Electrical Engineering-Systems Dept.

*** SEMINAR ***

Rabin Shaltiel

(M.Sc. student under the supervision of Prof. Uri Shaked(

on the subject:

Robust and time varying output-feedback control and its applications to missile control

One of the main merits of H_∞ control design is its ability to construct controllers that are robust in the sense that they are built to cope with prescribed ranges of parameter uncertainties. Although the full state-feedback problem has provided a simple convex solution, the output-feedback control problem has been shown to be a non convex problem.

Several different methods have been offered to overcome this problem. Recently, a new method was proposed by V. Suplin and U. Shaked for the design of robust continuous-time output-feedback controllers with polytopic type uncertainties. An augmented state-space model is constructed, which brings the output-feedback design problem to an equivalent problem of full state-feedback control. Unfortunately, the latter method cannot cope with multi-input multi-output (MIMO) unstable systems that have more outputs than inputs.

In this work, two extensions to the latter method are introduced. The first deals with the unstable MIMO issue. This is done by exploiting the H_∞-norm relation, which states that the H_∞-norm of a system is equal to the norm of its adjoint. Using this relation it is possible to transform the given system with more outputs than inputs into a new system with more inputs than outputs, overcoming the above mentioned MIMO difficulty. In order to reduce the conservatism of the solution for the adjoint system, a second extension is introduced. This is achieved by using linearly time varying Lyapunov function. Both extensions are obtained using Linear Matrix Inequalities (LMIs).

The theory derived is used to solve a problem of robust control design of a missile. The extension proposed here is first tested on the missile problem for the open-loop stable case. Applying the method of V. Suplin and U. Shaked on the missile problem, and comparing the results obtained with the current work, shows no major difference in the H_∞-norm achieved. Then, the missile problem for the unstable case is examined. The current method achieved plausible results, both for the obtained bound on the corresponding H_∞-norm and the behavior of the step and impulse responses.