Robust pole assignment by output feedback using optimization methods.

A robust output feedback pole assignment method, which seeks to achieve a robust solution in the sense that the assigned poles are as insensitive as possible to perturbations in the system parameters, is studied. In particular, this work is concerned with pole assignment in a specified region rather than assignment to exact positions, whereby the freedom to obtain a robust solution may be realized. The robust output feedback pole assignment problem is formulated as an optimization problem with a special structure in matrix form. Efficient optimization methods and numerical algorithms for solving such a problem are proposed by introducing a concept of the derivative of a matrix valued function. The homotopy method, which is known as a globally convergent method, is applied to solve the robust output feedback pole assignment problem to overcome possible difficulties with the choice of feasible starting point. A new algorithm based on the homotopy approach for solving the pole assignment problem is proposed. Numerical examples of the robust pole assignment problem demonstrate how the homotopy algorithm globally converges to optimal solutions regardless of initial starting points with an appropriately defined homotopy mapping. The proposed algorithms are illustrated using an aircraft case study. It is seen that the controllers obtained using robust pole assignment methods yield the robust flight control and maintain the closed-loop system properties closer to the nominal ones. They are shown to be more robust than those obtained by an alternative direct pole assignment method which is frequently used to develop aircraft control strategies without attempting to optimize any robustness criterion. Indeed, the robust output feedback pole assignment method proposed in this study is a method which can be applied for control system design to achieve one important design objective, robustness.