Controller synthesis using interval methods

Controller synthesis using interval methods

Kootstra, P.

De Schutter, B. (mentor)

Mechanical, Maritime and Materials Engineering

Delft Center for Systems and Control

Systems & Control

2014-07-07

This thesis investigates whether interval methods can be employed in the construction of a novel controller synthesis algorithm based on backward induction. Interval methods are methods employing interval arithmetic, which is an arithmetic defined on real-valued intervals rather than on real-valued numbers. In the controller synthesis algorithm presented in this thesis interval methods are used to determine pre-images, represent approximations of closed sets, implement operations on these sets, and solve non-linear constrained optimisation problems without the need for derivatives. While interval methods only impose modest requirements, i.e., they require that interval extensions of the difference equation describing (or approximating) the plant dynamics, cost function, and inequality constraints can be constructed, they do however suffer from the curse of dimensionality. In the presented synthesis algorithm the curse of dimensionality limits practical use to systems for which the number of states and control inputs are relatively low. The thesis can be divided into four parts: - The first part of this thesis (Chapters 2, 3 and 4) introduces interval arithmetic, a number of interval methods, and set computation. - In the second part of the thesis (Chapter 5) the controller synthesis algorithm is presented and implemented using the concepts presented in the first part of the thesis. - In the third part of the thesis (Chapter 6) the implemented synthesis algorithm is successfully used to generate, and test the viability of, controllers for two benchmark problems. - The fourth part (Chapter 7) concludes the thesis, gives recommendations for improving the synthesis algorithm and suggests a number of topics worth considering for future research. In conclusion, this thesis shows that interval methods can be used to construct a controller synthesis algorithm for non-trivial control problems.

control
controller synthesis
optimisation
interval methods
interval arithmetic
dynamic programming
backward induction

http://resolver.tudelft.nl/uuid:f0cb28a9-263c-40e3-ad94-b203ec3e095b

2014-07-07

Student theses

master thesis

(c) 2014 Kootstra, P.