A team theoretic approach to decentralized control of systems with stochastic parameters

Mishra, Anshuman; Langbort, Cédric; Dullerud, Geir E.

doi:10.1109/cdc.2012.6425872

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…There have been some studies in developing stopping criteria but these studies require global knowledge of the system [41,42]. Recently, there has been an attempt for designing optimal controllers using only local model information for linear systems with stochastically-varying parameters [43]. However, that setup is completely different from the problem that is considered in this paper.…”

Section: Related Studiesmentioning

confidence: 99%

“…However, that setup is completely different from the problem that is considered in this paper. First, the authors of [43] considered the case where the B-matrix was parameterized with stochastic variables but in our setup the A-matrix is assumed to be stochastic. Additionally, in [43], the infinite-horizon problem was only considered for the case of two subsystems, while here we present all the results for arbitrary number of subsystems.…”

Section: Related Studiesmentioning

confidence: 99%

“…First, the authors of [43] considered the case where the B-matrix was parameterized with stochastic variables but in our setup the A-matrix is assumed to be stochastic. Additionally, in [43], the infinite-horizon problem was only considered for the case of two subsystems, while here we present all the results for arbitrary number of subsystems. In this paper, we introduce the concept of performance degradation ratio as a measure to study the value information in optimal control design.…”

Section: Related Studiesmentioning

confidence: 99%

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Optimal Control Design Under Limited Model Information for Discrete-Time Linear Systems With Stochastically-Varying Parameters

Farokhi

Johansson

2015

IEEE Trans. Automat. Contr.

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The value of plant model information available in the control design process is discussed. We design optimal state-feedback controllers for interconnected discrete-time linear systems with stochastically-varying parameters. The parameters are assumed to be independently and identically distributed random variables in time. The design of each controller relies only on (i) exact local plant model information and (ii) statistical beliefs about the model of the rest of the system. We consider both finite-horizon and infinite-horizon quadratic cost functions. The optimal state-feedback controller is derived in both cases. The optimal controller is shown to be linear in the state and to depend on the model parameters and their statistics in a particular way. Furthermore, we study the value of model information in optimal control design using the performance degradation ratio which is defined as the supremum (over all possible initial conditions) of the ratio of the cost of the optimal controller with limited model information scaled by the cost of the optimal controller with full model information. An upper bound for the performance degradation ratio is presented for the case of fully-actuated subsystems. Comparisons are made between designs based on limited, statistical, and full model information. Throughout the paper, we use a power network example to illustrate concepts and results.

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Section: Related Studiesmentioning

confidence: 99%

Section: Related Studiesmentioning

confidence: 99%

Section: Related Studiesmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Control Design Under Limited Model Information for Discrete-Time Linear Systems With Stochastically-Varying Parameters

Farokhi

Johansson

2015

IEEE Trans. Automat. Contr.

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“…) is a unique solution of the backward stochastic differential equation (44) such that u o ∈ U (N ) [0, T ] satisfies the point wise almost sure inequalities with respect to the σ-algebras G I i 0,t ⊂ F 0,t , t ∈ [0, T ], i = 1, 2, . .…”

Section: Necessary Conditions For An Elementmentioning

confidence: 99%

Dynamic Team Theory of Stochastic Differential Decision Systems with Decentralized Noiseless Feedback Information Structures via Girsanov's Measure Transformation

Charalambous

2013

Preprint

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In this paper we generalized static team theory to dynamic team theory, in the context of stochastic differential decision system with decentralized noiseless feedback information structures.We apply Girsanov's theorem to transformed the initial stochastic dynamic team problem to an equivalent team problem, under a reference probability space, with state process and information structures independent of any of the team decisions. Subsequently, we show, under certain conditions, that continuous-time and discrete-time stochastic dynamic team problems, can be transformed to equivalent static team problems, although computing the optimal team strategies using this method might be computational intensive. Therefore, we propose an alternative method, by deriving team and Person-by-Person (PbP) optimality conditions, via the stochastic Pontryagin's maximum principle, consisting of forward and backward stochastic differential equations, and a set of conditional variational Hamiltonians with respect to the information structures of the team members.Finally, we relate the backward stochastic differential equation to the value process of the stochastic team problem.

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“…Since the late 1960's several articles have been written on decentralized decision making and information structures, and their applications in communication and queuing networks, sensor networks, and networked control systems. Some of the early references are [1,5,6,, while more recent are [29][30][31][32][33][34][35][36][37][38][39][40][41]. Among these references the most popular mathematical formalism is that of "Static Team Theory" 1 developed by Marschak and Radner [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Team Theory of Stochastic Differential Decision Systems with Decentralized Noisy Information Structures via Girsanov's Measure Transformation

Charalambous,

Ahmed

2013

Preprint

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In this paper, we present two methods which generalize static team theory to dynamic team theory, in the context of continuous-time stochastic nonlinear differential decentralized decision systems, with relaxed strategies, which are measurable to different noisy information structures. For both methods we apply Girsanov's measure transformation to obtain an equivalent decision system under a reference probability measure, so that the observations and information structures available for decisions, are not affected by any of the team decisions.The first method is based on function space integration with respect to products of Wiener measures. It generalizes Witsenhausen's [1] definition of equivalence between discrete-time static and dynamic team problems, and relates Girsanov's theorem to the so-called "Common Denominator Condition and Change of Variables".The second method is based on stochastic Pontryagin's maximum principle. The team optimality conditions are given by a "Hamiltonian System" consisting of forward and backward stochastic differential equations, and conditional variational Hamiltonians with respect to the information structure of each team member. Under global convexity conditions, we show that PbP optimality implies team optimality. We also obtain team and PbP optimality conditions for regular team strategies, which are measurable functions of decentralized information structures.In addition, we also show existence of team and PbP optimal relaxed decentralized strategies (conditional distributions), in the weak * sense, without imposing convexity on the action spaces of the team members, and their realization by regular team strategies.

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A team theoretic approach to decentralized control of systems with stochastic parameters

Cited by 6 publications

References 11 publications

Optimal Control Design Under Limited Model Information for Discrete-Time Linear Systems With Stochastically-Varying Parameters

Optimal Control Design Under Limited Model Information for Discrete-Time Linear Systems With Stochastically-Varying Parameters

Dynamic Team Theory of Stochastic Differential Decision Systems with Decentralized Noiseless Feedback Information Structures via Girsanov's Measure Transformation

Dynamic Team Theory of Stochastic Differential Decision Systems with Decentralized Noisy Information Structures via Girsanov's Measure Transformation

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