Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.

Area of Science:

• Control Theory
• Machine Learning
• Stochastic Systems

Background:

• Designing robust controllers for nonlinear stochastic systems with functional uncertainties is challenging.
• Probabilistic control methods offer a framework for addressing these challenges, particularly when reliable system models are unavailable.

Purpose of the Study:

• To present a generalized probabilistic controller design for minimizing Kullback-Leibler divergence between actual and ideal joint probability density functions (pdfs).
• To systematically incorporate system uncertainties in the absence of reliable models.
• To demonstrate the controller's ability to make conditional joint pdfs follow ideal ones.

Main Methods:

• Estimating probabilistic system models from process data using mixture density networks (MDNs).
• Modeling pdf parameters as dependent on state and control inputs.
• Utilizing dynamic programming and adaptive critic methods for optimal controller construction.

Main Results:

• Explicit formulations for optimal generalized probabilistic controllers were derived based on input-dependent density parameters.
• The proposed controller successfully minimized the divergence between actual and ideal joint pdfs.
• Simulation results demonstrated the algorithm's effectiveness and yielded encouraging outcomes.

Conclusions:

• The generalized probabilistic controller effectively manages functional uncertainties in nonlinear stochastic systems.
• Mixture density networks and dynamic programming provide a robust framework for controller design.
• The approach enables the achievement of desired probability density function లక్ష్యాలు in closed-loop systems.