TY - JOUR
AU - Yin, Xin
AU - Zhang, Qichun
TI - Backstepping-based state estimation for a class of stochastic nonlinear systems
JO - Complex Engineering Systems
PY - 2022
VL - 2
IS - 1
SP -
EP - 1
SN -
AB - The state estimation problem is investigated for a class of continuous-time stochastic nonlinear systems, where a novel filter design method is proposed based on backstepping design and stochastic differential equation. In particular, the structure of the filter is developed following the nonlinear system model, and then the estimation error dynamics can be described by a stochastic differential equation. Motivated by backstepping procedure, the nonlinear dynamics can be converted to an Ornsteinâ€“Uhlenbeck process via the control loop design. Thus, the estimation can be achieved once the estimation error is bounded and the variance of the error can be optimized. Since the ideal estimation error is a Brownian motion, the filter parameters can be selected following the Lyapunov stability theory and variance assignment method. Following the same framework, the multivariate stochastic systems can be handled with the block backstepping design. To validate the presented design approach, a numerical example is given as the simulation results to demonstrate the state estimation performance.
KW - Continuous-time stochastic systems
KW - stochastic differential equation
KW - Ornsteinâ€“Uhlenbeck process
KW - backstepping
DO - 10.20517/ces.2021.13
UR - http://dx.doi.org/10.20517/ces.2021.13