Data-Driven Predictive Control: Equivalence to Model Predictive Control Beyond Deterministic Linear Time-Invariant Systems

Abstract

In recent years, data-driven predictive control (DDPC) has emerged as an active research area, with well-known methods such as Data-enabled Predictive Control (DeePC) and Subspace Predictive Control (SPC) being validated through reliable experimental results. On the theoretical side, it has been established that both DeePC and SPC methods can generate equivalent control actions as one can obtain from Model Predictive Control (MPC), for deterministic linear time-invariant (LTI) systems. However, similar results do not yet exist for the application of DDPC beyond deterministic LTI systems. Therefore, the objective of our research is to generalize this theoretical equivalence between model-based and data-driven methods for more general classes of control systems.

In this thesis, we present our contributions to DDPC for linear time-varying (LTV) systems and stochastic LTI systems. In our first piece of work, we developed Periodic DeePC (P-DeePC) and Periodic SPC (P-SPC) methods, which generalize DeePC and SPC from LTI systems to linear time-periodic (LTP) systems, as a special case of LTV systems. Theoretically, we demonstrate that our P-DeePC and P-SPC methods have equivalence control actions as produced from MPC for deterministic LTP systems, under appropriate tuning conditions. As an intermediate step in our theoretical development, we extended certain aspects of behavioral systems theory from LTI systems to LTP/LTV systems. This includes extending Willems’ fundamental lemma to LTP systems and the defining the concepts of order and lag for LTV systems.

In our second piece of work, we proposed a control framework for stochastic LTI systems, namely Stochastic Data-Driven Predictive Control (SDDPC). Our SDDPC method theoretically achieves equivalent control performance to model-based Stochastic MPC, under idealized conditions of appropriate tuning and noise-free offline data. This method, which applies to general linear stochastic state-space systems, serves as an alternative to the data-driven method previously proposed by Pan et al., which also achieved theoretical equivalence to Stochastic MPC but was limited to a narrower class of systems. Beyond the theoretical assumption of noise-free offline data, we performed our SDDPC method in simulations with practical noisy offline data. The simulation results demonstrated that our SDDPC method outperforms benchmark methods, achieving lower cumulative tracking cost and lower rate and amount of constraint violation.