Optimal Finite-Time Control of Positive Linear Discrete-Time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. for this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity property of the optimal state trajectory of the closed-loop system is also guaranteed. furthermore, state variables of the closed-loop system converge to the origin in finite steps (finite-time stability). in this regard, the positive linear quadratic regulator (lqr+) problem for the linear discrete time systems is stated. once, the cost function with finite-time horizon is considered and another time the cost function with infinite-time horizon is assumed. in this regard, two theorems are given and proved which consider the problem of building positive and optimize linear time-varying discrete time systems. results can also be applied to linear time-invariant discrete time systems. finally, computer simulations are given to illustrate effective performance of the designed controller and also verify the theoretical results.