Set-membership state estimation with nonlinear equality constraints and quantization

In this paper, our previous results on set-membership state estimation for the systems with linear state equality constraints are extended to the systems with both nonlinear state equality constraints and quantized output measurements. The quantization errors in collecting the system output measurements are treated as bounded uncertainties. To achieve the objective in finding the consistent set of state estimates while removing the conservativeness introduced by the Finsler's Lemma, three main techniques are introduced in this paper. Firstly, an improved linearization technique is performed on the nonlinear equality constraints. Secondly, a system model with reduced dimensions is derived, based on which an ellipsoid set of estimates for the state subspace is obtained. Thirdly, we combine the state subspace estimation result with a full-space estimation result obtained by extending a representative method (called the Yang and Li's method) on state estimation with nonlinear state equality constraints and quantization. The estimation results for the full state space in this paper are finally obtained. It is proved that the final set of state estimates is not only ensured to contain the true state, but also less conservative than that obtained by directly extending the Yang and Li's method. Simulation results are provided to validate the theoretical analysis.