Nonsmooth optimization based multiple robust controller design under coupling partitioned uncertainty

This paper proposes a nonsmooth optimization technique to cope with the H_∞ synthesis problem under weak coupling uncertainty. For some kind of systems, a single controller cannot be found in terms of a given robust performance objective, whereas a multiple robust controller can satisfy the desired performances by introducing extra controllers and dividing the entire uncertainty into small partitioned sets. Such partitioned sets can be generated based on the small gain theorem and μ -analysis. In addition to solving the weak-coupled parametric uncertainty, the partition with decoupled algorithm can improve the design efficiency. However, the multiple robust controller design has to be transformed into a nonsmooth optimization problem. This paper uses the Clarke subdifferential and steepest descent method to acquire the gradient information of the nonsmooth function. The validity of our method is illustrated and verified by a practical controller design case-study for a satellite attitude control problem.