Decomposition methods for distributed control and identification

Decomposition methods for distributed control and identification

Massioni, P.

Verhaegen, M. (promotor)

Mechanical, Maritime and Materials Engineering

Delft Center for Systems and Control

2010-06-21

The recent progress in technology, as in miniaturization and microtechnologies, is now forcing control engineers to confront themselves with systems of incredibly high dimensionality, with an ever growing number of input and output channels. For such systems, which we call "large scale systems", it is necessary to take a new approach in order to solve control problems in a reasonable time, as well as for being able to design controllers which can be realized in a physically implementable way. This thesis concerns a class of linear time-invariant large scale systems which we call "decomposable systems". Decomposable systems describe systems made of a set of identical subsystems (or agents) that are interacting with each other, and they can be considered as an example of homogeneous systems with arbitrary interconnections. This means that each subsystem interacts only with a limited set of the others, and the interconnection pattern does not have to stick to a special structure or lattice. This class of systems describes very well a number of physical systems of interest, such as formations of vehicles or mechanical elements made of identical subparts. Decomposable systems are interesting under the point of view of the theory as they prove to be amenable to a kind of modal decomposition that depends only on the interconnection pattern and not on the specific system; this property, or "decomposition theorem", is at the basis of all the results shown in this thesis. The first part of this work concerns the problem of synthesizing distributed controllers for decomposable systems. By "distributed", we mean that the controller can be implemented as a set of simple, local controllers interacting with each other, each of them commanding a limited set of neighboring subsystems. This approach is demanded when the number of subsystems is very high: in this case it is not feasible to implement a centralized controller that reads all the outputs and decides all the control inputs. The decomposition property is exploited to convert the problem of controller synthesis for the global decomposable system into the problem of synthesizing controllers for the "modal" systems making up its decomposed version; such modal subsystems have the same order as a single agent. Then, by using techniques from robust control as well as a few results from graph theory, it is possible to cast the distributed controller synthesis problem as an optimization problem under Linear Matrix Inequality constraints. This leads to methods allowing performance-based synthesis of controllers in a variety of cases (e.g. H-2 or H-infinity performance, continuous or discrete time, state or output feedback). The methods only offer suboptimality results, which can be considered as the price to be paid in exchange for the distributed structure of the controller. The distributed controller methods are then used in simulation for two examples of relevant technological application. The first application is the distributed H-2 control of a deformable mirror for adaptive optics; as future Earth-based telescopes will feature deformable mirrors with actuators and sensors in the order of the thousands, the independence of the computational complexity from the system size makes the methods of this thesis very attractive. The second application considered is satellite formation flying, for which an extension of the H-infinity methods to the time-varying case is proposed. The controller is evaluated on two examples of space missions involving non-Keplerian orbits. The last part of the thesis concerns a problem that is complementary to the one of control; namely, it investigates the possibility of identifying models of decomposable systems from data. This possibility is useful in case such models are not available from first principles. It is shown that the decomposition property can be used in this case as well. The problem is first treated for a special case, namely for the class of circulant systems, and then examined in the general case. An approach based on subspace identification is proposed.

control engineering,
large scale systems

http://resolver.tudelft.nl/uuid:ac25ec15-698b-4c46-a02f-c7115cdcea27

2010-06-21

9789461130112

Institutional Repository

doctoral thesis

(c) 2010 Massioni, P.