This has the advantage of encompassing a wider class of models (such as infinite dimensional systems and systems with delays). The input-output approach leads to uncovering new tools such as stochastic block diagrams that have an intimate connection with the more general Stochastic Integral Equations (SIE), rather than Stochastic Differential Equations (SDE). Various stochastic interpretations are considered, such as Itō and Stratonovich, and block diagram conversion schemes between different interpretations are devised. The MSS conditions are given in terms of the spectral radius of a matrix operator that takes different forms when different stochastic interpretations are considered.

Bassam Bamieh, Maurice Filo

We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is to characterize second-order properties such as mean-square stability and performance. A purely input-output treatment of these systems is given without recourse to state space models, and thus the results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for mean-square stability in terms of the spectral radius of a linear matrix operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties. For cases where state space realizations are given, Linear Matrix Inequality (LMI) equivalents of the input-output conditions are given.

Max Emerick, Saroj Chhatoi, Bassam Bamieh

We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear) differential operators, in which control inputs depend only on local information about the state and environment. This perspective yields a fully local, PDE-based framework for analysis and design. We apply this framework to the problem of stabilizing a swarm density around an arbitrary target density, and investigate fundamental limitations of low-order distributed controllers in achieving this goal. In particular, we show that controllers which act in a purely pointwise manner are incompatible with natural system symmetries and strong forms of stability, and must rely on mixing-type behavior to achieve stabilization. In contrast, we present a simple first-order control law which achieves stabilization and enjoys substantially stronger properties.

Nicolas Allegra, Bassam Bamieh, Partha P. Mitra et al.

Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication resources, hindering centralized control; the communication is subjected to noise; and the number of variables can be very large. These three aspects make tools and techniques from statistical physics particularly suitable for the performance analysis of such networked systems in the limit of many variables (analogous to the thermodynamic limit in statistical physics). Perhaps not surprisingly, phase-transition like phenomena appear in these systems, where a sharp change in performance can be observed with a smooth parameter variation, with the change becoming discontinuous or singular in the limit of infinite system size. In this paper we analyze the so called network consensus problem, prototypical of the above considerations, that has been previously analyzed mostly in the context of additive noise. We show that qualitatively new phase-transition like phenomena appear for this problem in the presence of multiplicative noise. Depending on dimensions and on the presence or absence of a conservation law, the system performance shows a discontinuous change at a threshold value of the multiplicative noise strength. In the absence of the conservation law, and for graph spectral dimension less than two, the multiplicative noise threshold (the stability margin of the control problem) is zero. This is reminiscent of the absence of robust controllers for certain classes of centralized control problems. Although our study involves a toy model we believe that the qualitative features are generic, with implication for the robust stability of distributed control systems, as well as the effect of roundoff errors and communication noise on distributed algorithms.

Milad Siami, Nader Motee, Gentian Buzi et al.

This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. We consider a simplified model of Glycolysis pathway as our motivating application. First, the properties of these class of pathways are investigated through a simplified two-state model, which is obtained by lumping all the intermediate reactions into a single intermediate reaction. Then, we generalize our results to autocatalytic pathways that are composed of a chain of enzymatically catalyzed intermediate reactions. We explicitly derive a hard limit on the minimum achievable $\mathcal L_2$-gain disturbance attenuation and a hard limit on its minimum required output energy. Finally, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production.