Observer Design for Sampled-Data Systems via Deterministic Learning.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Machine Learning

Background:

• Designing observers for unknown nonlinear systems with recurrent motions is challenging.
• Existing methods often rely on high-gain observers (HGOs), which can amplify noise and limit applicability.
• Accurate state estimation is crucial for understanding and controlling complex dynamical systems.

Purpose of the Study:

• To propose a unified approach for designing sampled-data observers for unknown nonlinear systems.
• To develop a non-high-gain observer utilizing deterministic learning for improved state estimation.
• To accurately approximate nonlinear dynamics using recurrent estimated trajectories.

Main Methods:

• A discrete-time high-gain observer (HGO) was used to obtain state trajectories from sampled outputs.
• A dynamical radial basis function network (RBFN) was employed to approximate nonlinear dynamics using recurrent estimated trajectories.
• A novel RBFN-based observer was designed, integrating deterministic learning with the HGO framework.

Main Results:

• The proposed method accurately approximates nonlinear dynamics along the estimated sampled-data trajectory.
• The RBFN-based observer achieved correct state observation without resorting to high gains.
• Deterministic learning, combined with the discrete-time HGO, enabled accurate non-high-gain state estimation.

Conclusions:

• The unified approach effectively addresses state observation for unknown nonlinear systems with recurrent motions.
• Integrating deterministic learning with HGO offers a promising pathway for non-high-gain state estimation in sampled-data systems.
• Simulation results validate the effectiveness of the proposed observer design methodology.