REGULATION OF DISCRETE-TIME LINEAR SYSTEMS WITH POSITIVE STATE AND CONTROL CONSTRAINTS AND BOUNDED DISTURBANCES

Abstract A variety of control problems require the control action and/or state to be positive. Typical applications include situations where the operating point maximizes (steady state) efficiency so that the steady state control and/or the steady state itself lie on the boundaries of their respective constraint sets. Any deviation of the control and/or state from its steady state value must therefore be directed to the interior of its constraint set. To address these problems, we characterize a novel family of the robust control invariant sets for linear systems under positivity constraints. The existence of a constraint admissible member of this family can be checked by solving a single linear or quadratic programming problem. The solution of this optimization problem yields the corresponding controller. These results are then used to devise a robust time-optimal control scheme for regulation of uncertain linear systems under positivity constraints. Robust finite-time attractivity of an appropriately chosen member of this family is also established.

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