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

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