MISER: a FORTRAN program for solving optimal control problems
Advances in Engineering Software
A sparse nonlinear optimization algorithm
Journal of Optimization Theory and Applications
Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems
Computational Optimization and Applications
Spectral methods in MatLab
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
An efficient overloaded implementation of forward mode automatic differentiation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Computational Optimization and Applications
Automatica (Journal of IFAC)
Brief paper: Pseudospectral methods for solving infinite-horizon optimal control problems
Automatica (Journal of IFAC)
Optimization of microorganisms growth processes
Computer Methods and Programs in Biomedicine
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
A hierarchical approach for primitive-based motion planning and control of autonomous vehicles
Robotics and Autonomous Systems
On minimum-time paths of bounded curvature with position-dependent constraints
Automatica (Journal of IFAC)
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An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method. The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the cost functional and the differential-algebraic equations in each phase of the optimal control problem. The phases are then connected using linkage conditions on the state and time. A large-scale nonlinear programming problem (NLP) arises from the discretization and the significant features of the NLP are described in detail. A particular reusable MATLAB implementation of the algorithm, called GPOPS, is applied to three classical optimal control problems to demonstrate its utility. The algorithm described in this article will provide researchers and engineers a useful software tool and a reference when it is desired to implement the Gauss pseudospectral method in other programming languages.