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GESOP^® Details

GESOP can be devided into the following parts:

1. Programming Interface
2. Basic Gesop Modules
3. Initial Guess Generator
4. Simulator
5. Optimizer
6. Parameter and Grid Inspector
7. GISMO (Graphical Iteration Monitor)
8. Quick View
9. Result Summary
10. Simulink Interface

Programming Interface

The user has to supply his models describing the elements of the trajectory optimization problem at hand such as right hand sides, boundary constraints, path constraints, phase connect conditions etc. In addition he has to supply a control law in order to generate the initial guess as well as a file called model description which contains the problem description.

Standard input parameters of the GESOP programming interface are:

• general parameters:
  • optimizeable state, control and real design parameter vector
  • not optimizeable integer design parameter vector
  • initial and final phase times
• path constraints and Lagrangian cost function:
  • control derivative vector
• constraints:
  • enforced vector
• phase connect conditions:
  • is connected vector of states, controls and real design parameters

Standard output parameters of the GESOP programming interface are:

• right hand side: state derivative vector
• cost functions: cost function value
• constraint functions: constraint violation vector
• phase connect function: state, control and real design parameter vector with initial values at next phase

The user can program his own optimization problem - from a very simple educational example up to a very complex one, like ASTOS.

The programming interface allows FORTRAN 77, C, Ada 95 and Matlab scripts (The MathWorks) as programming languages on the user side. Together with Ada a comprehensive libary can be used including data import and interpolation, matrix and vector operations, transformations and much more.

Basic GESOP Modules

The GESOP software includes a user interface and a numerical part which contains the initial guess generator, the simulator and the optimizers. The initial guess generator creates the Trajectory Optimization Problem Structure (TOPS) which is the fundamental data structure. The simulator reads this data structure and produces simulation data which can either be used for the Quick View facility or exported to MATLAB or other applications for further analysis. The optimizers read, modify and write the TOPS.

Multiple Phase Structures

The problems can be split up into several phases. Within each phase the equations of motion must be differentiable. Phases must be defined whenever one of the following events occurs:

• discontinuities in one or several of the statevariables such as stage separation, fairing jettisoning, etc.,
• model changes such as engine-type changes (switching from one propulsion system to another one), or control model changes such as switching from Euler angles to load factors, or if different equations of motions are to be used in various phases.

Initial Guess Generator

The initial guess can be the most important preparatory work for a successful optimization. It can be defined either by a control and state time histories imported from an existing file or by a user supplied control law. Together with the control laws the differential equations are integrated in order to produce starting estimates for the states. The following quantities can be defined for each phase by the programming interface:

• control values
• initial state values
• real and integer design parameters
  (states and real parameter can be connected to the value of the phase before)
• bounds of controls, states and real design parameters
• initial and final phase times with bounds
• phase over conditions

Simulator

An initial or intermediate or final control time history can be integrated in several modes. This produces a simulation output file to be used for graphical output either with Quick View or after export with the MATLAB graphics facility.

Optimizers

Three optimizers can be selected via the user interface, one is a direct collocation (TROPIC), the other one a direct multiple shooting (PROMIS) method. Both methods use state/control parametrization. At present the NLP solvers are SLLSQP or SNOPT for PROMIS and SNOPT for TROPIC . The limitation for SLLSQP is about 500 parameters, for SNOPT about 3000 parameters. Features of the optimizers are:

• state variables are discretized over a collocation or a multiple-shooting mesh in each phase,
• control functions are parameterized over user specified control grids in each mesh. A separate grid is possible for each control, control approximations can be piecewise constant or piecewise linear. Different approximation types are possible for various control functions, control grid points can be adjusted by the optimizer subject to user supplied lower and upper bounds,
• grid definitions and initial estimates for states and controls at their respective grids are done mouse driven via the graphical input facility, control approximation type and continuity conditions are selected via this facility, too.

Since version 4.5 the high performance optimizer SOCS is available with GESOP. SOCS is licensed by The Boeing company. It is a collocation method using sparce matrice methods. Hence it is faster than TROPIC and useful for problems with over 10000 parameters. Furthermore SOCS supports automatic mesh refinement.

Parameter & Grid Inspector

The Parameter & Grid Inspector is part of the user interface where all optimization parameters can be edited in a graphical way of work. States and controls can be plotted, where the nodes can be edited by mouse clicks and other helpful modification functions. Values and bounds of design parameters can be changed and constraints as well as connect conditions can be enforced.

GISMO – Graphical Iteration Sequence Monitor

GISMO is a powerfull tool which plots most of the internal optimization quantities but also all parameters of the optimization problem of each iteration. This way the optimization process can be followed and analysed.

Quick View

Quick View is an internal plotting tool, which is useful for fast analysis of the simulation output. It supports 2-dimensional plots with multiple quantities in one plot and several plot windows.

Result Summary

In contrast to the Quick View tool the Result Summary shows all scalar values of the optimization problem. Most important it is for the analysis of all constraint violations.

Simulink Interface

A programming interface to Simulink (The MathWorks) allows the user to optimize his Simulink model with GESOP. Therefore the user has to connect a Simulink model with the GESOP Simulink Interface and to export the complete model into C using the Real-Time Workshop of The MathWorks.