John C. Doyle

Cell proliferation is necessary to maintain tissue homeostasis, but proliferation carries with it a risk of cancer. To understand how some organisms suppress cancer while maintaining homeostasis, we developed a dynamical model of cell populations. The model identifies two regimes. In one regime, as expected, proliferation drives accumulation of neoplastic cells. In another regime, unexpectedly, increasing proliferation suppresses accumulation of neoplastic cells. In this regime, as more cells proliferate, more cells also die as a consequence of homeostatic feedback. As long as neoplastic cells are targeted preferentially, the high flux effectively acts as a proofreader. High-flux proofreading works even when the system lacks a highly specific detector of neoplastic cells. As a first experimental test, we examined the jellyfish. Neoplasms are rarely observed in cnidarians, yet simply inhibiting proliferation promotes neoplasms. The quantitative framework developed here offers experimentally testable predictions to assess high-flux proofreading in other systems.

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.

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.

Human sensorimotor control is remarkably fast and accurate at the system level despite severe speed-accuracy trade-offs at the component level. The discrepancy between the contrasting speed-accuracy trade-offs at these two levels is a paradox. Meanwhile, speed accuracy trade-offs, heterogeneity, and layered architectures are ubiquitous in nerves, skeletons, and muscles, but they have only been studied in isolation using domain-specific models. In this article, we develop a mechanistic model for how component speed-accuracy trade-offs constrain sensorimotor control that is consistent with Fitts’ law for reaching. The model suggests that diversity among components deconstrains the limitations of individual components in sensorimotor control. Such diversity-enabled sweet spots (DESSs) are ubiquitous in nature, explaining why large heterogeneities exist in the components of biological systems and how natural selection routinely evolves systems with fast and accurate responses using imperfect components.

Complex engineered and natural control systems, such as those used in robotics, the power grid, human sensorimotor control, and the Internet, are characterized by needing to operate robustly and reliably across many spatiotemporal scales despite being implemented using highly constrained hardware and software. Remarkably, a universal design pattern centered around layered control architectures ( LCAs ) has emerged to address these challenges across vastly different domains. These LCAs are the central object of study of this article (see “Summary”).

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.

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control, drawing on control theory, 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. However, the sensorimotor 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 backward, from motor toward sensory areas. This internal feedback is ubiquitous in neural sensorimotor systems, and we show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components, effectively compressing the sensory input to more efficiently use feedforward pathways: Tracts of fast, giant neurons necessarily convey less accurate signals than tracts with many 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 the 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 the visual cortex, heterogeneous kinetics of sensory receptors, and the presence of giant cells in the cortex of humans as well as internal feedback patterns and unexplained heterogeneity in neural systems.

Metabolic dynamics such as stability of steady states, oscillations, lags and growth arrests in stress responses are important for microbial communities in human health, ecology, and metabolic engineering. Yet it is hard to model due to sparse data available on trajectories of metabolic fluxes. For this reason, a constraint-based approach called flux control (e.g., flux balance analysis) was invented to split metabolic systems into known stoichiometry (plant) and unknown fluxes (controller), so that data can be incorporated as refined constraints, and optimization can be used to find behaviors in scenarios of interest. However, flux control can only capture steady state fluxes well, limiting its application to scenarios with days or slower timescales. To overcome this limitation and capture dynamic fluxes, this work proposes a novel constraint-based approach, flux exponent control (FEC). FEC uses a different plant-controller split between the activities of catalytic enzymes and their regulation through binding reactions. Since binding reactions effectively regulate fluxes’ exponents (from previous works), this yields the rule of FEC, that cells regulate fluxes’ exponents, not the fluxes themselves as in flux control. In FEC, dynamic regulations of metabolic systems are solutions to optimal control problems that are computationally solvable via model predictive control. Glycolysis, which is known to have minute-timescale oscillations, is used as an example to demon-strate FEC can capture metabolism dynamics from network structure. More generally, FEC brings metabolic dynamics to the realm of control system analysis and design.

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.

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.