Observer design for stochastic nonlinear systems using contraction analysis

Ashwin P. Dani, Soon Jo Chung, Seth Hutchinson

Research output: Contribution to journalConference article

Abstract

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 L2 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.

Original languageEnglish (US)
Article number6425977
Pages (from-to)6028-6035
Number of pages8
JournalProceedings of the IEEE Conference on Decision and Control
DOIs
StatePublished - Dec 1 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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