Time-optimal L-1/L-2 norms optimal control for linear time-invariant systems

The theoretical properties of a novel time-optimal L-1/L-2 norms optimal control for linear time-invariant systems are investigated. The L-0-optimal control (or sparsest control) is converted to the time-optimal L-1/L-2 norms optimal control which can be solved efficiently. The proposed control is obtained via minimization of the time-optimal L-1/L-2 norms optimal control input along with the constraints on the state variable. Subsequently, by using the nonsmooth maximum principle, the uniqueness and continuity of the optimal solution of the time-optimal L-1/L-2 norms optimal control are proved. The superiority of the time-optimal L-1/L-2 norms optimal control is illustrated by numerical examples.

Automated summary

The theoretical properties of a novel time-optimal L-1/L-2 norms optimal control for linear time-invariant systems are investigated. The proposed control efficiently solves the L-0-optimal control problem by converting it to a time-optimal L-1/L-2 norms optimal control and enforcing constraints on the state variable. The uniqueness and continuity of the optimal solution of the time-optimal L-1/L-2 norms optimal control are proven using the nonsmooth maximum principle. Numerical examples demonstrate the superiority of the time-optimal L-1/L-2 norms optimal control.