Minimum energy control
In control theory, the minimum energy control is the control u ( t ) {\displaystyle u(t)} that will bring a linear time invariant system to a desired state with a minimum expenditure of energy. Let the linear time invariant (LTI) system be x ˙ ( t ) = A x ( t ) + B u ( t ) {\displaystyle {\dot {\mathbf {x} }}(t)=A\mathbf {x} (t)+B\mathbf {u} (t)} y ( t ) = C x ( t ) + D u ( t ) {\displaystyle \mathbf {y} (t)=C\mathbf {x} (t)+D\mathbf {u} (t)} with initial state x ( t 0 ) = x 0 {\displaystyle x(t_{0})=x_{0}} .