On the computation of lambda-contractive sets for linear constrained systems

Preprint English OPEN
Darup, Moritz Schulze ; Cannon, Mark (2016)
  • Subject: Mathematics - Optimization and Control
    acm: TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS

We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to approximate the maximal lambda-contractive set with a given precision using 1-step sets. Second, based on the former result, we provide a procedure for choosing lambda so that the associated maximal lambda-contractive set is guaranteed to approximate the maximal controlled invariant set with a given accuracy.
  • References (9)

    [1] F. Blanchini and S. Miani, Set-Theoretic Methods in Control. Birkh¨auser, 2008.

    [2] F. Blanchini, “Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions,” IEEE Trans. Autom. Control, vol. 39, no. 2, pp. 428-433, 1994.

    [3] D. P. Bertsekas, “Infinite-time reachability of state-space regions by using feedback control,” IEEE Trans. Autom. Control, vol. 17, no. 5, pp. 604-613, 1972.

    [4] M. Cwikel and P. O. Gutman, “Convergence of an algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states,” IEEE Trans. Autom. Control, vol. 31, no. 5, pp. 457-459, 1986.

    [5] P. O. Gutman and M. Cwikel, “An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded control and states,” IEEE Trans. Autom. Control, vol. 32, no. 3, pp. 251-253, 1987.

    [6] S. S. Keerthi and E. G. Gilbert, “Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints,” IEEE Trans. Autom. Control, vol. 32, no. 5, pp. 432-435, 1987.

    [7] F. Blanchini and S. Miani, “Constrained stabilization of continuous-time linear systems,” System and Control Letters, vol. 28, pp. 95-102, 1996.

    [8] M. Fiacchini, T. Alamo, and E. F. Camacho, “On the computation of local invariant sets for nonlinear systems,” in Proc. of 46th Conference on Decision and Control, pp. 3989-3994, 2007.

    [9] M. Schulze Darup and M. M¨onnigmann, “On general relations between nullcontrollable and controlled invariant sets,” in Proc. of 53th Conference on Decision and Control, pp. 6323-6328, 2014.

  • Similar Research Results (2)
  • Metrics
    No metrics available
Share - Bookmark