Scalable robust output feedback MPC of linear sampled-data systems

Abstract

Cyber-physical control systems typically consist of two components: a clocked digital controller and a physical plant evolving in continuous time. Clearly, the state and input constraints must be satisfied not only at, but also between sampling times of the controller. We address this issue by proposing a robust output feedback model predictive control approach for sampled-data systems, which are affected by additive disturbances and measurement noise. To guarantee robust constraint satisfaction for an infinite time horizon, we present a scalable approach to compute safe terminal sets. Based on these sets and using scalable reachability analysis and convex optimization algorithms, we construct real-time controllers that explicitly consider all online computation times. We demonstrate the usefulness of our robust control approach using a vehicle platooning benchmark from the literature.

Scalable Robust Safety Filter With Unknown Disturbance Set

“…The existence of Ω mRPI is also a widely used assumption in robust MPC [18]- [20]. If such an Ω mRPI does not exist, the mRPI set S ⊂ R nx has the following property: (S × KS) ̸ ⊆ (X × U) or S × KS touches the bounds of X × U.…”

“…be the solution of (20) for any k mRPI ∈ N >0 . Then, the controller in (13) with optimal correction input zonotope sequence Z ⋆ u,(•) safely steers the system in (7a) starting from…”

“…To efficiently solve the COP in (20), we subsequently recommend how to choose the involved parameters. To cover X , we can uniformly sample from the unit hypersphere and use the obtained points as columns of the user-defined fixed generator matrix G fixed .…”

“…Safety filters can be efficiently implemented using, e.g., reachability analysis [11], [12], invariance control [13], [14], barrier functions [15], [16], or command governors [17]. These implementations usually use predictive control techniques [18]- [20], where an optimal control problem is iteratively solved online on a moving time horizon. By increasing this time horizon, the region of operation of the safe backup controller, also known as the safe set, can be enlarged [21].…”

“…For instance, the disturbance set is assumed to be known while the system dynamics is unknown [36], [37], which is quite unrealistic. The availability of such a priori disturbance sets is also a standard assumption in most robust model predictive control (MPC) approaches [18]- [20]. Alternatively, to obtain a margin that ensures safety online, the tightest estimate of the disturbance set can be multiplied by a safety factor greater than one [38], [39].…”