Suboptimal strategy for the finite-time linear-quadratic optimal control problem

In this article the authors study analytically the impact of the optimal constant feedback gain of the steady-state linear-quadratic optimal control problem to the corresponding finite-time linear-quadratic optimal control problem. Contributions of the study are 3-fold: (i) conditions for applicability of this suboptimal procedure are presented; (ii) a formula for the performance loss because of this practical implementation (use of the constant instead of the time-varying gain) is derived; and (iii) a technique based on the prescribed degree of stability that can be successfully used in practice is discussed. Examples are included to demonstrate the performance loss owing to this simplified approximate (suboptimal) linear-quadratic finite-horizon optimal control problem implementation.