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

Abstract

In this paper, we present a data-driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time-invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured data and knowledge of an upper bound on the system order. First, we develop a state-feedback MPC scheme, based on input-state data, which guarantees closed-loop practical exponential stability and recursive feasibility as well as closed-loop constraint satisfaction. The scheme is extended by a suitable constraint tightening, which can also be constructed using only data. In order to control a priori unstable systems, the presented scheme contains a pre-stabilizing controller and an associated input constraint tightening. We first present the proposed data-driven MPC scheme for the case of full state measurements, and also provide extensions for obtaining similar closed-loop guarantees in case of output feedback. The presented scheme is applied to a numerical example.

Robust Data-Driven Moving Horizon Estimation for Linear Discrete-Time Systems

“…x . However, this procedure would be very conservative, because all terms related to the (cumulated) process noise would need to be upper bounded by the maximum cumulated process noise (as it is the case in the dual problem of robust datadriven MPC, compare [34]). A quantitative analysis and/or the development of less conservative data-driven MHE schemes for the case of process noise is an interesting topic for future research.…”

Stability in data-driven MPC: an inherent robustness perspective

“…Output constraints require a constraint tightening, compare [14], [19], and are omitted for simplicity. At time t and for a given set of (noisy) initial conditions {u k , ỹk } t−1 k=t−n , we consider the optimization problem…”

“…Moreover, the overall analysis is substantially shorter. On the other hand, the tailored approaches from [13], [17] yield more insightful and interpretable bounds related to system properties (e.g., controllability and observability), which can even be used to construct a constraint tightening guaranteeing robust output constraint satisfaction [14], [19].…”