Generalized Data-Driven Predictive Control: Merging Subspace and Hankel Predictors

Data-driven predictive control (DPC) is becoming an attractive alternative to model predictive control as it requires less system knowledge for implementation and reliable data is increasingly available in smart engineering systems. Two main approaches exist within DPC: the subspace approach, which estimates prediction matrices (unbiased for large data) and the behavioral, data-enabled approach, which uses Hankel data matrices for prediction (allows for optimizing the bias/variance trade-off). In this paper we develop a novel, generalized DPC (GDPC) algorithm by merging subspace and Hankel predictors. The predicted input sequence is defined as the sum of a known, baseline input sequence, and an optimized input sequence. The corresponding baseline output sequence is computed using an unbiased, subspace predictor, while the optimized predicted output sequence is computed using a Hankel matrix predictor. By combining these two types of predictors, GDPC can achieve high performance for noisy data even when using a small Hankel matrix, which is computationally more efficient. Simulation results for a benchmark example from the literature show that GDPC with a reduced size Hankel matrix can match the performance of data-enabled predictive control with a larger Hankel matrix in the presence of noisy data.