Abstract
An algorithm for computing the maximal controlled invariant set and the least restrictive controller for discrete time systems is proposed. We show how the algorithm can be encoded using quantifier elimination, which leads to a semi-decidability result for definable systems. For discrete time linear systems with all sets specified by linear inequalities, a more efficient implementation is proposed using linear programming and Fourier elimination. If in addition the system is in controllable canonical form, the input is scalar and unbounded, the disturbance is scalar and bounded and the initial set is a rectangle, then the problem is decidable.
Research supported by ONR under grant N00014-97-1-0946, by DARPA under contract F33615-98-C-3614, and by ARO under grant MURI DAAH04-96-1-0341.
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Vidal, R., Schaffert, S., Lygeros, J., Sastry, S. (2000). Controlled Invariance of Discrete Time Systems. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_36
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