Discrete-Time Nonlinear Systems Identification with Probabilistic Safety and Stability Constraints

TL;DR

This paper introduces a probabilistic approach to identify discrete-time nonlinear systems using ELMs, ensuring safety and stability with high probability through QCQP constraints validated on simulation examples.

Contribution

It develops a novel system identification method that incorporates probabilistic safety and stability constraints directly into the learning process.

Findings

Successfully guarantees safety for robot manipulator trajectories.

Ensures system stability with high probability in simulations.

Validates approach on hand-drawn shape motion data.

Abstract

This paper presents a discrete-time nonlinear system identification method while satisfying the stability and safety properties of the system with high probability. An Extreme Learning Machine (ELM) is used with a Gaussian assumption on the function reconstruction error. A quadratically constrained quadratic program (QCQP) is developed with probabilistic safety and stability constraints that are only required to be satisfied at sampled points inside the invariant region. The proposed method is validated using two simulation examples: a two degrees-of-freedom (DoF) robot manipulator with constraints on joint angles whose trajectories are guaranteed to remain inside a safe set and on motion trajectories data of a hand-drawn shape.