Design Of Gradienoptimal Robust Functional Observers

In this dissertation, a new approach for design of robust functional observers is presented. The purpose of robust functional observer design is to reconstruct the state combination of the system. When there are uncertainties in the original system, the reconstructed state combination of the system generally can not give out asymptotic estimate of the state combination of the original system. Therefore, consideration of robustness in the issue of observer design is necessary. Robust functional observer design is a large class of problems in robust control system design. In this dissertation, an index for design of robust functional observers is proposed properly, and then the problem of design of robust functional observers is turned into an optimization problem of the proposed index. Firstly, by solving Sylvester matrix equation, the parametric expressions of observer gain matrices T and L are obtained. Since these expressions are in the form of linear combination of design parameters, the calculations of gradients of T and L are much easy. Secondly, under the overall perturbations of the system matrices the optimization index of robust observer design is established. The index does not sacrifice any design freedom in the observer. Since the Frobenius norm is used in the proposed index, gradient formula of the index can be obtained easily. Finally, the optimization problem is solved by using Conjugate Gradient Method, and then the numerical solution for all observer gain matrices is obtained.Compared with the other approaches, the main advantage of this approach is as follows: (1) The optimization problem is solved by applying gradient method. This leads to rapid convergence of the algorithm of this optimization problem. (2) The problem for finding the general solution of the complex, nonlinear observer condition matrix equation is turned into an optimization problem for an optimization index. By this way, the algorithm for robust observer design is made much easy.Two numerical examples are given to demonstrate the effect of the proposed approach. Especially in the first example, numerical simulations are given to support our results.