Distributed MPC Via Dual Decomposition and Alternating Direction Method of Multipliers
For researchers and practitioners in distributed control, this provides theoretical guarantees on suboptimality when terminating dual decomposition or ADMM early in distributed MPC.
The paper addresses the issue of premature termination in distributed MPC solved via dual decomposition, analyzing convergence guarantees and distance to optimality. It extends similar validity results to the alternating direction method of multipliers.
A conventional way to handle model predictive control (MPC) problems distributedly is to solve them via dual decomposition and gradient ascent. However, at each time-step, it might not be feasible to wait for the dual algorithm to converge. As a result, the algorithm might be needed to be terminated prematurely. One is then interested to see if the solution at the point of termination is close to the optimal solution and when one should terminate the algorithm if a certain distance to optimality is to be guaranteed. In this chapter, we look at this problem for distributed systems under general dynamical and performance couplings, then, we make a statement on validity of similar results where the problem is solved using alternating direction method of multipliers.