Beyond Bounded Noise: Stochastic Set-Membership Estimation for Nonlinear Systems
This addresses robust control synthesis with probabilistic guarantees for nonlinear systems affected by sub-Gaussian noise, representing a novel method for a known bottleneck.
The paper tackles the problem of set-membership estimation for nonlinear dynamical systems with unbounded stochastic noise, deriving a procedure that provides a finite-sample uncertainty set containing the true parameters with high probability and establishing convergence conditions and rate bounds.
In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. By employing a bound on the sample covariance matrix, we are able to provide a finite-sample uncertainty set containing the true system parameters with high probability. Our approach can be natively applied to a wide class of nonlinear systems affected by sub- Gaussian noise. Through our analysis, we provide conditions under which the proposed uncertainty set converges to the true system parameters and establish an upper bound on the convergence rate. The proposed uncertainty set can be used directly for the synthesis of robust controllers with probabilistic stability and performance guarantees. Concluding numerical examples demonstrate the advantages of the proposed formulation over established approaches.