Discrete-Time Nonlinear System Identification: A Fixed-Time Concurrent Learning Approach

This article develops a fixed-time identifier for modeling unknown discrete-time nonlinear systems without requiring the standard persistence of excitation (PE) condition. A data-driven update law based on a modified gradient descent (GD) update law is presented to learn the system parameters, which relies on the concurrent learning approach under which the recorded past data and the current data are employed concurrently. Fixed-time convergence guarantees are provided for the modified GD update law under the condition that the recorded data fulfills a rank condition, which is less restrictive than the standard PE condition. To guarantee fixed-time convergence, fixed-time Lyapunov analysis is leveraged. Compared to typical GD-based update laws, two main advantages of the presented approach are: 1) the modified GD update law guarantees fixed-time convergence instead of asymptotic convergence and 2) the convergence guarantee is provided under an easy-to-check rank condition rather than the standard PE condition, which is hard or even impossible to check online. Simulation results are provided to verify the obtained results.