A new approach to LQ time-varying controllers with terminal equality constraints

Abstract

A two-interval LQ terminal controller is constructed by using the fact that the Lagrange multiplier of the variational principle is a constant. The new terminal controller not only overcomes the drawbacks that the feedback gains of conventional LQ terminal controllers tend to infinity when close to the final time, but also keeps a feedback- feedforward structure. The variational principle for the LQ terminal control problem is also improved by adding a soft constraint. Relation between the “soft term” and the feedback gain is presented that the “soft term” is an enhancer to improve the performance of the controller, especially for minimum energy control problems. Further more, based on the interval mixed energy theory, closed form solutions of generalized Riccati transformation matrices are given. Advantages of the proposed two-interval terminal controller and effectiveness of the closed-form solutions are verified by numerical examples of an optimal rendezvous problem of spacecrafts.