Leveraging Statistical Prior Knowledge in Adaptive Control of Nonlinear Systems

Abstract

Assuming access to prior knowledge about the unknown system parameter θ, given as a probability prior ϕ(θ), we study how such information can be incorporated into the adaptive control design of nonlinear systems. To this end, we propose a new parameter estimation law, and show that it pro-motes convergence of parameter estimates to high-probability regions of the parameter space. Our approach is particularly useful when employed as a single universal controller for a large population of systems with similar dynamic structure but different parameter values. In this scenario, our method, on average, leads to a more accurate parameter estimate, which consequently improves transient performance and accelerates state convergence. Numerical studies confirm the effectiveness of the proposed method.