Localized LQR optimal control

2015 54th IEEE Conference on Decision and Control (CDC)

2015

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The modern view of the nervous system as layering distributed computation and communication for the purpose of sensorimotor control and homeostasis has much experimental evidence but little theoretical foundation, leaving unresolved the connection between diverse components and complex behavior. As a simple starting point, we address a fundamental tradeoff when robust control is done using communication with both delay and quantization error, which are both extremely heterogeneous and highly constrained in human and animal nervous systems. This yields surprisingly simple and tight analytic bounds with clear interpretations and insights regarding hard tradeoffs, optimal coding and control strategies, and their relationship with well known physiology and behavior. These results are similar to reasoning routinely used informally by experimentalists to explain their findings, but very different from those based on information theory and statistical physics (which have dominated theoretical neuroscience). The simple analytic results and their proofs extend to more general models at the expense of less insight and nontrivial (but still scalable) computation. They are also relevant, though less dramatically, to certain cyber-physical systems.

Section: Additional Readingmentioning

confidence: 96%

Hard limits on robust control over delayed and quantized communication channels with applications to sensorimotor control

Nakahira

Matni

2015 54th IEEE Conference on Decision and Control (CDC)

2015

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“…Remark 8: The dimension reduction algorithm proposed here is a generalization of the algorithms proposed in our prior works [1], [3]. Specifically, the algorithms in [1], [3] only work for a particular type of locality constraint (called the d-localized constraint), while the algorithm proposed here can handle arbitrary sparsity constraints.…”

Section: Appendix a Dimension Reduction Algorithmmentioning

confidence: 99%

“…We then show that if additional locality (sparsity) constraints are imposed, then these subproblems can be solved in a localized way. We show that such locality and separability conditions are satisfied by many problems of interest, such as the Localized LQR (LLQR) and Localized Distributed Kalman Filter (LDKF) [1], [2]. We then introduce the weaker notion of partially separable objectives and constraints sets, and show that this allows for iterate subproblems of distributed optimization techniques such as the alternating direction method of multipliers (ADMM) [23] to be solved via parallel computation.…”

Section: Introductionmentioning

confidence: 99%

Separable and Localized System-Level Synthesis for Large-Scale Systems

Wang

Matni

IEEE Trans. Automat. Contr.

2018

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105

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, H2 optimal control with joint actuator and sensor regularization, and (localized) mixed H2/L1 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.

“…Nevertheless, recent progress has Dimitar Ho and John C. Doyle are with the Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA. dho@caltech.edu, doyle@caltech.edu been made by taking a new System Level approach [1], [7], [8], that allows to incorporate such constraints into optimal control problems in a tractable way. Aside from that, recent work [9], [4] has shown that the ideas in [8] can be used to provide robustness results that help to combine learning and control techniques with stability guarantees.…”

Section: Introductionmentioning

confidence: 99%

Scalable Robust Adaptive Control from the System Level Perspective

2019 American Control Conference (ACC)

2019

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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 [1]. 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 fivedimensional 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 closedloop 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.Corresponding to (Const.2), let's define R(i) to be the set of subsystems from which subsystem i receives information:Definition III.1. R(i) := {j |i ∈ S(j) } Constraint 3 (Limited Computation). Every subsystem j has limited computational resources.