Gradient-Based Distributed Model Predictive Control
Author
Summary, in English
Another topic of the thesis is to guarantee feasibility and stability when using the developed distributed optimization algorithm in a DMPC context. Traditional methods of proving stability in MPC usually involve terminal cost functions and terminal constraints that are non-separable. These methods are not directly applicable in DMPC based on dual decomposition because of the non-separable terms. Further, dual decomposition does not provide feasible iterations but is guaranteed to be primal feasible only in the limit. These issues have been addressed in the thesis. The stability issue is addressed by showing that for problems without a terminal cost or terminal constraints and if a certain controllability assumption on the stage costs is satisfied, the optimal value function is decreasing in every time step by a prespecified amount. It is also shown how the controllability assumption can be verified by solving a mixed integer linear program. The feasibility issue is addressed by a novel adaptive constraint tightening approach. The adaptive constraint tightening guarantees that a primal feasible solution can be constructed with finite number of algorithm iterations without compromising the stability guarantee.
The developed distributed optimization algorithm is evaluated on a hydro power valley benchmark problem. The hydro power valley consists of several dams connected in series where each dam is equipped with a turbine to extract power from the water. The objective is to control the water flow between the dams such that the total power from the turbines matches a power reference while respecting constraints on water levels and water flows. The control problem is formulated as an optimization problem, which is solved in receding horizon fashion using the distributed optimization algorithm presented in the thesis. The performance of the proposed distributed controller is compared to the performance of a centralized controller.
Department/s
Publishing year
2012
Language
English
Publication/Series
PhD Thesis TFRT-1094
Full text
Document type
Dissertation
Publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
Topic
- Control Engineering
Status
Published
Project
- LCCC
Supervisor
ISBN/ISSN/Other
- ISSN: 0280-5316
- ISSN: 0280-5316
Defence date
23 November 2012
Defence time
10:15
Defence place
Room M:B, M-building, Ole Römers väg 1, Lund University Faculty of Engineering
Opponent
- Colin Jones