Constrained controllability of fractional linear systems with delays in control. (English) Zbl 1376.93025
Summary: The paper presents finite-dimensional dynamical control systems described by linear fractional-order state equations with multiple delays in control. The constrained controls are considered. The set of admissible control values is assumed to be a compact set containing 0, a convex and compact set containing 0 in its interior, a cone with vertex at zero and a nonempty interior, or a convex and close cone with nonempty interior and vertex at zero. The definitions of various types of constrained controllability of the linear fractional systems with delays in control are formulated. New necessary and sufficient conditions for constrained relative controllability of fractional-order control systems with delayed controls are established and proved. Numerical examples are provided to illustrate the obtained theoretical results.
MSC:
| 93B05 | Controllability |
| 34A08 | Fractional ordinary differential equations |
| 93C05 | Linear systems in control theory |
Keywords:
fractional systems; linear control systems; constrained controllability; delays in control; pseudo-transition matrix; Caputo derivativeReferences:
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