The Minimum Energy Problem for Positive Discrete-Time Linear Systems with Fixed Final State

The non-negativity of controls in positive linear discrete-time systems usually gives rise to complementarity conditions in the first-order Karush-Kuhn-Tucker optimality conditions - this complicates the analytic solution and usually leads to numerical solutions. The intrinsic relationship between reachable sets anti the minimum-energy problem is exploited in this paper to obtain an analytic solution of the minimum-energy control problem for positive linear discrete-time systems with any pair of fixed terminal (initial and final) states.