Robust approximate symmetric model predictive control

Chuang, Frank; Danielson, Claus; Borrelli, Francesco

doi:10.1109/cdc.2015.7402567

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Instead, the symmetries appear in the system behavior. As shown in References 15 and 16, this symmetric behavior need only be approximate.…”

Section: Introductionmentioning

confidence: 99%

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An alternating direction method of multipliers algorithm for symmetric model predictive control

Danielson

2020

Optim Control Appl Methods

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SummaryThis article presents an alternating direction method of multipliers (ADMM) algorithm for solving large‐scale model predictive control (MPC) problems that are invariant under the symmetric‐group. Symmetry was used to find transformations of the inputs, states, and constraints of the MPC problem that decompose the dynamics and cost. We prove an important property of the symmetric decomposition for the symmetric‐group that allows us to efficiently transform between the original and decomposed symmetric domains. This allows us to solve different subproblems of a baseline ADMM algorithm in different domains where the computations are less expensive. This reduces the computational cost of each iteration from quadratic to linear in the number of repetitions in the system. In addition, we show that the memory complexity for our ADMM algorithm is also linear in number of repetitions in the system, rather than the typical quadratic complexity. We demonstrate our algorithm for two case studies; battery balancing and heating, ventilation, and air conditioning. In both case studies, the symmetric algorithm reduced the computation‐time from minutes to seconds and memory usage from tens of megabytes to tens or hundreds of kilobytes, allowing the previously nonviable MPCs to be implemented in real time on embedded computers with limited computational and memory resources.

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“…Instead, the symmetries appear in the system behavior. As shown in References 15 and 16, this symmetric behavior need only be approximate.…”

Section: Introductionmentioning

confidence: 99%

“…Symmetry has also been applied to control theory, see References 15,17‐23. Most relevant to this article are the works 21‐23 on exploiting symmetry for explicit MPC.…”

Section: Introductionmentioning

confidence: 99%

An alternating direction method of multipliers algorithm for symmetric model predictive control

Danielson

2020

Optim Control Appl Methods

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“…Symmetries are transformations of a system's inputs, outputs, and states for which the system is invariant. Symmetry has been used extensively to simplify control design [6,7,8,9,10,11,12,13,14]. In [6] the authors developed a linear matrix inequality (LMI) based controller design methodology that exploits symmetry to reduce computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Control Design for Multi-Evaporator Vapor Compression Systems

Danielson

2017

Volume 1: Aerospace Applications; Advances in Control Design Methods; Bio Engineering Applications; Advances in Non-Linear Cont

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Multi-evaporator vapor compression systems (ME-VCS) are inherently multi-input multi-output (MIMO) systems, often with complex, highly coupled dynamics. Thus, they require more sophisticated control schemes than traditional on-off logic, or decentralized proportional-integral controllers. Unfortunately, many MIMO control design techniques are not well suited for this problem since they require complex numerical computations that do not scale gracefully for the high-dimensional dynamics of ME-VCS systems. This paper exploits the observed similarity of the room dynamics to reduce the computational complexity of designing controllers. We use a linear matrix inequality based controller synthesis technique that exploits symmetry for designing controllers for large-scale ME-VCS systems. This controller synthesis technique was applied to an ME-VCS system with 50 rooms. Using tradition control design methods required 41 hours to synthesize a controller, while our technique designed an identical controller in less than 1 second.

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