Constrained ℋ2 Optimization

As an extension of the constrained linear quadratic optimization algorithm, a constrained ℋ 2 optimization algorithm is proposed, where the initial state dependency of the optimal solution is removed under certain assumptions. This algorithm aims to optimize the required parameters by hybridizing the direct computation of the projection gradient and line search of the optimal step in an iterative framework, where the determination of the unconstrained gradient for the standard ℋ 2 problem in both finite and infinite horizons, and the projection of the gradient onto the constrained hyperplane are provided with theoretical analysis. Similar to the constrained linear quadratic optimization algorithm, by the execution of the proposed constrained ℋ 2 optimization algorithm, the functional cost is monotonically decreasing while the stability of the closed-loop system is guaranteed throughout the optimization process. The algorithm can be used for a class of integrated mechatronic design problems as well. A case study on a mechatronic design problem in a flexure-linked DHG is addressed and the experimental results demonstrate the practical appeal of the proposed constrained ℋ 2 optimization algorithm.