Separable Model Predictive Control via Alternating Direction Method of Multipliers for Large-scale Systems

In this paper, an alternating direction method of multipliers (ADMM) based realtime model predictive control (MPC) algorithm is presented. With the use of indicator function and by introducing extra consensus constraints, the constrained MPC problem can be formulated as a separable MPC problem, which can be computed very efficiently by projected gradient descent ADMM update steps and Riccati recursions. The sequence of the objective value of this constrained real-time ADMM-type MPC algorithm satisfies a linear convergence rate. The procedure is also extended to distributed systems with constraints, in which the variables of each subsystems communicate with their neighbors and update in the Gauss-Seidel way. An illustrative example shows the effectiveness of this approach.