Probabilistic Control for Uncertain Systems

TL;DR

This paper introduces a probabilistic control framework using mixture density networks to handle nonlinear, uncertain systems, minimizing system uncertainty and ensuring stability in stochastic environments.

Contribution

It presents a novel probabilistic control approach that models forward and inverse dynamics with mixture density networks, accounting for uncertainties and nonlinearity.

Findings

Successfully applied to nonlinear stochastic control examples

Demonstrated stability of the closed-loop system

Effective in handling additive and multiplicative noise

Abstract

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.