Imbedding the Multiplier in a Discretized Optimal Control Problem With Real Coefficients Via the Penalty and Multiplier Methods

Abstract

Problem statement: Many earlier schemes, particularly the Function Space Algorithm (FSA) which sidetracks the knowledge of operator, for solving quadratic optimal control problems have been computationally involving and iteratively high. Approach: Though, some of these earlier schemes developed operators consisting of complicated integrals still very difficult to evaluate. Here, objectively, a new scheme, Discretized Continuous Algorithm (DCA), is proposed with developed associated operator consisting of a series of summation replacing the integrals of the earlier schemes, thus enhancing much more feasible results and lower iterations. Results: Methodologically, the new scheme uses the penalty-multiplier method to obtain an unconstrained formulation whose bilinear form expression leads to the construction of operator amenable to the Conjugate Gradient Method (CGM). Conclusion/Recommendations: An hypothetical example is considered and results, tabulated per cycle, are more feasible and less iterative than some of the existing methods.