Constrained ℋ2 Guaranteed Cost Optimization

Since the model uncertainties are not explicitly handled in the linear-quadratic-based and the ℋ 2 -based constrained optimization algorithms, a class of motion control problem for an uncertain system can be converted to an ℋ 2 guaranteed cost control problem considering convex-bounded model uncertainties, such that the upper bound to the ℋ 2 -norm of the closed-loop system transmittance from the exogenous disturbance to the regulated variables is minimized. Since the gain matrix is under certain structural constraints, algorithms are proposed to convert this problem to a decentralized control system design problem without structural constraints. As supported by relevant theoretical results, the constraints from the state space are transformed into the extended parameter space, then all the stabilizing gains that satisfy the structural constraints are parameterized over the intersection of a convex set and a non-convex set defined by a nonlinear real-valued function. Eventually, numerical procedures are developed to obtain the global optimal solution, and the closed-loop robust stability is ensured with guaranteed performance. A mechatronic design problem in a flexure-linked DHG is presented, and the experimental results successfully validate the optimality and the robustness by using the proposed optimization algorithm.