Decentralized model predictive control via dual decomposition

Wakasa, Yuji; Arakawa, Mizue; Tanaka, Kanya; Akashi, Takuya

doi:10.1109/cdc.2008.4739012

Cited by 24 publications

(15 citation statements)

References 6 publications

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“…However, this bound becomes quite conservative and a tighter bound can be computed. To achieve this, we introduce the following decomposition of the dual variables, λ = λ p + λ n and µ = µ p + µ n , where (22) and N denotes the null-space. We denote by Z an orthonormal basis to the null-space of [A T C T ], i.e., [A T C T ]Z = 0 and Z T Z = I.…”

Section: Lagrange Multiplier Norm Boundsmentioning

confidence: 99%

“…where λ * p , λ * n , µ * p and µ * n satisfy (22) and the optimal dual variables λ * , µ * satisfy λ * = λ * p + λ * n and µ * = µ * p + µ * n . Proof.…”

Section: Lagrange Multiplier Norm Boundsmentioning

confidence: 99%

“…Proof. The result is immediate from the KKT conditions [4, §5.5.3], the dual variable decomposition λ * = λ * p + λ * n , µ * = µ * p + µ * n , and due to (22) which implies that A T λ * n + C T µ * n = 0. Remark 4: The variables λ * p and µ * p satisfy the stationarity conditions while λ * n and µ * n do not affect the stationarity conditions but instead ensure dual feasibility and complementarity.…”

Section: Lagrange Multiplier Norm Boundsmentioning

confidence: 99%

“…where the first equality comes from (23), the first inequality from (28), the second equality from (23) the third equality holds since λ * = λ * p + λ * n and µ * = µ * p + µ * n and due to (11) and the last equality is due to (22) which implies A T λ * n + C T µ * n = 0. Further, the KKT conditions for the dual problem (24)-(25) give that…”

Section: And the Kkt Conditions (24)-(27)mentioning

confidence: 99%

“…These include [13], [22], [6] in which different reformulations of the classical gradient method with suboptimal step sizes are used to solve the dual problem. In [9] an accelerated gradient method is used to solve the DMPC problem and the optimal step size is provided.…”

Section: Introductionmentioning

confidence: 99%

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A generalized distributed accelerated gradient method for distributed model predictive control with iteration complexity bounds

Giselsson

2013

2013 American Control Conference

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Most distributed optimization methods used for distributed model predictive control (DMPC) are gradient based. Gradient based optimization algorithms are known to have iterations of low complexity. However, the number of iterations needed to achieve satisfactory accuracy might be significant. This is not a desirable characteristic for distributed optimization in distributed model predictive control. Rather, the number of iterations should be kept low to reduce communication requirements, while the complexity within an iteration can be significant. By incorporating Hessian information in a distributed accelerated gradient method in a well-defined manner, we are able to significantly reduce the number of iterations needed to achieve satisfactory accuracy in the solutions, compared to distributed methods that are strictly gradient-based. Further, we provide convergence rate results and iteration complexity bounds for the developed algorithm.

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Section: Lagrange Multiplier Norm Boundsmentioning

confidence: 99%

“…where λ * p , λ * n , µ * p and µ * n satisfy (22) and the optimal dual variables λ * , µ * satisfy λ * = λ * p + λ * n and µ * = µ * p + µ * n . Proof.…”

Section: Lagrange Multiplier Norm Boundsmentioning

confidence: 99%

Section: Lagrange Multiplier Norm Boundsmentioning

confidence: 99%

Section: And the Kkt Conditions (24)-(27)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A generalized distributed accelerated gradient method for distributed model predictive control with iteration complexity bounds

Giselsson

2013

2013 American Control Conference

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Cooperative distributed model predictive control for wind farms

Spudić

Conte

Baotić

et al. 2014

Optim Control Appl Methods

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SUMMARYThis paper focuses on cooperative distributed model predictive control (MPC) of wind farms, where the farms respond to active power control commands issued by the transmission system operator. A distributed MPC scheme is proposed, which aims at satisfying the requirements imposed by the grid code while minimizing the farm-wide mechanical structure fatigue. The distributed MPC control law is defined by a global finite-horizon optimal control problem, which is solved at every time step by distributed optimization. The computational approach is completely distributed, that is, every turbine evaluates its own globally optimal input by considering local measurements and communicating to neighboring turbines only. Two MPC versions are compared, in the first of which the farm-wide power output constraint is implemented as a hard constraint, whereas in the second, it is implemented as a soft constraint. As for distributed optimization methods, the alternating direction method of multipliers as well as a dual decomposition scheme based on fast gradient updates are compared. The performance of the proposed distributed MPC controller, as well as the performance of the distributed optimization methods used for its operation, are compared in the simulation on four exemplary scenarios. The results of the simulations imply that the use of cooperative distributed MPC in wind farms is viable both from a performance and from a computational viewpoint.

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Distributed MPC Via Dual Decomposition and Alternative Direction Method of Multipliers

Farokhi

Shames

Johansson

2013

Intelligent Systems, Control and Automation: Science and Engineering

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A conventional way to handle model predictive control (MPC) problems distributedly is to solve them via dual decomposition and gradient ascent. However, at each time-step, it might not be feasible to wait for the dual algorithm to converge. As a result, the algorithm might be needed to be terminated prematurely. One is then interested to see if the solution at the point of termination is close to the optimal solution and when one should terminate the algorithm if a certain distance to optimality is to be guaranteed. In this chapter, we look at this problem for distributed systems under general dynamical and performance couplings, then, we make a statement on validity of similar results where the problem is solved using alternating direction method of multipliers.

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Decentralized model predictive control via dual decomposition

Cited by 24 publications

References 6 publications

A generalized distributed accelerated gradient method for distributed model predictive control with iteration complexity bounds

A generalized distributed accelerated gradient method for distributed model predictive control with iteration complexity bounds

Cooperative distributed model predictive control for wind farms

Distributed MPC Via Dual Decomposition and Alternative Direction Method of Multipliers

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