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").

On November 28--29, 2023, Northwestern University hosted a workshop titled "Towards Re-architecting Today's Internet for Survivability" in Evanston, Illinois, US. The goal of the workshop was to bring together a group of national and international experts to sketch and start implementing a transformative research agenda for solving one of our community's most challenging yet important tasks: the re-architecting of tomorrow's Internet for "survivability", ensuring that the network is able to fulfill its mission even in the presence of large-scale catastrophic events. This report provides a necessarily brief overview of two full days of active discussions.

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 (MJSs) 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. To make our method applicable to real-world dynamics, 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 just 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.

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 demonstrate FEC can capture metabolism dynamics from network structure. More generally, FEC brings metabolic dynamics to the realm of control system analysis and design.

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.

We develop convex parameterizations for ℒ 1 -robust controllers in the System Level Synthesis (SLS) framework, allowing us to find robust decentralized controllers that preserve design constraints on sparsity, locality, and delay. The parameterizations have interpretable relationships with the set of nominally stabilizing SLS controllers. We show that the state feedback robust performance SLS problem can be posed exactly and end-to-end as a linear program applicable to large-scale distributed control. We generalize these results to unstructured uncertainties in the output feedback setting, providing new decentralized robust performance guarantees in this setting.

We present D-Φ 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 ${\mathcal{L}_1},{\mathcal{L}_\infty }$, and ν 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.

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

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.

We present a new, scalable alternative to the structured singular value, which we call v, provide a convex upper bound, study their properties and compare them to l 1 robust control. The analysis relies on a novel result on the relationship between robust control of dynamical systems and non-negative constant matrices.

The past year unfortunately highlighted intrinsic and systemic unsustainability and fragilities in our society and technologies.While detailed mechanisms underlying "systemic fragilities" in immune, medical, computing, social, legal, energy, and transportation systems are incredibly diverse, all are enabled by shared universal features of their architectures, which are largely ad hoc historical artifacts.AI has many well-known fragilities, but outside social media has not so far contributed substantially to the catastrophes unfolding in these systems.This is poised to change dramatically.We need to more systematically design architectures that produce more robust and sustainable systems, including allowing higher layer learning and lower layer efficiencies to contribute.I'll sketch the basic concepts of laws, layers, levels, speed-efficiencyaccuracy-flexibility tradeoffs (SEAFTs), diversity-enable sweet spots (DeSS), how crucial hardware layer constraints on sparsity, locality, and delay limit system layer functionality, and how proper layering can mitigate this via DeSS.Examples include all our tech nets, layered brains (e.g., throwing and hitting 100mph fastballs), layered immunity augmented by medicine and policy (and insights into the current pandemic), systemic legal fragilities and the 14th amendment, cascading failures in energy, climate change, language and its hijacking in social media, encouraging animal models for social architectures, and wildfire ecosystems.

Intercommunication of the microbiome-gut-brain axis occurs through various signaling pathways including the vagus nerve, immune system, endocrine/paracrine, and bacteria-derived metabolites. But how these pathways integrate to influence cognition remains undefined. In this paper, we create a systems level mathematical framework comprised of interconnected organ-level dynamical subsystems to increase conceptual understanding of how these subsystems contribute to cognitive performance. With this framework we propose that control of hippocampal long-term potentiation (hypothesized to correlate with cognitive performance) is influenced by interorgan signaling with diet as the external control input. Specifically, diet can influence synaptic strength (LTP) homeostatic conditions necessary for learning. The proposed model provides new qualitative information about the functional relationship between diet and output cognitive performance. The results can give insight for optimization of cognitive performance via diet in experimental animal models.

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.

The presence of internal feedback pathways (IFP) is an ubiquitous yet unexplained phenomenon in the brain. Motivated by experimental observations on 1) motor-related signals in visual areas, and 2) massively distributed processing in the brain, we approach this problem from a sensorimotor standpoint and make use of distributed optimal controllers to explain IFP. We use the System Level Synthesis (SLS) controller to model neuronal phenomena such as signaling delay, local processing, and local reaction. Based on the SLS controller, we make qualitative theoretical predictions about IFP that has strong alignment with experimental and imaging studies. In particular, we introduce a necessary `mesocircuit' for optimal performance with distributed and local processing, and local disturbance rejection; this `mesocircuit' requires extreme amounts of IFP and memory for proper function. This is the first theory that can replicate the massive amounts of IFP in the brain purely from a priori principles, providing a new and promising theoretical basis upon which we can build to better understand the inner workings of the brain.

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.

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.

Dramatic variation in SARS-CoV-2 virulence and transmission between hosts has driven the COVID-19 pandemic. The complexity and dynamics of the immune response present a challenge to understanding variation in SARS-CoV-2 infections. To address this challenge, we apply control theory, a framework used to study complex feedback systems, to establish rigorous mathematical bounds on immune responses. Two mechanisms of SARS-CoV-2 biology are sufficient to create extreme variation between hosts: (1) a sparsely expressed host receptor and (2) potent, but not unique, suppression of interferon. The resulting model unifies disparate and unexplained features of the SARS-CoV-2 pandemic, predicts features of future viruses that threaten to cause pandemics, and identifies potential interventions.

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building control through such structures. In this work, we show that log derivatives can capture the structural regimes of biocircuits in regulating the production and degradation rates of molecules. We show that log derivatives can establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through structure. Due to the method's simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations.