Decentralized non-convex optimization via bi-level SQP and ADMM

Stomberg, Gösta; Engelmann, Alexander; Faulwasser, Timm

doi:10.1109/cdc51059.2022.9992379

Cited by 3 publications

(16 citation statements)

References 21 publications

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“…To solve non-convex OCPs, we consider the dSQP algorithm proposed by (Stomberg et al, 2022b). Similar to (Engelmann et al, 2020), the method admits a bi-level structure, i.e., we index outer SQP iterations by q and inner ADMM iterations by l. Let z .…”

Section: The Decentralized Sqp Methods For Nonlinear Mpcmentioning

confidence: 99%

“…= E i 0 , and η q ≥ 0. If this stopping criterion is employed, then dSQP is guaranteed to converge locally as described in Theorem 1 below, which appeared as Theorem 2 in (Stomberg et al, 2022b).…”

Section: The Decentralized Sqp Methods For Nonlinear Mpcmentioning

confidence: 99%

“…Theorem 1 (dSQP convergence (Stomberg et al, 2022b)). Let p be a KKT point of (2) which, for all i ∈ S, satisfies…”

Section: The Decentralized Sqp Methods For Nonlinear Mpcmentioning

confidence: 99%

“…ADMM is guaranteed to converge for convex problems (Boyd et al, 2011), but lacks convergence guarantees for general nonconvex constraints arising from nonlinear dynamics or otherwise. A decentralized method with convergence guarantees also for non-convex problems is the recently proposed decentralized sequential quadratic programming (dSQP), which combines an SQP scheme with ADMM (Stomberg et al, 2022b) in a bi-level fashion.…”

Section: Introductionmentioning

confidence: 99%

“…This article presents experimental results for ADMM-and dSQP-based DMPC schemes for a team of omnidirectional mobile robots. We use ADMM (Boyd et al, 2011) if the OCP transfers into a convex quadratic program (QP), and we use dSQP (Stomberg et al, 2022b) if a non-convex NLP is obtained. In both cases, only QPs are solved on a subsystem level, which allows to use the efficient active set method qpOASES tailored to MPC (Ferreau et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

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Cooperative Distributed MPC via Decentralized Real-Time Optimization: Implementation Results for Robot Formations

Stomberg¹,

Ebel²,

Faulwasser³

et al. 2023

Preprint

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Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

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Section: The Decentralized Sqp Methods For Nonlinear Mpcmentioning

confidence: 99%

Section: The Decentralized Sqp Methods For Nonlinear Mpcmentioning

confidence: 99%

“…Theorem 1 (dSQP convergence (Stomberg et al, 2022b)). Let p be a KKT point of (2) which, for all i ∈ S, satisfies…”

Section: The Decentralized Sqp Methods For Nonlinear Mpcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Cooperative Distributed MPC via Decentralized Real-Time Optimization: Implementation Results for Robot Formations

Stomberg¹,

Ebel²,

Faulwasser³

et al. 2023

Preprint

View full text Add to dashboard Cite

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Iterative distributed model predictive control for nonlinear systems with coupled non‐convex constraints and costs

Wu,

Dai,

Xia

2024

Intl J Robust & Nonlinear

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This paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method.

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