Abstract
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 Ornstein–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.
Highlights
Since state space has been widely used to present the model of the dynamic system, state estimation is a key research problem to characterize the system properties as the internal states are mostly unmeasurable
The state estimation problem is investigated for a class of stochastic nonlinear systems, where the system model is described by the stochastic differential equation
The design scheme is divided into two components: (1) The filtering structure can be confirmed based on the system model while the nonlinear estimation error can be further formulated
Summary
Since state space has been widely used to present the model of the dynamic system, state estimation is a key research problem to characterize the system properties as the internal states are mostly unmeasurable. Process noise and measurement noise widely exist in the state space model It is a filtering problem for state estimation if the random noises have been considered in the design procedure. To deal with the continuous-time model, the Kalman-Bucy filter[9] was proposed by solving linear Riccati equation. Trying to eliminate the nonlinear effects in the closed-loop, in this paper, the backstepping design is adopted for the estimation error dynamics as the system model is represented by stochastic differential equation. Note that the system states are Gaussian due to the fact that the system dynamics are converted to being linear, while the stochastic differential equation is subjected to Brownian motion.
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