A Control Approach for Nonlinear Stochastic State Uncertain Systems with Probabilistic Safety Guarantees

TL;DR

This paper introduces a control method for nonlinear stochastic systems with partial observations, leveraging deterministic control policies and importance sampling to ensure safety and efficiency in control sequence evaluation.

Contribution

It develops a novel sampling-based control design that combines deterministic nonlinear control with probabilistic safety guarantees for stochastic systems.

Findings

The approach guarantees safety over the prediction horizon.

It is computationally efficient, independent of state dimension.

Numerical simulations validate effectiveness and safety guarantees.

Abstract

This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state access and, often, relative degree one. We propose a control design approach that first generates a control policy for nonlinear deterministic models with full state observation. The resulting control policy is then used to build an importance-like probability distribution over the space of control sequences which are to be evaluated for the true stochastic and state-uncertain dynamics. This distribution serves in the sampling step within a random search control optimization procedure, to focus the exploration effort on certain regions of the control space. The sampled control sequences are assigned costs determined by a prescribed finite-horizon performance and safety measure, which is based on the stochastic dynamics. This sampling algorithm is parallelizable and shown to have computational complexity indifferent to the state dimension, and to be able to guarantee safety over the prescribed prediction horizon. A numerical simulation is provided to test the applicability and effectiveness of the presented approach and compare it to a certainty equivalence controller.