Observer Design For Incremental Nonlinear Systems With Application To Vehicle State Estimation

In recent years,more and more vehicles have equipped with active safety control systems.Its work principle is based on obtaining the real-time information of vehicles,such as yaw rate and vehicle sideslip angle.Generally,the direct measurement of vehicle side-slip angle is very expensive,which limits its applications to family cars.Therefore,it needs indirect estimation via soft-sensing techniques.The dynamic methodology is one of the main methods for vehicle state estimation,and it is realized through the state observer technique.State estimation or observer design is also a central issue in control system design.The well-known Kalman filter and Luenberger observers have already provided a complete solution for state estimation of linear systems.Nowadays,the efforts in this field are mainly focused on the observer design for nonlinear systems.The existing techniques for nonlinear observer designs,including those for vehicle state estimation,generally need assume that the system satisfies a class of Lipschitz-like conditions and are usually only applicable to the case in which the Lipschitz constant is small.Therefore,many existing results are quite conservative.In this paper,we study the design of circle-criterion observers for a class of monotone increasing systems and the design of an exponential observer with output nonlinearities by introducing the so-called incremental quadratic constraints.We also apply the proposed state observers for incremental nonlinear systems to vehicle state estimation and flexible manipulator systems.The main research contents and novelty can be summarized as follows:(1)Based on the classical Luenberger observers,we design a circle-criterion observer for incremental quadratic nonlinear systems via mapping the output estimation errors into the nonlinear term of the observer system.The new design of the observer includes the Luenberger observer as a special case,and extend the design degree of freedom,and reduce the conservatism in existing designs.As an application,we apply the proposed circle-criterion observer to vehicle dynamic state space model.We simulate the vehicle yaw rate and vehicle sideslip angle via the SCILAB and MATLAB software platform.The simulation results verify the effectiveness of circle-criterion based observer design method for vehicle state estimation.(2)Consider a class of nonlinear systems with output nonlinearities and satisfy incremental quadratic constraints.We study the exponential observer design and establish sufficient conditions in term of linear matrix inequalities(LMIs)which ensure exponential convergence of estimation error systems.The proposed results extended Arcak’s circle-criterion observers from the sector nonlinearity to a class of nonlinear systems satisfying incremental quadratic constraints.It also includes the existing observers for Lipschitz or one-sided Lipschitz nonlinear systems as some special cases.The effectiveness of the proposed observer design is verified by MATLAB for a class of single link flexible manipulator systems with output nonlinearities.