Localized LQG optimal control for large-scale systems

Wang, Yuh-Shyang; Matni, Nikolai

doi:10.1109/acc.2016.7525205

Cited by 35 publications

(31 citation statements)

References 13 publications

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“…Example 20: Consider the LLQG problem proposed in [3]. When the global optimization problem is decomposed into parallel subproblems, each subproblem is a convex quadratic program restricted to an affine set.…”

Section: Analytic Solution and Accelerationmentioning

confidence: 99%

“…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%

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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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Section: Analytic Solution and Accelerationmentioning

confidence: 99%

Section: Appendix a Dimension Reduction Algorithmmentioning

confidence: 99%

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

Wang

Matni

Doyle

2018

IEEE Trans. Automat. Contr.

Self Cite

105

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show abstract

“…Given this equality, we can find that ARE(A, B 2 P T u P u , C 1 , P T u P u D T 12 D 12 P T u P u ) = X, ARE(A T , C T 2 P T y P y , B T 1 , P T y P y D 21 D T 21 P T y P y ) = Y, from which it can be verified that the state space solution of (29) is same as K opt from Theorem 3.3. Therefore, (29) is equivalent to (12).…”

Section: Proof Of Lemma 52mentioning

confidence: 99%

Hierarchical $\mathcal{H}_{2}$ Control of Large-Scale Network Dynamic Systems

Xue

Chakrabortty

2018

2018 Annual American Control Conference (ACC)

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Standard H2 optimal control of networked dynamic systems tend to become unscalable with network size. Structural constraints can be imposed on the design to counteract this problem albeit at the risk of making the solution nonconvex. In this paper, we present a special class of structural constraints such that the H2 design satisfies a quadratic invariance condition, and therefore can be reformulated as a convex problem. This special class consists of structured and weighted projections of the input and output spaces. The choice of these projections can be optimized to match the closedloop performance of the reformulated controller with that of the standard H2 controller. The advantage is that unlike the latter, the reformulated controller results in a hierarchical implementation which requires significantly lesser number of communication links, while also admitting model and controller reduction that helps the design to scale computationally. We illustrate our design with simulations of a 500-node network.

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“…Theorem 1 (Structural Recovery) Fix a horizon 1 ≤ t < ∞, and a controller order 1 ≤ v ≤ t such that Assumption 1 holds. If (40) we have thatÛ as defined in (30) is the unique optimal solution to (29), and that the row support ofÛ is contained within the row support of U * . Further if A ∈ M * and…”

Section: Sufficient Conditions For Recoverymentioning

confidence: 99%

“…In order to allow the RFD framework, and distributed optimal control theory in general, to scale to large heterogeneous systems, the first author and co-authors have developed the localized optimal control framework (cf. [40] and references therein). The algorithmic component of the RFD framework has already been ported [41]; it is of interest to see if analogous recovery conditions can also be developed.…”

Section: Future Workmentioning

confidence: 99%

Regularization for design

Matni

Chandrasekaran

2014

53rd IEEE Conference on Decision and Control

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When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given. The task of designing this architecture is now as important as the design of the control laws themselves. By interpreting controller synthesis (in a model matching setup) as the solution of a particular linear inverse problem, we view the challenge of obtaining a controller with a desired architecture as one of finding a structured solution to an inverse problem. Building on this conceptual connection, we formulate and analyze a framework called Regularization for Design (RFD), in which we augment the variational formulations of controller synthesis problems with convex penalty functions that induce a desired controller architecture. The resulting regularized formulations are convex optimization problems that can be solved efficiently; these convex programs provide a unified computationally tractable approach for the simultaneous co-design of a structured optimal controller and the actuation, sensing and communication architecture required to implement it. Further, these problems are natural control-theoretic analogs of prominent approaches such as the Lasso, the Group Lasso, the Elastic Net, and others that are employed in statistical modeling. In analogy to that literature, we show that our approach identifies optimally structured controllers under a suitable condition on a "signal-to-noise" type ratio. * N. Matni is with the

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Localized LQG optimal control for large-scale systems

Cited by 35 publications

References 13 publications

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

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

Hierarchical $\mathcal{H}_{2}$ Control of Large-Scale Network Dynamic Systems

Regularization for design

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