This paper investigates an alternative approximation to the maximal viability set for linear systems with constrained states and input. Current ellipsoidal and polyhedral approximations are either too conservative or too complex for many applications. As the primary contribution, it is shown that the intersection of a controlled invariant ellipsoid and a set of state constraints (referred to as a semi-ellipsoidal set) is itself controlled invariant under certain conditions. The proposed semi-ellipsoidal approach is less conservative than the ellipsoidal method but simpler than the polyhedral method. Two examples serve as proof-of-concept of the approach.
Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division April 17, 2000. Associate Editor: P. Voulgaris.
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O’Dell , B. D., and Misawa, E. A. (April 17, 2000). "Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems ." ASME. J. Dyn. Sys., Meas., Control. March 2002; 124(1): 98–103. https://doi.org/10.1115/1.1434269
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