An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states

Model predictive driving simulator motion cueing algorithm with actuator-based constraints

“…The resulting controller matches the perceived accelerations until a platform limit is imminent, at which point the platform returns to centre; if the sign of the vehicle acceleration subsequently changes, perception matching resumes. An issue with MPC is the computational burden of doing an optimization at each time step; Dagdelen et al [7] reduce the online computation time using the invariant set method of Gutman and Cwikel [8]. Their initial tests indicated that the transition between full acceleration rendering and the washout phase was too abrupt, and an artificial smoothing of the transition was added.…”

Complexity-driven construction of controlled invariant polytopic sets

“…[12] (106 vertices, red dots) and the low-complexity set X 11 produced by iteratively applying the method presented in this article (10 vertices, blue circles).…”

“…For comparison purposes with other methods in the literature, we also apply the method described in [12] for the computation of the largest controlled invariant set. The method in [12] is based on computing a sequence {Y i } of monotonically increasing controlled invariant sets Y i , using the one-step inverse reachability mapping starting from the singleton set…”

“…In Figure 2 the sets X i , i = 1, .., 10 are shown in yellow color while set X 11 is depicted in blue. Applying the method in [12], the maximal controlled invariant set was reached in 148 iterations, resulting in the maximal controlled invariant set Y 148 of complexity q Y148 = 106. In Figure 3 sets Y 7i , i = 1, .., 20 are shown in yellow color while the set Y 148 is depicted in blue.…”

An Invariance Based Algorithm for the l 1 Optimal Control Problem

“…Using the polyhedral (and possibly approximated) description S F of S ∞ (Ω), the problem reduces to the computation of the supremal controlled invariant set contained in a given polyhedron. Several algorithms have been proposed for such a computation [9], [2], [6], [12].…”