Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM

Ma, Jun; Cheng, Zilong; Zhang, Xiaoxue; Tomizuka, Masayoshi; Lee, Tong Heng

doi:10.48550/arxiv.2001.00306

Cited by 2 publications

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then it is straightforward to see that the second part in (27) is the conjugate function of h, which can be denoted by h * (µ i3 ). It is well-known the conjugate function of a norm function is an indicator function with respect to the corresponding dual norm ball, that is…”

Section: A First Sub-problem In Admmmentioning

confidence: 99%

“…With a suitable decomposition approach, the subproblems can be efficiently solved in a parallel framework. The ADMM algorithm has been successfully applied in many areas such as neural networks [25], image processing [26], optimal control [27], [28], and general optimization problem solver [29]. Some similar works have been proposed in the existing literature.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ADMM-Based Parallel Optimization for Multi-Agent Collision-Free Model Predictive Control

Cheng¹,

Ma²,

Zhang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper investigates the multi-agent collisionfree control problem for medium and large scale systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or even the distributed counterpart, would suffer from substantial difficulty in balancing optimality and computational efficiency. Additionally, the non-convex characteristics that invariably arise in such collision-free control and optimization problems render it difficult to effectively derive a reliable solution (and also to thoroughly analyze the associated convergence properties). To overcome these challenging issues, this work establishes a suitably novel parallel computation framework through an innovative mathematical problem formulation; and then with this framework and formulation, the alternating direction method of multipliers (ADMM) algorithm is presented to solve the sub-problems arising from the resulting parallel structure. Furthermore, an efficient and intuitive initialization procedure is developed to accelerate the optimization process, and the optimum is thus determined with significantly improved computational efficiency. As supported by rigorous proofs, the convergence of the proposed ADMM iterations for this nonconvex optimization problem is analyzed and discussed in detail. Finally, a multi-agent system with a group of unmanned aerial vehicles (UAVs) serves as an illustrative example here to demonstrate the effectiveness and efficiency of the proposed approach.

show abstract

Section: A First Sub-problem In Admmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

ADMM-Based Parallel Optimization for Multi-Agent Collision-Free Model Predictive Control

Cheng¹,

Ma²,

Zhang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nowadays, the alternating direction method of multipliers (ADMM), which solves a convex optimization problem by breaking it into smaller and manageable ones, has become a considerable technique with remarkable scalability. It has been recently found the broad applicability in various areas, such as optimal control, distributed computation, machine learning, and so on [21]- [24]. Remarkably, the ADMM can solve a convex optimization problem with converging to a global optimum and achieve the parallel computation after decomposition, which exceedingly alleviates the typical computational burden resulted from the dimension growth of the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Semi-Definite Relaxation Based ADMM for Cooperative Planning and Control of Connected Autonomous Vehicles

Zhang

Cheng

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper investigates the cooperative planning and control problem for multiple connected autonomous vehicles (CAVs) in different scenarios. In the existing literature, most of the methods suffer from significant problems in computational efficiency. Besides, as the optimization problem is nonlinear and nonconvex, it typically poses great difficultly in determining the optimal solution. To address this issue, this work proposes a novel and completely parallel computation framework by leveraging the alternating direction method of multipliers (ADMM). The nonlinear and nonconvex optimization problem in the autonomous driving problem can be divided into two manageable subproblems; and the resulting subproblems can be solved by using effective optimization methods in a parallel framework. Here, the differential dynamic programming (DDP) algorithm is capable of addressing the nonlinearity of the system dynamics rather effectively; and the nonconvex coupling constraints with small dimensions can be approximated by invoking the notion of semi-definite relaxation (SDR), which can also be solved in a very short time. Due to the parallel computation and efficient relaxation of nonconvex constraints, our proposed approach effectively realizes real-time implementation and thus also extra assurance of driving safety is provided. In addition, two transportation scenarios for multiple CAVs are used to illustrate the effectiveness and efficiency of the proposed method.

show abstract

Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM

Cited by 2 publications

References 32 publications

ADMM-Based Parallel Optimization for Multi-Agent Collision-Free Model Predictive Control

ADMM-Based Parallel Optimization for Multi-Agent Collision-Free Model Predictive Control

Semi-Definite Relaxation Based ADMM for Cooperative Planning and Control of Connected Autonomous Vehicles

Contact Info

Product

Resources

About