Robust Data-Enabled Predictive Control: Tractable Formulations and Performance Guarantees

Abstract

We introduce a general framework for robust dataenabled predictive control (DeePC) for linear time-invariant (LTI) systems. The proposed framework enables us to obtain model-free optimal control for LTI systems based on noisy input/output data. More specifically, robust DeePC solves a min-max optimization problem to compute the optimal control sequence that is resilient to all possible realizations of the uncertainties in the input/output data within a prescribed uncertainty set. We present computationally tractable reformulations of the min-max problem with various uncertainty sets. Furthermore, we show that even though an accurate prediction of the future behavior is unattainable in practice due to inaccessibility of the perfect input/output data, the obtained robust optimal control sequence provides performance guarantees for the actually realized input/output cost. We further show that the robust DeePC generalizes and robustifies the regularized DeePC (with quadratic regularization or 1-norm regularization) proposed in the literature. Finally, we demonstrate the performance of the proposed robust DeePC algorithm on high-fidelity, nonlinear, and noisy simulations of a grid-connected power converter system.

A novel constraint tightening approach for robust data-driven predictive control

“…Note that the following results can be easily extended to the case where, apart from the process disturbance w k , also additive measurement noise on the state measurements is present. In this case, the disturbance sequence in (6) has to be extended by the actual measurement noise instant occurring at time k and, in case of K = 0, the past measurement noise which are fed back into and propagated through the system dynamics. However, for the sake of simplicity, we consider only process disturbances throughout the paper.…”

“…Guarantees for recursive feasibility, stability, and robustness (in the presence of measurement noise) of the closed loop were first proven by Berberich et al [4]. In recent years, various further properties and extensions of this data-driven MPC framework have been studied, compare, e.g., the works by Coulson et al [5], Huang et al [6], Yin et al [7], [8], Xue and Matni [9], Furieri et al [10], Berberich et al [11] and the overview paper by Markovsky and Dörfler [12].…”

Data-Driven Model Predictive Control for Linear Time-Periodic Systems

“…By leveraging the fundamental lemma, system outputs can be predicted without a parametric system model. From this observation, data-driven MPC (DDMPC) methods have been developed wherein the need for a parametric system model is eliminated [9]- [16]. A particular DDMPC algorithm named Data-enabled Predictive Control (DeePC) [12]- [16], has been successfully applied to control problems in power systems [17], [18], motor drives [19] and quad-copters [20].…”

“…From this observation, data-driven MPC (DDMPC) methods have been developed wherein the need for a parametric system model is eliminated [9]- [16]. A particular DDMPC algorithm named Data-enabled Predictive Control (DeePC) [12]- [16], has been successfully applied to control problems in power systems [17], [18], motor drives [19] and quad-copters [20]. While the methods [9]- [16] focus on LTI systems, some extensions have been developed for linear parametervarying systems [21] and for specific types of nonlinear systems [22].…”

Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics

“…Typically, observer design techniques rely on the system's model for estimating the state in real-time. However, as modern engineering systems are becoming increasingly complex, developing accurate models to describe a system's behavior is quite challenging [1], [2]. This motivates the development of a data-driven approach for set-based state estimation.…”