Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling

Area of Science:

• * Nonlinear Dynamics and Control
• * Computational Neuroscience
• * Time-Series Analysis

Background:

• * Estimating and controlling dynamical systems from time-series data is crucial for understanding nonlinear behaviors.
• * Existing methods often struggle with noisy observations and the inherent nonlinearities of complex systems.
• * Accurate state estimation and control are vital for applications ranging from physics to biology.

Purpose of the Study:

• * To develop a unified probabilistic framework for simultaneous state estimation and control of nonlinear dynamical systems.
• * To address challenges posed by noisy observations and latent state uncertainties.
• * To demonstrate the framework's efficacy on diverse nonlinear systems.

Main Methods:

• * A probabilistic framework utilizing the particle filter is proposed.
• * The particle filter serves a dual role: state/dynamics estimator and controller.
• * The method is validated using the Lorenz chaotic system and the Morris-Lecar neuron model.

Main Results:

• * The proposed framework successfully estimates and controls nonlinear dynamical systems.
• * The particle filter effectively manages system nonlinearity and state uncertainty.
• * Both chaotic and neuronal system models showed positive results.

Conclusions:

• * The developed probabilistic framework offers a robust solution for simultaneous estimation and control.
• * This approach enhances the ability to understand and manipulate complex nonlinear dynamics.
• * The method shows promise for various scientific and engineering domains involving time-series data.