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Stability and Computations in Cooperative Distributed Model Predictive Control


C. Conte


The main theme of this thesis is the development of cooperative distributed model predictive control (MPC) methods for large-scale networks of constrained dynamic systems. MPC is a modern control methodology, which is particularly suited for constrained systems and has proven successful in practice. For large-scale networks of systems, which are often subject to communication constraints, MPC controllers have to be operated in a distributed way, i.e. each system in the network has to take local control decisions based on local measurements and communication with neighboring systems. Moreover, for networks of systems with a common objective function, it is desirable for the systems to take their control decisions cooperatively, which implies the need for cooperative distributed MPC. Distributed optimization is a well-established methodology which allows the combination of the cooperative and the distributed aspect within the MPC framework. Specifically, one finite-horizon optimal control problem, in the following referred to as MPC problem, can be formulated for the whole network of systems, and it can be solved by a distributed optimization method at each time step. This thesis is concerned with issues arising from the use of distributed optimization in MPC. In the first part of the thesis, distributed optimization based cooperative distributed MPC controllers for networks of linear systems are presented. All controllers guarantee stability and feasibility in closed-loop. The first controller presented is a nominal MPC controller. Closed-loop stability and feasibility are guaranteed by adapting well-established methodologies from the centralized MPC literature. Specifically, the global MPC problem is equipped with a suitably designed terminal cost, which is a Lyapunov function for the unconstrained system, and a terminal set, which is positively invariant (PI). In order to make the MPC problem amenable to distributed optimization algorithms, the terminal cost is designed as a separable function and the terminal set is a Cartesian product of local sets, which are time-varying. Specific synthesis methods for terminal cost and set are presented, where these methods can be executed in a distributed fashion themselves. In the following, two cooperative distributed MPC controller are presented, which extend the nominal one described above. The first is a robust MPC controller for networks of linear systems subject to bounded additive noise, the second is an MPC controller for reference tracking. In both cases, well established methodologies from the centralized MPC literature x Abstract are adapted for the use in a cooperative distributed setup, where the MPC problem is solved by distributed optimization. For distributed robust MPC, the main additional ingredients are structured robust positive invariant (RPI) sets, as well as constraint tightening methods, which can be executed in a distributed way. For distributed reference tracking MPC, the main additional ingredient is an invariant set for tracking, again designed as a Cartesian product, and again equipped with a synthesis method that can be carried out in a distributed fashion. In the second part of the thesis, computational aspects of specific distributed optimization methods in MPC are investigated. In particular, the performance of these methods on the MPC problem, i.e. the number of iterations to convergence, is computationally analyzed under various system setups and operational modes. A first study contains computational results for general networks of linear systems, which are controlled by standard nominal cooperative distributed MPC controllers. In the computational scenarios considered, various system properties, such as the strength of the dynamic coupling between the systems or the network topology, are varied. The results show that the performance of distributed optimization is sensitive to changes in these properties. In particular, as a general qualitative observation, the performance decreases in cases where coordination among the systems in the network is crucial, which usually manifests in Lagrange multipliers of large magnitude. These observations could be confirmed in a wind farm application study. In particular, it is shown that the performance of the distributed optimization methods decreases in operational conditions where the power production has to be dynamically reallocated across the wind farm. This is the case for example when there is not enough wind to fulfill the farm-wide power production requirements.


Type of Publication:

(03)Ph.D. Thesis

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2014:IFA_4809,
    author={C. Conte},
    title={{Stability and Computations in Cooperative Distributed Model
	  Predictive Control}},
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