In the behavioral framework for continuous-time linear scalar systems, simple sufficient conditions for the solution of the minimum-time rest-to-rest feedforward constrained control problem are provided. The investigation of the time-optimal input–output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure. The resulting optimal input is composed of sequences of bang–bang functions and linear combinations of the modes associated to the zero dynamics. This signal behavior constitutes a generalizedbang–bang control that can be fruitfully exploited for feedforward constrained regulation. Using discretization, an arbitrarily good approximation of the optimal generalizedbang–bang control is found by solving a sequence of linear programming problems. Numerical examples are included.
Generalized Bang-Bang Control for Feedforward Constrained Regulation / Consolini, Luca; Piazzi, Aurelio. - In: AUTOMATICA. - ISSN 0005-1098. - 45:(2009), pp. 2234-2243. [10.1016/j.automatica.2009.06.030]
Generalized Bang-Bang Control for Feedforward Constrained Regulation
CONSOLINI, Luca;PIAZZI, Aurelio
2009-01-01
Abstract
In the behavioral framework for continuous-time linear scalar systems, simple sufficient conditions for the solution of the minimum-time rest-to-rest feedforward constrained control problem are provided. The investigation of the time-optimal input–output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure. The resulting optimal input is composed of sequences of bang–bang functions and linear combinations of the modes associated to the zero dynamics. This signal behavior constitutes a generalizedbang–bang control that can be fruitfully exploited for feedforward constrained regulation. Using discretization, an arbitrarily good approximation of the optimal generalizedbang–bang control is found by solving a sequence of linear programming problems. Numerical examples are included.File | Dimensione | Formato | |
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