GPOPS-II

GPOPS-II (General Pseudospectral Optimal Control Software - Version II) is a software package designed for solving multiple-phase optimal control problems. It uses a pseudospectral method, which approximates the state and control trajectories with global polynomial interpolants. These interpolants are typically Lagrange polynomials defined on a set of collocation points, such as Legendre-Gauss-Lobatto (LGL) points.

The core functionality of GPOPS-II involves transcribing the continuous-time optimal control problem into a nonlinear programming (NLP) problem. This transcription process involves discretizing the differential equations that govern the system's dynamics and approximating the integral terms in the objective function and constraints using quadrature rules. The resulting NLP is then solved using a numerical solver, such as SNOPT or IPOPT.

Key features of GPOPS-II include:

• Multiple-Phase Problems: GPOPS-II allows for the formulation and solution of optimal control problems with multiple phases, where each phase can have its own set of dynamics, constraints, and objective functions.

• Automatic Differentiation: GPOPS-II utilizes automatic differentiation to compute the derivatives required by the NLP solver, improving accuracy and efficiency.

• Constraint Handling: The software supports a wide range of constraints, including path constraints, boundary constraints, and event constraints.

• Scalability: GPOPS-II is designed to handle large-scale optimal control problems with many state and control variables.

• MATLAB Integration: GPOPS-II is primarily implemented in MATLAB, providing a user-friendly environment for problem formulation, solution, and analysis.

GPOPS-II is commonly used in various engineering and scientific applications, including aerospace engineering, robotics, chemical process control, and biomechanics. Its ability to efficiently solve complex optimal control problems makes it a valuable tool for researchers and practitioners.