Quantization design for distributed optimization with time-varying parameters

We consider the problem of solving a sequence of distributed optimization problems with time-varying parameters and communication constraints, i.e. only neighbour-to-neighbour communication and a limited amount of information exchanged. By extending previous results and employing a warm-starting strategy, we propose an on-line algorithm for solving optimization problems under the given constraints and show that there exists a trade-off between the number of iterations for solving each problem in the sequence and the accuracy achieved by the algorithm. For a given accuracy ∈, we can find a number of iterations K, which guarantees that for the sequential realization of the parameter, the sub-optimal solution given by the algorithm satisfies the accuracy. We apply the method to solve a distributed model predictive control problem by considering the state measurement at each sampling time as the time-varying parameter and show that the simulation supports the theoretical results.