arXiv subjects

Jing Shuang Li

Publications and source records attributed to Jing Shuang Li.

27 records · Page 2Linked to original sources

arXiv2022

Internal Feedback in Biological Control: Locality and System Level Synthesis

The presence of internal feedback pathways (IFPs) is a prevalent 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 IFPs. We use the System Level Synthesis (SLS) controller to model neural phenomena such as signaling delay, local processing, and local reaction. Based on the SLS controller, we make qualitative predictions about IFPs that strongly align with existing experimental observations. We introduce a `mesocircuit' for optimal performance with distributed and local processing, and local disturbance rejection; this mesocircuit requires extreme amounts of IFPs and memory for proper function. This is the first theory that replicates the massive amounts of IFPs in the brain purely from a priori principles, providing a new theoretical basis upon which we can build to better understand the inner workings of the brain.

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arXiv2022

Distributed and Localized Model Predictive Control. Part I: Synthesis and Implementation

The increasing presence of large-scale distributed systems highlights the need for scalable control strategies where only local communication is required. Moreover, in safety-critical systems it is imperative that such control strategies handle constraints in the presence of disturbances. In response to this need, we present the Distributed and Localized Model Predictive Control (DLMPC) algorithm for large-scale linear systems. DLMPC is a distributed closed-loop model predictive control (MPC) scheme wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We use the System Level Synthesis (SLS) framework to reformulate the centralized MPC problem, and show that this allows us to naturally impose localized communication constraints between sub-controllers. The structure of the resulting problem can be exploited to develop an Alternating Direction Method of Multipliers (ADMM) based algorithm that allows for distributed and localized computation of closed-loop control policies. We demonstrate that computational complexity of the subproblems solved by each subsystem in DLMPC is independent of the size of the global system. To the best of our knowledge, DLMPC is the first MPC algorithm that allows for the scalable distributed computation as well as implementation of distributed closed-loop control policies, and seemingly deals with additive disturbances. In our companion paper, we show that this approach enjoys recursive feasibility and asymptotic stability.

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arXiv2022

Distributed and Localized Model Predictive Control. Part II: Theoretical Guarantees

Engineered cyberphysical systems are growing increasingly large and complex. These systems require scalable controllers that robustly satisfy state and input constraints in the presence of additive noise -- such controllers should also be accompanied by theoretical guarantees on feasibility and stability. In our companion paper, we introduced Distributed and Localized Model Predictive Control (DLMPC) for large-scale linear systems; DLMPC is a scalable closed-loop MPC scheme in which subsystems need only exchange local information in order to synthesize and implement local controllers. In this paper, we provide recursive feasibility and asymptotic stability guarantees for DLMPC. We leverage the System Level Synthesis framework to express the maximal positive robust invariant set for the closed-loop system and its corresponding Lyapunov function, both in terms of the closed-loop system responses. We use the invariant set as the terminal set for DLMPC, and show that this guarantees feasibility with minimal conservatism. We use the Lyapunov function as the terminal cost, and show that this guarantees stability. We provide fully distributed and localized algorithms to compute the terminal set offline, and also provide necessary additions to the online DLMPC algorithm to accommodate coupled terminal constraint and cost. In all algorithms, only local information exchanges are necessary, and computational complexity is independent of the global system size -- we demonstrate this analytically and experimentally. This is the first distributed MPC approach that provides minimally conservative yet fully distributed guarantees for recursive feasibility and asymptotic stability, for both nominal and robust settings.

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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

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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arXiv2021

Robust Distributed and Localized Model Predictive Control

We present a robust Distributed and Localized Model Predictive Control (rDLMPC) framework for large-scale structured linear systems. The proposed algorithm uses the System Level Synthesis to provide a distributed closed-loop model predictive control scheme that is robust to exogenous disturbances. The resulting controllers require only local information exchange for both synthesis and implementation. We exploit the fact that for polytopic disturbance constraints, SLS- based distributed control problems have been shown to have structure amenable for distributed optimization techniques. We show that similar to the disturbance-free DLMPC algorithm, the computational complexity of rDLMPC is independent of the size of the global system. To the best of our knowledge, robust DLMPC is the first MPC algorithm that allows for the scalable distributed computation of distributed closed-loop control policies in the presence of additive disturbances.

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arXiv2020

SLSpy: Python-Based System-Level Controller Synthesis Framework

Synthesizing controllers for large, complex, and distributed systems is a challenging task. Numerous proposed methods exist in the literature, but it is difficult for practitioners to apply them -- most proposed synthesis methods lack ready-to-use software implementations, and existing proprietary components are too rigid to extend to general systems. To address this gap, we develop SLSpy, a framework for controller synthesis, comparison, and testing. SLSpy implements a highly extensible software framework which provides two essential workflows: synthesis and simulation. The workflows are built from five conceptual components that can be customized to implement a wide variety of synthesis algorithms and disturbance tests. SLSpy comes pre-equipped with a workflow for System Level Synthesis (SLS), which enables users to easily and freely specify desired design objectives and constraints. We demonstrate the effectiveness of SLSpy using two examples that have been described in the literature but do not have ready-to-use implementations. We open-source SLSpy to facilitate future controller synthesis research and practical usage.

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arXiv2020

Separating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis

We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints. We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller.

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