Optimal local and remote controllers with unreliable communication

Ouyang, Yuanxin; Asghari, Seyed Mohammad; Nayyar, Ashutosh

doi:10.1109/cdc.2016.7799194

Cited by 21 publications

(17 citation statements)

References 32 publications

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“…One can follow the argument of[1, Lemma 1] to see that the results of this paper hold for anyH 1 t = H 0 t ∪Ĥ 1 t where {X 1 t , M 1 t } ⊆Ĥ 1 t ⊆ {X 1 0:t , M 1 0:t , U 1 0:t−1 }. For simplicity of presentation, we restrict toĤ 1 t = {X 1 t , M 1 t }.The instantaneous cost c t (X 0:1 t , M 0:1 t , U 0:1 t ) of the system is a quadratic function given byc t (X 0:1 t , M 0:1 t , U 0:1 t ) = X ⊺ t Q t (M 0:1 t )X t + U ⊺ t R t (M 0:1 t )U t ,(9)…”

mentioning

confidence: 79%

“…Hence, they can be chosen arbitrarily or set to be zero as described in (25) and (26). Since H t (m 0 t , l) is PD, it follows from [1,Lemma 4] that the optimal solution of (102) is given by (24) and…”

Section: Appendix VI Proof Of Theoremmentioning

confidence: 99%

“…Consequently, in order to solve the optimization problem in the (101), we need to solve the two optimization problemsmin u 0 t ∈R d 0 U ,qt∈Q QF Ht(m 0 t , ∅),S θt t ,(102)miñ qt∈Q(θt) m 1 t ∈M 1 tr π M 1 (m 1 t )Ht(m 0:1 t ) cov(S θt,m 1 t t )(103)Since H t (m 0 t ,z t ) is PD, it follows from [1, Lemma 4] that the optimal solution of (102) is given by(22) andmin u 0 t ∈R d 0 U ,qt∈Q QF Ht(m 0 t , ∅),S θt t = QF Pt(m 0 t , ∅), vec x 0 t , µ(θt) . (104) Furthermore, P t (m 0 , ∅) is PSD because it is Schur complement of H t (m 0 ,z) with respect to H UU t (m 0 , ∅).Similarly, sinceH t (m 0:1 t ) is also PD, from[1, Lemma 4], the optimal solution of (103) is given by(26) andmiñ qt∈Q(θt) m 1 t ∈M 1 tr π M 1 (m 1 t )Ht(m 0:1 t ) cov(S θt,m 1 t t ) m 1 t ∈M 1 miñ qt(·,m 1 t ): qt(x 1 t ,m 1 t )θt(dx 1 t )=0tr π M 1 (m 1 t )Ht(m 0:1 t ) cov(S θt,m 1 t t…”

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confidence: 98%

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Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

Asghari

Ouyang

Nayyar

2018

2018 Annual American Control Conference (ACC)

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We consider a networked control system (NCS) consisting of two plants, a global plant and a local plant, and two controllers, a global controller and a local controller. The global (resp. local) plant follows discrete-time stochastically switched linear dynamics with a continuous global (resp. local) state and a discrete global (resp. local) mode. We assume that the state and mode of the global plant are observed by both controllers while the state and mode of the local plant are only observed by the local controller. The local controller can inform the global controller of the local plant's state and mode through an unreliable TCP-like communication channel where successful transmissions are acknowledged. The objective of the controllers is to cooperatively minimize a modes-dependent quadratic cost over a finite time horizon. Following the method developed in [1] and [2], we construct a dynamic program based on common information and a decomposition of strategies, and use it to obtain explicit optimal strategies for the controllers. In the optimal strategies, both controllers compute a common estimate of the local plant's state. The global controller's action is linear in the state of the global plant and the common estimated state, and the local controller's action is linear in the actual states of both plants and the common estimated state. Furthermore, the gain matrices for the global controller depend on the global mode and its observation about the local mode, while the gain matrices for the local controller depend on the actual modes of both plants and the global controller's observation about the local mode.

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confidence: 79%

Section: Appendix VI Proof Of Theoremmentioning

confidence: 99%

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confidence: 98%

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Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

Asghari

Ouyang

Nayyar

2018

2018 Annual American Control Conference (ACC)

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“…Each subproblem is a special case of Problem 1. Problems with one local and one remote controller were also investigated in our prior work [1].…”

Section: Special Cases 1) No Control Action For Some Controllersmentioning

confidence: 99%

Optimal Local and Remote Controllers With Unreliable Uplink Channels

Asghari

Ouyang

Nayyar

2019

IEEE Trans. Automat. Contr.

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We consider a networked control system consisting of a remote controller and a collection of linear plants, each associated with a local controller. Each local controller directly observes the state of its co-located plant and can inform the remote controller of the plant's state through an unreliable uplink channel. We assume that the downlink channels from the remote controller to local controllers are perfect. The objective of the local controllers and the remote controller is to cooperatively minimize a quadratic performance cost. We provide a dynamic program for this decentralized control problem using the common information approach. Although our problem is not a partially nested problem, we obtain explicit optimal strategies for all controllers. In the optimal strategies, all controllers compute common estimates of the states of the plants based on the common information obtained from the communication network. The remote controller's action is linear in the common state estimates, and the action of each local controller is linear in both the actual state of its co-located plant and the common state estimates.We illustrate our results with numerical experiments using randomly generated models. Contributions of the PaperThe main contributions of the paper are as follows.1) We investigate a decentralized stochastic control problem in which local controllers send their information to a remote controller over unreliable links. To the best of our knowledge, this is the first paper that solves an optimal decentralized control problem with unreliable communication between controllers (in contrast to problems in networked control systems and remote estimation problems where the unreliable communication is between sensors/encoders and controller or between controllers and actuators).2) The information structure of our problem is not partially nested, hence we cannot a priori restrict to linear strategies for optimal control. We use ideas from the common information approach of [43] to compute optimal controllers. Since the state and action spaces of our problem are Euclidean spaces, the results and arguments of [43] for finite spaces cannot be directly applied. We provide a complete set of results to adapt the common information approach to our linear-quadratic setting with non-partially nested information structure.Our rigorous proofs carefully handle the issues of measurability constraints, the existence of well-defined value functions and infinite dimensional strategy spaces.3) We show that the optimal control strategies of this problem admit simple structures-the optimal remote control is linear in the common estimates of system states and each optimal local control is linear in both the common estimates of system states and the perfectly observed local state. The main strengths of our result are that (i) it provides a simple strategy that is proven to be optimal: not only is the strategy in Theorem 3 linear, it uses estimates that can be easily updated; (ii) it provides a tractable way of computing the gain ma...

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“…For such systems, existing work has mainly focused on identifying specific dynamics and information structures that yield tractable strategies [9], [10]. For systems with linear dynamics, quadratic costs and Gaussian noise (LQG), variations of the partially nested property have been used to derive optimal control actions as functions of expected value of the state at each time step [6], [18].…”

Section: Introductionmentioning

confidence: 99%

Decentralized Control of Two Agents with Nested Accessible Information

Dave¹,

Nishanth²,

Malikopoulos³

2021

Preprint

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We investigate a decentralized stochastic control problem with two agents, where a part of the memory of the second agent is always available to the first agent. We derive a structural form for optimal control strategies that allows us to restrict their domain to a set that does not grow in size with time, and subsequently, utilize them for systems with arbitrarily long time horizons. We utilize our results to present a common information based dynamic program (DP). However, we observe that it is computationally challenging to use this DP to derive control strategies because they are functions of a vector of probability mass functions. Thus, we present simplified strategies for a special case of our model, and an approximation technique that can be used to implement our results by trading a gain in computational tractability with a loss in optimality.

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Optimal local and remote controllers with unreliable communication

Cited by 21 publications

References 32 publications

Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

Optimal Local and Remote Controllers With Unreliable Uplink Channels

Decentralized Control of Two Agents with Nested Accessible Information

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