Ensuring safety for sampled data systems: An efficient algorithm for filtering potentially unsafe input signals

Invariant, viability and discriminating kernel under-approximation via zonotope scaling

“…Although we have insu cient space to make a detailed comparison with the ellipsoid-based results from [17], we can observe that in roughly the same computational time (albeit on a slightly faster laptop) our zonotope-based algorithm is able to nd a much larger discriminating set over twice the time horizon with double the time resolution. Furthermore, the zonotope representation is much less conservative with its treatment of the disturbance input, and hence we do not need to hybridize or to restrict the range of x 5 and u 1 so severely.…”

“…The need to develop scalable algorithms for viability / invariance in addition to those for reachability is therefore practical: The former require under-approximation while the latter overapproximation, and some analyses are more naturally amenable to parametric representations in one formulation or the other, but rarely both. Although we do not have space to explore it in this paper, an example of an application which naturally ts into the viability framework is testing at run-time whether an exogenous input signal-such as might arise from a human-in-the-loop control-will maintain safety; for example, see [17].…”

“…• Extend the formulation to allow control inputs and thereby underapproximate nite horizon viability and discriminating kernels with zonotopes via a convex program. • Demonstrate the use of the discriminating kernel to compute a larger robust controlled invariant set for a moderate dimensional nonlinear quadrotor model than was achieved using an ellipsoidal representation in [17].…”

Scalable Robust Model Predictive Control for Linear Sampled-Data Systems

“…To accommodate for the state-dependent control input in our set-based reachability analysis, we consider an augmented statex ∈ R nx+nu [16]. The corresponding dynamics are ẋ(t) u(t)…”

“…In this paper, we propose a scalable robust reachableset-based MPC approach for constrained linear sampleddata systems. As in [11], [16], our controller receives state measurements and outputs piecewise constant control signals only at discrete time steps. Additionally, we take computation times explicitly into account, which is neglected by most robust MPC approaches, with the exception of, e.g., [17], [18].…”