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

@article{Mao2018SuccessiveCA, title={Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problems}, author={Yuanqi Mao and Michael Szmuk and Xiangru Xu and Behçet Açikmese}, journal={arXiv: Optimization and Control}, year={2018} }

This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm handles nonlinear dynamics and non-convex state and control constraints by linearizing them about the solution of the previous iterate, and solving the resulting convex subproblem to obtain a solution for the current iterate. Additionally, the algorithm incorporates several…

## 39 Citations

Lossless convexification of non-convex optimal control problems with disjoint semi-continuous inputs

- Mathematics, Computer Science
- 2019

This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems, and achieves the first lossless convexification result for mixed- integer optimization problems.

A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints

- Mathematics, Computer Science
- 2018

A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending…

PySCP: A Multiple-Phase Optimal Control Software Using Sequential Convex Programming

- Computer ScienceInternational Journal of Aerospace Engineering
- 2022

A Python software program called PySCP is described for solving multiple-phase optimal control problems using sequential convex programming methods by constructing a series of approximated second-order cone programming subproblems and approaches to the solution of the original optimal control problem in an iterative way.

A symplectic pseudospectral method for constrained time-delayed optimal control problems and its application to biological control problems

- MathematicsOptimization
- 2020

ABSTRACT Time-delays are often involved in modelling biological processes, which arise more difficulties for the control task. In fact, once the control goal is given, a constrained optimal control…

Fast Trajectory Optimization via Successive Convexification for Spacecraft Rendezvous with Integer Constraints

- Computer Science
- 2019

This paper presents a fast method based on successive convexification for generating fuel-optimized spacecraft rendezvous trajectories in the presence of mixed-integer constraints and demonstrates that it is able to obtain trajectories that are up to 90 percent more fuel efficient than non-optimization based Apollo-era design targets.

Constrained Spacecraft Attitude Optimal Control via Successive Convex Optimization

- EngineeringJournal of Physics: Conference Series
- 2021

Rapid attitude path planning is the key technique in autonomous spacecraft operation missions. An efficient method is proposed for energy-optimal spacecraft attitude control in presence of…

Sequential convex programming method using adaptive mesh refinement for entry trajectory planning problem

- Computer Science
- 2020

Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification

- Computer Science2019 International Conference on Robotics and Automation (ICRA)
- 2019

A contact-implicit trajectory optimization (CITO) method based on a variable smooth contact model (VSCM) and successive convexification (SCvx) that combines the advantages of direct and shooting methods for CITO is proposed.

A Real-Time Algorithm for Non-Convex Powered Descent Guidance

- Computer Science
- 2020

This paper builds on previous work and refines a successive convexification algorithm to be compatible with common flight code requirements and suggests that the same design methodology applied to the full 6-degree-of-freedom landing problem is capable of producing fast enough runtimes to be viable for future entry, descent and landing systems.

Dual Quaternion-Based Powered Descent Guidance with State-Triggered Constraints

- Computer Science
- 2019

This paper presents a numerical algorithm for computing 6-degree-of-freedom free-final-time powered descent guidance trajectories that includes a special line of sight constraint that is enforced only within a specified band of slant ranges relative to the landing site.

## References

SHOWING 1-10 OF 74 REFERENCES

Successive convexification of non-convex optimal control problems and its convergence properties

- Computer Science2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

Several safe-guarding techniques are incorporated into the algorithm, namely virtual control and trust regions, which add another layer of algorithmic robustness and convergence results will be independent from any numerical schemes used for discretization.

Successive Convexification of Non-Convex Optimal Control Problems with State Constraints

- Computer Science
- 2017

Solving Nonconvex Optimal Control Problems by Convex Optimization

- Mathematics
- 2014

Motivated by aerospace applications, this paper presents a methodology to use second-order cone programming to solve nonconvex optimal control problems. The nonconvexity arises from the presence of…

Lossless convexification of a class of optimal control problems with non-convex control constraints

- Mathematics, Computer ScienceAutom.
- 2011

Lossless convexification of non-convex optimal control problems for state constrained linear systems

- Mathematics, Computer ScienceAutom.
- 2014

Optimal control problems with a continuous inequality constraint on the state and the control

- Mathematics, Computer ScienceAutom.
- 2009

Convexification and Real-Time Optimization for MPC with Aerospace Applications

- MathematicsHandbook of Model Predictive Control
- 2018

This chapter gives an overview of recent developments of convexification and real-time convex optimization based control methods, in the context of Model Predictive Control (MPC). Lossless…

SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

- Computer ScienceSIAM J. Optim.
- 2002

An SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems is discussed.

Convergence Rate for a Gauss Collocation Method Applied to Constrained Optimal Control

- MathematicsSIAM J. Control. Optim.
- 2018

A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity…

Interior-point polynomial algorithms in convex programming

- MathematicsSiam studies in applied mathematics
- 1994

This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.