Before revision: One seeks an input so that the system will be in the state at time , and for any other input , which also drives the system from to at time the energy expenditure would be larger To choose this input, first compute the controllability gramian Assuming is nonsingular ( iff the system is controllable), the minimum energy control is then Substitution into the solution verifies the achievement of state at .
After revision: One seeks an input so that the system will be in the state at time , and for any other input , which also drives the system from to at time the energy expenditure would be larger To choose this input, first compute the controllability gramian Assuming is nonsingular ( if and only if the system is controllable), the minimum energy control is then Substitution into the solution verifies the achievement of state at .