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.

[1]  Arthur M. Hopkin,et al.  A Phase-Plane Approach to the Compensation of Saturating Servomechanisms , 1951, Transactions of the American Institute of Electrical Engineers.

[2]  R. Bellman,et al.  On the “bang-bang” control problem , 1956 .

[3]  N. N Krasovskii,et al.  On the theory of optimum control , 1959 .

[4]  M. Athanassiades,et al.  Theory and design of high-order bang-bang control systems , 1961 .

[5]  P. Falb,et al.  Time-Optimal Velocity Control of a Spinning Space Body , 1963, IEEE Transactions on Applications and Industry.

[6]  M. Athans.  Minimum-Fuel Feedback Control Systems: Second-Order Case , 1963, IEEE Transactions on Applications and Industry.

[7]  A. E. Pearson.  Synthesis of a Minimum-Energy Controller Subject to an Average Power Constraint , 1963, IEEE Transactions on Applications and Industry.