Distributed Optimization for Model Predictive Control of Linear Dynamic Networks With Control-Input and Output Constraints

Camponogara, Eduardo; Scherer, Helton Fernando

doi:10.1109/tase.2010.2061842

Cited by 79 publications

(66 citation statements)

References 19 publications

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“…V 4 = |v [4] | ≤ 1.9 Algorithm 1 terminates in one iteration. The lower controllers LC i , i ∈ M, are synthesized using explicit MPC for system (8) based on the quadratic cost function The matrices Q i , R i and S i , i ∈ M have been computed so as to guarantee stability of the origin of (8) and (17).…”

Section: Numerical Examplementioning

confidence: 99%

“…However, they require all-to-all communication between regulators and each MPC controller requires knowledge on how subsystem operations impact on the whole plant. Furthermore, existing solutions account for input constraints only with the exception of [4] where a DMPC scheme avoiding all-to-all communication and accounting for box constraints on inputs and outputs has been presented. Many other contributions [3,5,21,7,6] focused on non-cooperative schemes where each MPC controller minimizes a performance index local to each subsystem.…”

Section: Introductionmentioning

confidence: 99%

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Tube-based distributed control of linear constrained systems

Riverso

Ferrari-Trecate

2012

Automatica

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In this paper we consider a linear system structured into physically coupled subsystems and propose an innovative distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Our method hinges on the availability of a decentralized stabilizing regulator for the unconstrained system and provides a two-layer controller for each subsystem. Upper controllers receive planned state trajectories from neighboring subsystems and exploit the notion of tubes [12] for achieving robustness of stability with respect to coupling. Lower controllers generate planned trajectories using Model Predictive Control (MPC) independently of the other subsystems. The proposed control scheme is arguably easier to design and apply than existing distributed controllers with similar features. A comparison of the proposed approach with existing centralized and distributed MPC regulators is conducted using an illustrative example.

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Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tube-based distributed control of linear constrained systems

Riverso

Ferrari-Trecate

2012

Automatica

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“…We consider the ordinary gradient method, Nesterov's method, and D-ADMM [8], which was designed to solve the more general problem (2), not (1). D-ADMM thus requires exchanging full solution estimates between the nodes.…”

Section: Simulationsmentioning

confidence: 99%

“…Although both problems have been studied extensively (see [1], [2], [3], [4] for centralized and distributed MPC, and [5], [6] for congestion control), their distributed implementation still relies on classical techniques, for example, the gradient algorithm [2], [5]. On the other hand, in the optimization field, it has recently been shown that the Alternating Direction Method of Multipliers (ADMM) is more appropriate for distributed or parallel implementations [7], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

“…Another approach for solving (1) is with a distributed implementation of the barrier method with Newton's algorithm, yielding an algorithm with two nested loops; this approach was taken in [2] in the context of distributed MPC. Their simulations show that it slightly improves the convergence rate of the gradient method, both algorithms requiring about the same number of iterations.…”

Section: Introductionmentioning

confidence: 99%

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Distributed ADMM for model predictive control and congestion control

Mota

Aguiar²,

Püschel³

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-Many problems in control can be modeled as an optimization problem over a network of nodes. Solving them with distributed algorithms provides advantages over centralized solutions, such as privacy and the ability to process data locally. In this paper, we solve optimization problems in networks where each node requires only partial knowledge of the problem's solution. We explore this feature to design a decentralized algorithm that allows a significant reduction in the total number of communications. Our algorithm is based on the Alternating Direction of Multipliers (ADMM), and we apply it to distributed Model Predictive Control (MPC) and TCP/IP congestion control. Simulation results show that the proposed algorithm requires less communications than previous work for the same solution accuracy.

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Distributed Model Predictive Control Method for Optimal Coordination of Signal Splits in Urban Traffic Networks

Ye¹,

Wu²,

Mao³

2014

Asian Journal of Control

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Coordination and control approaches based on model predictive control (MPC) have been widely investigated for traffic signal control in urban traffic networks. However, due to the complex non‐linear characters of traffic flows and the large scale of traffic networks, a basic challenge faced by these approaches is the high online computational complexity. In this paper, to reduce the computational complexity and improve the applicability of traffic signal control approaches based on MPC in practice, we propose a distributed MPC approach (DCA‐MPC) to coordinate and optimize the signal splits. Instead of describing the dynamics of traffic flow within each link of the traffic network with a simplified linear model, we present an improved nonlinear traffic model. Based on the nonlinear model, an MPC optimization framework for the signal splits control is developed, whereby the interactions between subsystems are accurately modeled by employing two interconnecting constraints. In addition, by designing a novel dual decomposition strategy, a distributed coordination algorithm is proposed. Finally, with a benchmark traffic network, experimental results are given to illustrate the effectiveness of the proposed method.

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Distributed Optimization for Model Predictive Control of Linear Dynamic Networks With Control-Input and Output Constraints

Cited by 79 publications

References 19 publications

Tube-based distributed control of linear constrained systems

Tube-based distributed control of linear constrained systems

Distributed ADMM for model predictive control and congestion control

Distributed Model Predictive Control Method for Optimal Coordination of Signal Splits in Urban Traffic Networks

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