In this thesis we have studied balanced model reduction techniques for linear control systems, specifically balanced truncation and singular perturbation approximation. Aspecialfeatureofthesemethods,ascomparedtocloselyrelatedrational approximation techniques for linear systems, is that they allow for an a priori L2 and (frequency domain) H∞ bounds of the approximation error. These methods have been successfully applied for system with homogeneous initial conditions but only little attention has been paid to systems with inhomogeneous initial conditions or feedback systems. For open-loop control proplems, we have derived an L2 error bound for balanced truncation and singular perturbation approximation for system with nonhomogeneous initial condition, extending research work by Antoulas etal. The theoretical results have been validated numerically with extensive comparison between different systems and balanced truncation and singular perturbation model reduction. For closed-loop, one of the most important methods in control problems called linear quadratic regulator (LQR) has been introduced. This is used to find an optimal control that minimizes the quadratic cost function. In order to do that we have used formal asymptotics for the Pontryagin maximum principle (PMP) and the underlying algebraic Riccati equation. The outcome of this section are case description under which balanced truncation and the singular perturbation approximation give good closed-loop performance. The formal calculations are validated by numerical experiments, illustrating that the reduced-order can be used to approximate the optimal control of the original system. Finally, we studied two different test cases to demonstrate the validity of the theoritical results.
 

العنوان

Berlin, den

الناشر

Berlin, den

بلد الناشر

ألمانيا

نوع المنشور

مطبوع فقط

المجلد

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السنة

2016

الصفحات

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