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John C. Doyle

Publications and source records attributed to John C. Doyle.

At least 19 recordsLinked to original sources
arXiv2025

Rate-cost tradeoffs in continuous-time control with a biomolecular application

This paper focuses on rate-limited control of the generalized Ornstein-Uhlenbeck process where the control action can be either multiplicative or additive, and the noise variance can depend on the control action. We derive a lower bound on the data rate necessary to achieve the desired control cost. The lower bound is attained with equality if the control is performed via an additive white Gaussian channel. The system model approximates the dynamics of a discrete-state molecular birth-death process, and the result has direct implications on the control of a biomolecular system via chemical reactions, where the multiplicative control corresponds to the degradation rate, the additive control corresponds to the production rate, and the control objective is to decrease the fluctuations of the controlled molecular species around their desired concentration levels.

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arXiv2024

Towards a Theory of Control Architecture: A quantitative framework for layered multi-rate control

This paper focuses on the need for a rigorous theory of layered control architectures (LCAs) for complex engineered and natural systems, such as power systems, communication networks, autonomous robotics, bacteria, and human sensorimotor control. All deliver extraordinary capabilities, but they lack a coherent theory of analysis and design, partly due to the diverse domains across which LCAs can be found. In contrast, there is a core universal set of control concepts and theory that applies very broadly and accommodates necessary domain-specific specializations. However, control methods are typically used only to design algorithms in components within a larger system designed by others, typically with minimal or no theory. This points towards a need for natural but large extensions of robust performance from control to the full decision and control stack. It is encouraging that the successes of extant architectures from bacteria to the Internet are due to strikingly universal mechanisms and design patterns. This is largely due to convergent evolution by natural selection and not intelligent design, particularly when compared with the sophisticated design of components. Our aim here is to describe the universals of architecture and sketch tentative paths towards a useful design theory.

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arXiv2023

Predictive Control of Linear Discrete-Time Markovian Jump Systems by Learning Recurrent Patterns

Incorporating pattern-learning for prediction (PLP) in many discrete-time or discrete-event systems allows for computation-efficient controller design by memorizing patterns to schedule control policies based on their future occurrences. In this paper, we demonstrate the effect of PLP by designing a controller architecture for a class of linear Markovian jump systems (MJS) where the aforementioned ``patterns'' correspond to finite-length sequences of modes. In our analysis of recurrent patterns, we use martingale theory to derive closed-form solutions to quantities pertaining to the occurrence of patterns: 1) the expected minimum occurrence time of any pattern from some predefined collection, 2) the probability of a pattern being the first to occur among the collection. Our method is applicable to real-world dynamics because we make two extensions to common assumptions in prior pattern-occurrence literature. First, the distribution of the mode process is unknown, and second, the true realization of the mode process is not observable. As demonstration, we consider fault-tolerant control of a dynamic topology-switching network, and empirically compare PLP to two controllers without PLP: a baseline based on the novel System Level Synthesis (SLS) approach and a topology-robust extension of the SLS baseline. We show that PLP is able to reject disturbances as effectively as the topology-robust controller at reduced computation time and control effort. We discuss several important tradeoffs, such as the size of the pattern collection and the system scale versus the accuracy of the mode predictions, which show how different PLP implementations affect stabilization and runtime performance.

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arXiv2023

Internal feedback in the cortical perception-action loop enables fast and accurate behavior

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. This loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backwards, from motor towards sensory areas. Internal feedback is ubiquitous in neural sensorimotor systems and recent advances in control theory show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes in early sensory areas so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components. For example, fast, giant neurons are necessarily less accurate than smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function -- how different parts of cortex control different parts of the body -- and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological and behavioral observations, including motor signals in visual cortex, heterogeneous kinetics of sensory receptors and the presence of giant Betz cells in motor cortex, Meynert cells in visual cortex and giant von Economo cells in the prefrontal cortex of humans as well as internal feedback patterns and unexplained heterogeneity in other neural systems.

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arXiv2022

Distributed Robust Control for Systems with Structured Uncertainties

We present D-Phi iteration: an algorithm for distributed, localized, and scalable robust control of systems with structured uncertainties. This algorithm combines the System Level Synthesis (SLS) parametrization for distributed control with stability criteria from L1, LInf, and nu robust control. We show in simulation that this algorithm achieves good nominal performance while greatly increasing the robust stability margin compared to the LQR controller. To the best of our knowledge, this is the first distributed and localized algorithm for structured robust control; furthermore, algorithm complexity depends only on the size of local neighborhoods and is independent of global system size. We additionally characterize the suitability of different robustness criteria for distributed and localized computation.

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arXiv2022

Internal Feedback in Biological Control: Diversity, Delays, and Standard Theory

Neural architectures in organisms support efficient and robust control that is beyond the capability of engineered architectures. Unraveling the function of such architectures is challenging; their components are highly diverse and heterogeneous in their morphology, physiology, and biochemistry, and often obey severe speed-accuracy tradeoffs; they also contain many cryptic internal feedback pathways (IFPs). We claim that IFPs are crucial architectural features that strategically combine highly diverse components to give rise to optimal performance. We demonstrate this in a case study, and additionally describe how sensing and actuation delays in standard control (state feedback, full control, output feedback) give rise to independent and separable sources of IFPs. Our case study is an LQR problem with two types of sensors, one fast but sparse and one dense but slow. Controllers using only one type of sensor perform poorly, often failing even to stabilize; controllers using both types of sensors perform extremely well, demonstrating a strong diversity-enabled sweet spot (DESS). We demonstrate that IFPs are key in enabling this DESS, and additionally that with IFPs removed, controllers with delayed sensing perform poorly. The existence of strong DESS and IFP in this simple example suggest that these are fundamental architectural features in any complex system with diverse components, such as organisms and cyberphysical systems.

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arXiv2021

Internal Feedback in Biological Control: Architectures and Examples

Feedback is ubiquitous in both biological and engineered control systems. In biology, in addition to typical feedback between plant and controller, we observe feedback pathways within control systems, which we call internal feedback pathways (IFPs), that are often very complex. IFPs are most familiar in neural systems, our primary motivation, but they appear everywhere from bacterial signal transduction to the human immune system. In this paper, we describe these very different motivating examples and introduce the concepts necessary to explain their complex IFPs, particularly the severe speed-accuracy tradeoffs that constrain the hardware in biology. We also sketch some minimal theory for extremely simplified toy models that nevertheless highlight the importance of diversity-enabled sweet spots (DESS) in mitigating the impact of hardware tradeoffs. For more realistic models, standard modern and robust control theory can give some insights into previously cryptic IFPs, and the new System Level Synthesis theory expands this substantially. These additional theories explaining IFPs will be explored in more detail in several companion papers.

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arXiv2021

Online Robust Control of Nonlinear Systems with Large Uncertainty

Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system uncertainty, and thus require significant effort in system identification prior to controller design. We present an online approach that robustly controls a nonlinear system under large model uncertainty. Our approach is based on decomposing the problem into two sub-problems, "robust control design" (which assumes small model uncertainty) and "chasing consistent models", which can be solved using existing tools from control theory and online learning, respectively. We provide a learning convergence analysis that yields a finite mistake bound on the number of times performance requirements are not met and can provide strong safety guarantees, by bounding the worst-case state deviation. To the best of our knowledge, this is the first approach for online robust control of nonlinear systems with such learning theoretic and safety guarantees. We also show how to instantiate this framework for general robotic systems, demonstrating the practicality of our approach.

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arXiv2021

Diversity-enabled sweet spots in layered architectures and speed-accuracy trade-offs in sensorimotor control

Nervous systems sense, communicate, compute and actuate movement using distributed components with severe trade-offs in speed, accuracy, sparsity, noise and saturation. Nevertheless, brains achieve remarkably fast, accurate, and robust control performance due to a highly effective layered control architecture. Here we introduce a driving task to study how a mountain biker mitigates the immediate disturbance of trail bumps and responds to changes in trail direction. We manipulated the time delays and accuracy of the control input from the wheel as a surrogate for manipulating the characteristics of neurons in the control loop. The observed speed-accuracy trade-offs (SATs) motivated a theoretical framework consisting of layers of control loops with components having diverse speeds and accuracies within each physical level, such as nerve bundles containing axons with a wide range of sizes. Our model explains why the errors from two control loops -- one fast but inaccurate reflexive layer that corrects for bumps, and a planning layer that is slow but accurate -- are additive, and show how the errors in each control loop can be decomposed into the errors caused by the limited speeds and accuracies of the components. These results demonstrate that an appropriate diversity in the properties of neurons across layers helps to create "diversity-enabled sweet spots" (DESSs) so that both fast and accurate control is achieved using slow or inaccurate components.

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arXiv2021

Frontiers in Scalable Distributed Control: SLS, MPC, and Beyond

The System Level Synthesis (SLS) approach facilitates distributed control of large cyberphysical networks in an easy-to-understand, computationally scalable way. We present an overview of the SLS approach and its associated extensions in nonlinear control, MPC, adaptive control, and learning for control. To illustrate the effectiveness of SLS-based methods, we present a case study motivated by the power grid, with communication constraints, actuator saturation, disturbances, and changing setpoints. This simple but challenging case study necessitates the use of model predictive control (MPC); however, standard MPC techniques often scales poorly to large systems and incurs heavy computational burden. To address this challenge, we combine two SLS-based controllers to form a layered MPC-like controller. Our controller has constant computational complexity with respect to the system size, gives a 20-fold reduction in online computation requirements, and still achieves performance that is within 3% of the centralized MPC controller.

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arXiv2021

Descending Predictive Feedback: From Optimal Control to the Sensorimotor System

Descending predictive feedback (DPF) is an ubiquitous yet unexplained phenomenon in the central nervous system. Motivated by recent observations on motor-related signals in the visual system, we approach this problem from a sensorimotor standpoint and make use of optimal controllers to explain DPF. We define and analyze DPF in the optimal control context, revisiting several control problems (state feedback, full control, and output feedback) to explore conditions that necessitate DPF. We find that even small deviations from the unconstrained state feedback problem (e.g. incomplete sensing, communication delay) necessitate DPF in the optimal controller. We also discuss parallels between controller structure and observations from neuroscience. In particular, the system level (SLS) controller displays DPF patterns compatible with predictive coding theory and easily accommodates signaling restrictions (e.g. delay) typical to neurons, making it a candidate for use in sensorimotor modeling.

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arXiv2019

Fitts' Law for speed-accuracy trade-off describes a diversity-enabled sweet spot in sensorimotor control

Human sensorimotor control exhibits remarkable speed and accuracy, and the tradeoff between them is encapsulated in Fitts' Law for reaching and pointing. While Fitts related this to Shannon's channel capacity theorem, despite widespread study of Fitts' Law, a theory that connects implementation of sensorimotor control at the system and hardware level has not emerged. Here we describe a theory that connects hardware (neurons and muscles with inherent severe speed-accuracy tradeoffs) with system level control to explain Fitts' Law for reaching and related laws. The results supporting the theory show that diversity between hardware components is exploited to achieve both fast and accurate control performance despite slow or inaccurate hardware. Such "diversity-enabled sweet spots" (DESSs) are ubiquitous in biology and technology, and explain why large heterogeneities exist in biological and technical components and how both engineers and natural selection routinely evolve fast and accurate systems using imperfect hardware.

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arXiv2019

A System Level Approach to Controller Synthesis

Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance (QI). SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs, is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. The resulting System Level Synthesis (SLS) problems that arise define the broadest known class of constrained optimal control problems that can be solved using convex programming. An example illustrates how this system level approach can systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity.

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arXiv2019

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.

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arXiv2019

Scalable Robust Adaptive Control from the System Level Perspective

We will present a new general framework for robust and adaptive control that allows for distributed and scalable learning and control of large systems of interconnected linear subsystems. The control method is demonstrated for a linear time-invariant system with bounded parameter uncertainties, disturbances and noise. The presented scheme continuously collects measurements to reduce the uncertainty about the system parameters and adapts dynamic robust controllers online in a stable and performance-improving way. A key enabler for our approach is choosing a time-varying dynamic controller implementation, inspired by recent work on System Level Synthesis. We leverage a new robustness result for this implementation to propose a general robust adaptive control algorithm. In particular, the algorithm allows us to impose communication and delay constraints on the controller implementation and is formulated as a sequence of robust optimization problems that can be solved in a distributed manner. The proposed control methodology performs particularly well when the interconnection between systems is sparse and the dynamics of local regions of subsystems depend only on a small number of parameters. As we will show on a five-dimensional exemplary chain-system, the algorithm can utilize system structure to efficiently learn and control the entire system while respecting communication and implementation constraints. Moreover, although current theoretical results require the assumption of small initial uncertainties to guarantee robustness, we will present simulations that show good closed-loop performance even in the case of large uncertainties, which suggests that this assumption is not critical for the presented technique and future work will focus on providing less conservative guarantees.

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arXiv2019

WheelCon: A wheel control-based gaming platform for studying human sensorimotor control

Feedback control theory has been extensively implemented to theoretically model human sensorimotor control. However, experimental platforms capable of manipulating important components of multiple feedback loops lack development. This paper describes the WheelCon, which is an open source platform aimed at resolving such insufficiencies. WheelCon enables safely simulation of the canonical sensorimotor task such as riding a mountain bike down a steep, twisting, bumpy trail etc., with provided only a computer, standard display, and an inexpensive gaming steering wheel with a force feedback motor. The platform provides flexibility, as will be demonstrated in the demos provided, so that researchers may manipulate the disturbances, delay, and quantization (data rate) in the layered feedback loops, including a high-level advanced plan layer and a low-level delayed reflex layer. In this paper, we illustrate WheelCon's graphical user interface (GUI), the input and output of existing demos, and how to design new games. In addition, we present the basic feedback model, and we show the testing results from our demo games which align well with prediction from the model. In short, the platform is featured as cheap, simple to use, and flexible to program for effective sensorimotor neuroscience research and control engineering education.

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arXiv2018

Passive-Aggressive Learning and Control

In this work, we investigate the problem of simultaneously learning and controlling a system subject to adversarial choices of disturbances and system parameters. We study the problem for a scalar system with $l_\infty$-norm bounded disturbances and system parameters constrained to lie in a known bounded convex polytope. We present a controller that is globally stabilizing and gives continuously improving bounds on the worst-case state deviation. The proposed controller simultaneously learns the system parameters and controls the system. The controller emerges naturally from an optimization problem and balances exploration and exploitation in such a way that it is able to efficiently stabilize unstable and adversarial system dynamics. Specifically, if the controller is faced with large uncertainty, the initial focus is on exploration, retrieving information about the system by applying state-feedback controllers with varying gains and signs. In a pre-specified bounded region around the origin, our control strategy can be seen as passive in the sense that it learns very little information. Only once the noise and/or system parameters act in an adversarial way, leading to the state exiting the aforementioned region for more than one time-step, our proposed controller behaves aggressively in that it is guaranteed to learn enough about the system to subsequently robustly stabilize it. We end by demonstrating the efficiency of our methods via numerical simulations.

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