This paper presents a data-driven approach to the design of predictive controllers. The prediction matrices utilized in standard model predictive control (MPC) algorithms are typically constructed using knowledge of a system model such as, state-space or input-output models. Instead, we directly estimate the prediction matrices relating future outputs with current and future inputs from measured data, off-line. Online, the developed data-driven predictive controller reduces to solving a quadratic program with a similar structure and complexity as linear MPC. Additionally, we develop a new procedure for estimating prediction matrices from data for predictive controllers with integral action, corresponding to the rate-based formulation of linear MPC. The effectiveness of the developed data-driven predictive controller is illustrated on position control of a linear motor model.
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, which mostly differ in the construction of the predictor: estimated prediction matrices (unbiased for large data) or Hankel data matrices as predictor (allows for optimizing the bias/variance trade-off). In this paper we develop a novel, generalized DPC (GDPC) algorithm that constructs the predicted input sequence as the sum of a known input sequence and an optimized input sequence. The predicted output corresponding to the known input sequence is computed using an unbiased, least squares predictor, while the optimized predicted output is computed using a Hankel matrix based 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 minimal size Hankel matrix can match the performance of data-enabled predictive control with a larger Hankel matrix in the presence of noisy data.
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