Trajectory-based data-driven predictive control and the state-space predictor

TL;DR

This paper introduces a trajectory-based data-driven predictive control framework that unifies various existing methods and demonstrates superior performance with small datasets using a state-space predictor.

Contribution

It proposes a new state-space predictor within trajectory predictive control that unifies multiple DDPC methods and leverages linear MPC theory for improved performance.

Findings

TPC encompasses many DDPC methods.

The state-space predictor enables TPC to be a form of linear MPC.

Performance approaches oracle $H_2$-optimal control, especially with small datasets.

Abstract

We define trajectory predictive control (TPC) as a family of output-feedback indirect data-driven predictive control (DDPC) methods that represent the output trajectory of a discrete-time system as a linear function of the recent input/output history and the planned input trajectory. This paper shows that for different choices of the trajectory predictor, TPC encompasses a wide variety of DDPC methods, including subspace predictive control (SPC), closed-loop SPC, $\gamma$-DDPC, causal-$\gamma$-DDPC, transient predictive control, and others. This paper introduces a trajectory predictor that corresponds to a linear state-space model with the recent input/output history as the state. With this state-space predictor, TPC is a special case of linear model predictive control and therefore inherits its mature theory. In numerical experiments, TPC performance approaches the limit of oracle $H_2$-optimal control with perfect knowledge of the underlying system model. For TPC with small training datasets, the state-space predictor outperforms other predictors because it has fewer parameters.