A Lyapunov Approach to H2 Iterative Adjustment for Fixed Structure Controllers

The adjustment of fixed structure controllers becomes a major issue in the development of complex control systems. Indeed, for long term project, the controller structure is often fixed at an early stage while the tuning of controller parameters remains possible all along the project. It is also a key point whenever multi-objective design problems are tackled. The objective of the fixed structure controllers H2 adjustment is to adjust selected gains of a given control law in order to reduce the H2 norm of a transfer function representative of some performance criterium while minimizing all other changes in the closed loop behavior. This paper deals with methodological aspects of H2 adjustment. We present the development of a Lyapunov approach based on the classical Lyapunov computation of H2 norms. An analytic sensitivity analysis is carried out that leads to an efficient gradient like search. Furthermore we show that fast and accurate numerical procedures may be derived allowing to work with large scale models often encountered in adjustment aeronautical applications.