A Study On Distributed Model Predictive Consensus

We investigate convergence properties of a proposed distributed model predictive control (DMPC) scheme, where agents negotiate to compute an optimal consensus point using an incremental subgradient method based on primal decomposition as described in Johansson et al. [2006, 2007]. The objective of the distributed control strategy is to agree upon and achieve an optimal common output value for a group of agents in the presence of constraints on the agent dynamics using local predictive controllers. Stability analysis using a receding horizon implementation of the distributed optimal consensus scheme is performed. Conditions are given under which convergence can be obtained even if the negotiations do not reach full consensus.Comment: 20 pages, 4 figures, longer version of paper presented at 17th IFAC World Congres

A Parallel Dual Fast Gradient Method for MPC Applications

We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying algorithm first splits the original problem in as many independent subproblems as the length of the prediction horizon. Then, our algorithm computes a solution for these subproblems in parallel by exploiting auxiliary tightened subproblems in order to certify the control law in terms of suboptimality and recursive feasibility, along with closed-loop stability of the controlled system. Compared to prior approaches based on constraint tightening, our algorithm computes the tightening parameter for each subproblem to handle the propagation of errors introduced by the parallelization of the original problem. Our simulations show the computational benefits of the parallelization with positive impacts on performance and numerical conditioning when compared with a recent nonparallel adaptive tightening scheme.Comment: This technical report is an extended version of the paper "A Parallel Dual Fast Gradient Method for MPC Applications" by the same authors submitted to the 54th IEEE Conference on Decision and Contro

Decentralized Control of Uncertain Multi-Agent Systems with Connectivity Maintenance and Collision Avoidance

This paper addresses the problem of navigation control of a general class of uncertain nonlinear multi-agent systems in a bounded workspace of $\mathbb{R}^n$ with static obstacles. In particular, we propose a decentralized control protocol such that each agent reaches a predefined position at the workspace, while using only local information based on a limited sensing radius. The proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance, as well as, collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a class of Decentralized Nonlinear Model Predictive Controllers (DNMPC) under the presence of disturbances and uncertainties. Finally, simulation results verify the validity of the proposed framework.Comment: IEEE European Control Conference (ECC), Limassol, Cyprus, June 201

A hierarchical time-splitting approach for solving finite-time optimal control problems

We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the prediction horizon. Each subproblem is solved in parallel and further split into three by separating the objective from the equality and inequality constraints respectively, such that an analytic solution can be achieved for each subproblem. The proposed solution approach leads to a nested decomposition scheme, which is highly parallelizable. We present a numerical comparison with standard state-of-the-art solvers, and provide analytic solutions to several elements of the algorithm, which enhances its applicability in fast large-scale applications