Localized LQR control with actuator regularization

Wang, Yuh-Shyang; Matni, Nikolai; Doyle, John C.

doi:10.1109/acc.2016.7526485

Cited by 21 publications

(29 citation statements)

References 18 publications

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“…In Section III we define and analyze SLPs for state and output feedback problems, and provide a novel characterization of stable closed loop system responses and the controllers that achieve them -the corresponding controller realization makes clear that SLCs imposed on the system responses carry over to the internal structure of the controller that achieves them. In Section IV, we provide a catalog of SLCs that can be imposed on the system responses parameterized by the SLPs described in the previous section -in particular, we show that by appropriately selecting these SLCs, we can provide convex characterizations of all stabilizing controllers satisfying QI subspace constraints, convex constraints on the Youla parameter, finite impulse response (FIR) constraints, sparsity constraints, spatiotemporal constraints [1]- [4], controller internal robustness constraints, multi-objective performance constraints, controller architecture constraints [5], [40], [41], and any combination thereof. In Section V, we define and analyze the SLS problem, which incorporates SLPs and SLCs into an optimal control problem, and show that the distributed optimal control problem ( 5in Section II-C) is a special case of SLS.…”

Section: B Paper Structurementioning

confidence: 99%

“…In the references cited above, locally acquired measurements are exchanged between subcontrollers subject to delays imposed by the communication network, 4 which manifest as subspace constraints on the controller itself. 5 Let C be a subspace enforcing the information sharing constraints imposed on the controller K. A distributed optimal control problem can then be formulated as [21], [30], [43], [44]:…”

Section: Structured Controller Synthesis and Qimentioning

confidence: 99%

“…As we discuss in our companion paper [47], the idea of locality is essential to allowing controller synthesis and implementation to scale to arbitrarily large systems, and hence such a structured controller is desirable. Now suppose that we naively attempt to solve optimal control problem (30) by converting it to its equivalent H 2 model matching problem (5) and constraining the controller K to have the same support as A, i.e., K =…”

Section: Beyond Qimentioning

confidence: 99%

“…Indeed, selecting an appropriate (feasible) localized SLC, as defined by the subspace L, is a subtle task: it depends on an interplay between actuator and sensor density, information exchange delay and disturbance propagation delay. Formally defining and analyzing a procedure for designing a localized SLC is beyond the scope of this paper: as such, we refer the reader to our recent paper [5], in which we present a method that allows for the joint design of an actuator architecture and corresponding feasible localized SLC.…”

Section: Subspace and Sparsity Constraintsmentioning

confidence: 99%

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A System-Level Approach to Controller Synthesis

Wang

Matni

Doyle

2019

IEEE Trans. Automat. Contr.

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139

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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. Index Terms-constrained & structured optimal control, decentralized control, large-scale systems, system level parameterization, system level constraint, system level synthesis Preliminaries & Notation: We use lower and upper case Latin letters such as x and A to denote vectors and matrices, respectively, and lower and upper case boldface Latin letters such as x and G to denote signals and transfer matrices, respectively. We use calligraphic letters such as S to denote sets. In the interest of clarity, we work with discrete time linear time invariant systems, but unless stated otherwise, all results extend naturally to the continuous time setting. We use standard definitions of the Hardy spaces H 2 and H ∞ , and denote their restriction to the set of real-rational proper transfer matrices by RH 2 and RH ∞. We use G[i] to denote the ith spectral component of a transfer function G, i.e., G(z) = ∞ i=0 1 z i G[i] for |z| > 1. Finally, we use F T to denote the space of finite impulse response (FIR) transfer matrices with horizon T , i.e., F T := {G ∈ RH ∞ | G = T i=0 1 z i G[i]}.

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Section: B Paper Structurementioning

confidence: 99%

Section: Structured Controller Synthesis and Qimentioning

confidence: 99%

Section: Beyond Qimentioning

confidence: 99%

Section: Subspace and Sparsity Constraintsmentioning

confidence: 99%

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A System-Level Approach to Controller Synthesis

Wang

Matni

Doyle

2019

IEEE Trans. Automat. Contr.

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139

271

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“…We plot the normalized H 2 norm and the normalized L 1 norm in Figure 7. 4 The left-top point in Figure 7 is the localized H 2 solution. When we start reducing the L 1 sublevel set, the H 2 norm of the closed loop response gradually increases, thus tracing out a tradeoff curve.…”

Section: Localized Mixed H 2 /L 1 Optimal Controlmentioning

confidence: 99%

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

Wang

Matni

Doyle

2018

IEEE Trans. Automat. Contr.

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105

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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.

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