Quadratic Convergence Ratio of Constrained Optimal Control Problems

Abstract

Problem statement: Earlier Researchers developed algorithms for solving quadratic control problems, but did not address the quadratic convergence ratio profile. Approach: Hence, the objective of this work is using our developed scheme, Discretized Continuous Algorithm (DCA), to examine both convergence profile and quadratic ratio profile demonstrating the effectiveness and efficiency of the scheme. Methodologically, we obtained generalized unconstrained formulation of the constrained problem. Using Conjugate Gradient Method (CGM) and linear ratio of the deviation of the generated iterates from the exact solution, we obtained respectively the objective values and the quadratic ratio values. Results: If these quadratic ratio values fall within the interval [1, ∞], then the convergence is quadratically convergent. Two examples were examined and satisfied the condition for quadratic convergence. Conclusion: Thus, we can conclude that the algorithm is optimally effective and efficient.