Mixed HZ/H,-Control Using Parameter Optimization Methods

In this paper we consider the problem of minimum nominal Hz-norm with H,-constraints for systems with multiple operating points. The performance measure is defined as a weighted sum of the corresponding nominal H2norms while robust stability of the individual closed-loop systems is defined in terms of a H,-bound for each plant condition. In this paper we define a new time-domain scalar cost function J, ( t , ) representing the H,-bounds in an overall cost function for the mixed H’/H,-design. J , ( t j ) is, for finite time t f , a penalty function and, for t j + 00, a barrier function. Using J m ( t j ) , the mixed Hz/H,-design problem results in an unconstrained o p timization problem, that, for I! -, 00, recovers the original objective of minimizing the performance measure s u b ject to the Hm-bounds. The resulting optimization problem is smooth and hence standard gradient-based software can be applied. The class of controllers considered includes proper and strictly proper LTI controllers with fixed structure and/or fixed order.