Simultaneous Optimal Design of Structural and Control Systems Including Discrete Design Variables

摘要

We formulate a simultaneous optimal design problem of structural and control systems including discrete design variables. The problem generally becomes nonlinear and/or nondifferentiable optimization problem whose design variables are continuous or discrete. Since the nondifferenti- ability of the problem, we can not apply standard descent-based nonlinear optimization techniques such as steepest descent method, Quasi-Newton method etc.. Even if a subproblem, which is generated by fixing discrete design variables of the original problem, is corresponding to BMI (Bilinear Matrix Inequality), it is difficult to obtain the (global) optimal solution efficiently because of NP hardness nature of BMI. In this paper, we apply SA (Simulated Annealing) which is known as the one of the probabilistic optimization method. We present a new controller parametrization of the controller based on Youla parametrization. This parametrization does not need numerical computational procedure, such as solving Riccati equation or LMI to obtain stabilizing controller. Moreover, the class of the controller is at least larger than that of DVFB control (which is also a stabilizing control law without numerical computational procedure). We give a design example and show the effectiveness of the proposed design method.