Identification of LTV Dynamical Models with Smooth or Discontinuous Time Evolution by means of Convex Optimization
This work addresses the challenge of system identification for time-varying models, which is incremental as it builds on existing trend filtering and convex optimization techniques to improve modeling in specific domains like robotics and reinforcement learning.
The authors tackled the problem of identifying linear time-varying dynamical models by connecting trend filtering with system identification, resulting in new convex optimization methods that can handle both smooth and discontinuous changes in model parameters, and demonstrated their applicability in simulations including jump-linear systems, a nonlinear robot arm, and model-based reinforcement learning.
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.