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This paper presents the SCvx algorithm, a successive convexificationalgorithm designed to solve non-convex constrained optimal control problemswith global convergence and superlinear convergence-rate guarantees. Theproposed algorithm can handle nonlinear dynamics and non-convex state andcontrol constraints. It solves the original problem to optimality bysuccessively linearizing non-convex dynamics and constraints about the solutionof the previous iteration. The resulting convex subproblems are numericallytractable, and can be computed quickly and reliably using convex optimizationsolvers, making the SCvx algorithm well suited for real-time applications.Analysis is presented to show that the algorithm converges both globally andsuperlinearly, guaranteeing i) local optimality recovery: if the convergedsolution is feasible with respect to the original problem, then it is also alocal optimum; ii) strong convergence: if the Kurdyka-Lojasiewicz (KL)inequality holds at the converged solution, then the solution is unique. Thesuperlinear rate of convergence is obtained by exploiting the structure ofoptimal control problems, showcasing that faster rate of convergence can beachieved by leveraging specific problem properties when compared to genericnonlinear programming methods. Numerical simulations are performed for anon-convex quad-rotor motion planning problem, and corresponding resultsobtained using Sequential Quadratic Programming (SQP) and general purposeInterior Point Method (IPM) solvers are provided for comparison. The resultsshow that the convergence rate of the SCvx algorithm is indeed superlinear, andthat SCvx outperforms the other two methods by converging in less number ofiterations.

Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problems