Optimal Control of Self-Adjoint Systems

Given the system ẋ(t)=A(t)x(t)+u(t),where A(t)=-A'(t) and ||u(t)||≤1, it will be shown that the control u=-x(t)/||x(t)|| drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized. The theory is applied to the optimum angular velocity cotrol of a tumbling space body.