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This paper proposes a new algorithm that solves non-convex optimal controlproblems with a theoretical guarantee for global convergence to a feasiblelocal solution of the original problem. The proposed algorithm extends therecently proposed successive convexification (SCvx) algorithm by addressing oneof its key limitations, that is, the converged solution is not guaranteed to befeasible to the original non-convex problem. The main idea behind the proposedalgorithm is to incorporate the SCvx-based iteration into an algorithmicframework based on the augmented Lagrangian method to enable the feasibilityguarantee while retaining favorable properties of SCvx. Unlike the originalSCvx, this approach iterates on both of the optimization variables and theLagrange multipliers, which facilitates the feasibility guarantee as well asefficient convergence, in a spirit similar to the alternating direction methodof multipliers (ADMM) for large-scale convex programming. Convergence analysisshows the proposed algorithm's strong global convergence to a feasible localoptimum of the original problem and its convergence rate. These theoreticalresults are demonstrated via numerical examples with comparison against theoriginal SCvx algorithm.

Successive Convexification with Feasibility Guarantee via Augmented Lagrangian for Non-Convex Optimal Control Problems