LMI-Based Set-Membership Estimation of Uncertain Dynamic Systems Research and Application
|School||Changsha University of Science and Technology|
|Course||Control Theory and Control Engineering|
|Keywords||Set-membership Estimation Uncertain Systems Linear Matrix Inequality Semidefinite Programming Mobile Robot Localization|
In the case of the accurate system model and noise boundary, Fogel and Huang proposed the optimal bounded ellipsoid set-membership estimation. This algorithm is set to become a member of an important branch of state estimation theory. Typically, the use of various methods can only try to get the system model accurately reflects characteristic of the system, The error always exists between them. There are irreconcilable contradictions bewteen precision and complexity of the system. For this situation, large number of studies over a period of time as a prerequisite for the accurate system model, studied the problem that how to expression the uncertainty of the system through the state disturbance and measurement noise. In this hypothesis, the researchers made a lot of results. But suppose there can not make up their own shortcomings.In this thesis, semidefinite programming as the main framework, the new set-membership state estimation algorithm was proposed for the robust problem of uncertain system using Linear Matrix Inequality (LMI) constraints. First, the uncertainties structured are norm bounded and represented by linear fractional resprestation (LFR), so that the estimation of the relative situation is computed by robust filtering techniques. Second, the proposed technique is based on a classical prediction/measurement update recursion which requires at each step the solution of a convex semidefinite optimization problem under LMI.For linear system, the main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using set-membership state estimation for convex optimization. For nonlinear system, the efficient scheme takes into explicit account the effects of nonlinearities via second-order information of Taylor formula, thus to improve the accuracy of estimation. From the actual needs, And then, replacing the traditional extended Kalman filter algorithm, LMI-based set-membership state estimation algorithm is applied to mobile robot location using odometer sensor and visual sensor. Simulation results demonstrate the effectiveness of the algorithm. Not only the system state estimation accuracy improved, but more significant is the greatly enhanced the robustness of the algorithm.