Minh Dang Doan

A distributed optimization-based approach for hierarchical MPC of large-scale systems with coupled dynamics and constraints

We present a hierarchical MPC approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible solution within a finite number of iterations, using primal averaging and a constraint tightening approach. The primal update is performed in a distributed way and does not require exact solutions, while the dual problem uses an approximate subgradient method. Stability of the scheme is established using bounded suboptimality.

A dual decomposition-based optimization method with guaranteed primal feasibility for hierarchical MPC problems

Abstract We present a gradient-based dual decomposition method that is suitable for hierarchical MPC of large-scale systems. The algorithm generates a primal feasible solution within a finite number of iterations and solves the problem by applying a hierarchical conjugate gradient method in each dual iterative ascent step. The proposed scheme uses constraint tightening and a suboptimality bound to ensure stability and feasibility in a hierarchical MPC problem.

An improved distributed version of Han's method for distributed MPC of canal systems

Abstract Recently, we have introduced a distributed version of Hans method that can be used for distributed model predictive control (DMPC) of dynamically coupled linear systems, under coupling constraints (Doan et al., 2009). Some DMPC problems of water networks can be cast into this type. In this paper, we propose an improved version of this method and apply it to a canal system. The simulation results show that the modifications lead to faster convergence of the method, thus making it more practical in control of water networks.

A Hierarchical MPC Approach with Guaranteed Feasibility for Dynamically Coupled Linear Systems

In this chapter we describe an iterative two-layer hierarchical approach to MPC of large-scale linear systems subject to coupled linear constraints. The algorithm uses constraint tightening and applies a primal-dual iterative averaging procedure to provide feasible solutions in every sampling step. This helps overcome typical practical issues related to the asymptotic convergence of dual decomposition based distributed MPC approaches. Bounds on constraint violation and level of suboptimality are provided. The method can be applied to large-scale MPC problems that are feasible in the first sampling step and for which the Slater condition holds (i.e., there exists a solution that strictly satisfies the inequality constraints). Using this method, the controller can generate feasible solutions of the MPC problem even when the dual solution does not reach optimality, and closed-loop stability is also ensured using bounded suboptimality.

Linear model predictive control based on approximate optimal control inputs and constraint tightening

In this paper we propose a model predictive control scheme for discrete-time linear time-invariant systems based on inexact numerical optimization algorithms. We assume that the solution of the associated quadratic program produced by some numerical algorithm is possibly neither optimal nor feasible, but the algorithm is able to provide estimates on primal suboptimality and primal feasibility violation. By tightening the complicating constraints we can ensure the primal feasibility of the approximate solutions generated by the algorithm. Finally, we derive a control strategy that has the following properties: the constraints on the states and inputs are satisfied, asymptotic stability of the closed-loop system is guaranteed, and the number of iterations needed for a desired level of suboptimality can be determined.

Application of Distributed and Hierarchical Model Predictive Control in Hydro Power Valleys

Abstract We provide an overview on the application of distributed and hierarchical model predictive control (MPC) algorithms for the power reference tracking problem of the HD-MPC Hydro Power Valley (HPV) system (Savorgnan and Diehl, 2011). Serving as a case study for distributed and hierarchical MPC, the HPV benchmark has various challenging features, including nonlinear, non-smooth, and coupled cost function and nonlinear coupled subsystem dynamics. We propose different approaches to address these challenges and summarize our recently developed hierarchical and distributed MPC frameworks that could be applied to the HPV control problem. A comparison of distributed MPC based on a state-of-the-art distributed optimization method (Giselsson et al., 2012) with centralized and decentralized MPC is provided via numerical simulations. It is shown that by using a dynamic division of total power reference to deal with the coupling in the cost function and a specific formulation of the dual optimization problem, distributed MPC achieves almost the same tracking performance as centralized MPC, with the advantage of being implementable in a distributed setting.