A generalized distributed accelerated gradient method for distributed model predictive control with iteration complexity bounds

Abstract

Most distributed optimization methods used for distributed model predictive control (DMPC) are gradient based. Gradient based optimization algorithms are known to have iterations of low complexity. However, the number of iterations needed to achieve satisfactory accuracy might be significant. This is not a desirable characteristic for distributed optimization in distributed model predictive control. Rather, the number of iterations should be kept low to reduce communication requirements, while the complexity within an iteration can be significant. By incorporating Hessian information in a distributed accelerated gradient method in a well-defined manner, we are able to significantly reduce the number of iterations needed to achieve satisfactory accuracy in the solutions, compared to distributed methods that are strictly gradient-based. Further, we provide convergence rate results and iteration complexity bounds for the developed algorithm.

Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots

“…In Reference [16], the authors address linear networked systems in cooperative control regarding the consensus via static couplings, which are imposed on the input of each subsystem from the output of other systems. For gradient-based DMPC schemes based on dual decomposition, an upper bound on the system dynamics is used to improve the convergence rate [17]. The results were extended in Reference [18] to general DMPC problems, and convergence is shown via a stopping criterion which computes lower and upper bounds when a sufficient control is found to keep the system in the desired state.…”

Improved Dual Decomposition for Distributed Model Predictive Control

“…Although the use of fast gradient methods in dual decomposition have significantly improved the convergence, see , it is not enough for realistic implementation in a distributed control system. In Giselsson (2013), a generalized version of dual decomposition was presented that allows for different curvature in different directions in the quadratic upper bound that is minimized in every iteration of the algorithm. This gives a significantly reduced number of iterations.…”

“…This gives a significantly reduced number of iterations. The algorithm in Giselsson (2013) is restricted to problems having a quadratic cost, linear equality constraints, and linear inequality constraints. Dual variables for all these constraints are introduced, which results in the dual problem being a quadratic program.…”

“…Dual variables for all these constraints are introduced, which results in the dual problem being a quadratic program. The algorithm in this paper is an extension and generalization of the algorithm in Giselsson (2013) that allows for any (local) convex inequality constraints. Also, only the equality constraints are dualized in this paper.…”

Distributed and cooperative control with applications to building HVAC systems

“…This issue is resolved in [118] where an adaptive constraint tightening technique is introduced to ensure that a feasible solution for the tightened dual problem is also feasible for the original primary problem. In [119] and [120], an accelerated sub-gradient algorithm is proposed to increase the convergence rate of the dual-decomposition algorithm from O( 1 k ) to O( 1 k 2 ). However, these approaches are difficult to generalize to nonlinear systems since convexity is a key assumption for dual-decomposition.…”