arXiv subjects

John C. Doyle

Publications and source records attributed to John C. Doyle.

30 records · Page 2Linked to original sources

arXiv2017

Fundamental Limits and Tradeoffs in Autocatalytic Pathways

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.

eess.SY↗

arXiv2017

Separable and Localized System Level Synthesis for Large-Scale Systems

A major challenge faced in the design of large-scale cyber-physical systems, such as power systems, the Internet of Things or intelligent transportation systems, is that traditional distributed optimal control methods do not scale gracefully, neither in controller synthesis nor in controller implementation, to systems composed of millions, billions or even trillions of interacting subsystems. This paper shows that this challenge can now be addressed by leveraging the recently introduced System Level Approach (SLA) to controller synthesis. In particular, in the context of the SLA, we define suitable notions of separability for control objective functions and system constraints such that the global optimization problem (or iterate update problems of a distributed optimization algorithm) can be decomposed into parallel subproblems. We then further show that if additional locality (i.e., sparsity) constraints are imposed, then these subproblems can be solved using local models and local decision variables. The SLA is essential to maintaining the convexity of the aforementioned problems under locality constraints. As a consequence, the resulting synthesis methods have $O(1)$ complexity relative to the size of the global system. We further show that many optimal control problems of interest, such as (localized) LQR and LQG, $\mathcal{H}_2$ optimal control with joint actuator and sensor regularization, and (localized) mixed $\mathcal{H}_2/\mathcal{L}_1$ optimal control problems, satisfy these notions of separability, and use these problems to explore tradeoffs in performance, actuator and sensing density, and average versus worst-case performance for a large-scale power inspired system.

math.OC↗

arXiv2016

Understanding Robust Control Theory Via Stick Balancing

Robust control theory studies the effect of noise, disturbances, and other uncertainty on system performance. Despite growing recognition across science and engineering that robustness and efficiency tradeoffs dominate the evolution and design of complex systems, the use of robust control theory remains limited, partly because the mathematics involved is relatively inaccessible to nonexperts, and the important concepts have been inexplicable without a fairly rich mathematics background. This paper aims to begin changing that by presenting the most essential concepts in robust control using human stick balancing, a simple case study popular in both the sensorimotor control literature and extremely familiar to engineers. With minimal and familiar models and mathematics, we can explore the impact of unstable poles and zeros, delays, and noise, which can then be easily verified with simple experiments using a standard extensible pointer. Despite its simplicity, this case study has extremes of robustness and fragility that are initially counter-intuitive but for which simple mathematics and experiments are clear and compelling. The theory used here has been well-known for many decades, and the cart-pendulum example is a standard in undergrad controls courses, yet a careful reconsidering of both leads to striking new insights that we argue are of great pedagogical value.

math.OC↗

arXiv2015

Primal robustness and semidefinite cones

This paper reformulates and streamlines the core tools of robust stability and performance for LTI systems using now-standard methods in convex optimization. In particular, robustness analysis can be formulated directly as a primal convex (semidefinite program or SDP) optimization problem using sets of gramians whose closure is a semidefinite cone. This allows various constraints such as structured uncertainty to be included directly, and worst-case disturbances and perturbations constructed directly from the primal variables. Well known results such as the KYP lemma and various scaled small gain tests can also be obtained directly through standard SDP duality. To readers familiar with robustness and SDPs, the framework should appear obvious, if only in retrospect. But this is also part of its appeal and should enhance pedagogy, and we hope suggest new research. There is a key lemma proving closure of a grammian that is also obvious but our current proof appears unnecessarily cumbersome, and a final aim of this paper is to enlist the help of experts in robust control and convex optimization in finding simpler alternatives.

eess.SY↗

arXiv2014

The H2 Control Problem for Quadratically Invariant Systems with Delays

This paper gives a new solution to the output feedback H2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized H2 problem is cast as a convex model matching problem. The main result shows that the model matching problem can be reduced to a finite-dimensional quadratic program. A recursive state-space method for computing the optimal controller based on vectorization is given.

eess.SY↗

arXiv2014

Localized LQR Optimal Control

This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality constraints, and show that the resulting feasibility test can be solved in a localized and distributed way. We also show that the solution of the local feasibility tests can be used to synthesize a receding horizon like controller that achieves the desired closed loop response in a localized manner as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem and derive an analytic solution for the optimal controller. Through a numerical example, we show that the LLQR optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance as an unconstrained H2 optimal controller, but can be designed and implemented in a localized and distributed way.

eess.SY↗

arXiv2014

Optimal Two Player LQR State Feedback With Varying Delay

This paper presents an explicit solution to a two player distributed LQR problem in which communication between controllers occurs across a communication link with varying delay. We extend known dynamic programming methods to accommodate this varying delay, and show that under suitable assumptions, the optimal control actions are linear in their information, and that the resulting controller has piecewise linear dynamics dictated by the current effective delay regime.

math.OC↗

arXiv2012

Output Feedback H_2 Model Matching for Decentralized Systems with Delays

This paper gives a new solution to the output feedback H_2 model matching problem for a large class of delayed information sharing patterns. Existing methods for such problems typically reduce the decentralized problem to a centralized problem of higher state dimension. In contrast, the controller given in this paper is constructed from the solutions to the centralized control and estimation Riccati equations for the original system. The problem is solved by decomposing the controller into two components. One is centralized, but delayed, while the other is decentralized with finite impulse response (FIR). It is then shown that the optimal controller can be constructed through a combination of centralized spectral factorization and quadratic programming.

eess.SY↗

arXiv2010

Amplification and Nonlinear Mechanisms in Plane Couette Flow

We study the input-output response of a streamwise constant projection of the Navier-Stokes equations for plane Couette flow, the so-called 2D/3C model. Study of a streamwise constant model is motivated by numerical and experimental observations that suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures. Periodic spanwise/wall-normal (z-y) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity field that is qualitatively similar to a fully turbulent spatial field of DNS data. The input-output response associated with the 2D/3C nonlinear coupling is used to estimate the energy optimal spanwise wavelength over a range of Reynolds numbers. The results of the input-output analysis agree with previous studies of the linearized Navier-Stokes equations. The optimal energy corresponds to minimal nonlinear coupling. On the other hand, the nature of the forced 2D/3C streamwise velocity field provides evidence that the nonlinear coupling in the 2D/3C model is responsible for creating the well known characteristic "S" shaped turbulent velocity profile. This indicates that there is an important tradeoff between energy amplification, which is primarily linear and the seemingly nonlinear momentum transfer mechanism that produces a turbulent-like mean profile.

physics.flu-dyn↗

arXiv2010

On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements

In this paper, we take a control-theoretic approach to answering some standard questions in statistical mechanics, and use the results to derive limitations of classical measurements. A central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless. We show that a linear system is dissipative if, and only if, it can be approximated by a linear lossless system over arbitrarily long time intervals. Hence lossless systems are in this sense dense in dissipative systems. A linear active system can be approximated by a nonlinear lossless system that is charged with initial energy. As a by-product, we obtain mechanisms explaining the Onsager relations from time-reversible lossless approximations, and the fluctuation-dissipation theorem from uncertainty in the initial state of the lossless system. The results are applied to measurement devices and are used to quantify limits on the so-called observer effect, also called back action, which is the impact the measurement device has on the observed system. In particular, it is shown that deterministic back action can be compensated by using active elements, whereas stochastic back action is unavoidable and depends on the temperature of the measurement device.

math.DS↗

arXiv2009

A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is however critical both for basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brain-wide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brain-wide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open access data repository; compatibility with existing resources, and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.

q-bio.NC↗

arXiv2005

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.

cond-mat.dis-nn↗