An Optimal Penalty Constant For Discrete Optimal Control Regulator Problems

Abstract

Indiscriminate and imprecise use of penalty constants can lead to substantial computational problems and consequently erroneous conclusions and deductions. This paper view this, with utmost seriousness and thus establish an optimal penalty constant φ that optimizes the minimization of the cost functional while solving discrete optimal control problems using extended conjugate gradient method (ECGM). I employed some measures that examine optimal control of dynamic processes that can be described by Differential Algebraic Equations (DAEs) that entails integer restriction on some or all of the control functions. I established the construction of an optimal penalty constant which can be employed in the extended conjugate gradient method algorithm for discrete optimal control regulator problems. Comparative results emanating from the use of different penalty constants/algorithms on some problems are given. The obtained numerical results reveal that the proposed optimal penalty constant expression is efficient.