Observer Design for Stochastic Nonlinear Systems using Contraction Analysis
This paper presents a new observer for Itô stochastic nonlinear systems with guaranteed stability. Contraction analysis is used to analyze incremental stability of the observer for an Itô stochastic nonlinear system. A bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of contraction rate and maximum noise intensity. The observer design is based on non-unique state-dependent coefficient (SDC) forms which parametrize the nonlinearity in an extended linear form. In this paper, a convex combination of several parametrizations is used. An optimization problem with state-dependent linear matrix inequality (SDLMI) constraints is formulated to select the free parameters of the convex combination for achieving faster convergence and robustness against disturbances. Moreover, the L_2 norm of the disturbance and noise to the estimation error is shown to be finite. The present algorithm shows improved performance in comparison to the extended Kalman filter (EKF) and the state-dependent differential Riccati equation (SDDRE) filter in simulation.
© 2012 IEEE. Date Added to IEEE Xplore: 04 February 2013. This project was supported by the Office of Naval Research (ONR) under Award No. N00014-11-1-0088. This paper benefited from discussions with Prof. Jean-Jacques Slotine. We thank the anonymous reviewers for their valuable comments.