Energy and power optimization in a behavioural framework

Abstract

We tackle a number of quadratic optimization problems in the behavioural framework, in the spirit of the classical linear quadratic regulator problem for systems in state-space form. The central theme is dissipativity of the system at hand: we interpret our problems in terms of the exchange of energy between the system and the outside world. Using the Kalman-Yakubovich-Popov lemma in the behavioural framework, we arrive at energy and power optimizing control laws in terms of the solutions to a linear matrix inequality in the original data that is used to specify the problems.Keywords dissipative systems theory, linear quadratic (LQ) optimal control, H2 optimal control, behavioural approach, quadratic differential form (QDF), linear matrix inequality (LkII)