Identification of LTV Dynamical Models with Smooth or Discontinuous Time Evolution by means of Convex Optimization

TL;DR

This paper introduces convex optimization-based methods for identifying linear time-varying models, capable of capturing both smooth and abrupt changes in system dynamics, with applications demonstrated in various simulation scenarios.

Contribution

It connects trend filtering with system identification to develop new convex optimization methods for LTV models, allowing for both continuous and sparse discontinuous changes.

Findings

Effective identification of jump-linear systems.

Successful modeling of nonlinear robot arm dynamics.

Application to trajectory-centric reinforcement learning.

Abstract

We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamics over time, or causes discontinuous changes in model coefficients occurring at a finite (sparse) set of time instances. We further discuss the introduction of priors on the model parameters for situations where excitation is insufficient for identification. The identification problems are cast as convex optimization problems and are applicable to, e.g., ARX models and state-space models with time-varying parameters. We illustrate usage of the methods in simulations of jump-linear systems, a nonlinear robot arm with non-smooth friction and stiff contacts as well as in model-based, trajectory centric reinforcement learning on a smooth nonlinear system.