Static/dynamic control for optimizing a useful objective

Details Static/dynamic control for optimizing a useful objective Static/dynamic control for optimizing a useful objective

1999-03-25

2002-12-17

Patel, Ramesh (Department: 2121)

Data processing: generic control systems or specific application

Generic control system, apparatus or process

Optimization or adaptive control

C700S029000, C700S030000, C700S031000, C700S090000, C700S088000, C700S262000, C318S561000, C318S563000, C318S565000, C318S566000, C244S159200, C244S164000, C244S164000, C244S164000, C244S174000, C244S171900

Reexamination Certificate

active

06496741

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Technical Field
The present invention relates to a method, computer system, and program product for optimizing a useful objective function with respect to a dynamic parameter vector and a static parameter vector, and more particularly, to optimizing a spacecraft objective such as a spacecraft trajectory objective and a spacecraft design objective.
2. Related Art
A goal of spacecraft trajectory optimization is to obtain the best trajectory. Spacecraft trajectory optimization is a dynamic problem. A dynamic problem involves a sequence of decisions made over time. For example, the thrust direction for a spacecraft engine must be selected on day one of a space flight. Then a new thrust direction must be selected for day two, and so on. Each previous decision affects all future decisions. A complete set of decisions for the total flight time is necessary to define a trajectory.
A goal of spacecraft design optimization is to obtain the best design. Spacecraft design optimization is a not a dynamic problem. Design decisions are not linked to a time sequence. For example, the decisions of how large a solar array to build, how much fuel to carry, and when to launch a spacecraft are static or non-dynamic decisions.
The overall performance of a spacecraft is a function of both the spacecraft trajectory and the spacecraft design. Further, the spacecraft design will impact the spacecraft trajectory and vice versa. Since spacecraft design and spacecraft trajectory are not independent, the most efficient spacecraft design and the most efficient spacecraft trajectory cannot be determined independently.
Current methods for optimization are constructed to solve either dynamic problems or static problems. Related art optimization methods cannot solve problems which have both a static part and a dynamic part without approximation. Related art methods for optimization can be divided into two categories. The first category is non-dynamic or static optimization methods known as “parameter optimization”. The second category is dynamic optimization methods known as “optimal control.”
Parameter optimization was originally developed to solve static problems. Parameter optimization is directly applicable to static problems, such as spacecraft design. However, parameter optimization is not easily or accurately applicable to dynamic problems such as space flight trajectories. Parameter optimization can only be applied to dynamic problems when the true dynamic nature of the problem is approximated or removed entirely. Since parameter optimization cannot solve general dynamic problems without approximation, parameter optimization cannot solve the combined static and dynamic problem of spacecraft design and trajectory without approximation.
Optimal control was developed for exclusively dynamic problems. Optimal control is applicable to dynamic problems such as spacecraft trajectory optimization. However, optimal control is not suited to static problems such as spacecraft design.
The related art uses either parameter optimization or optimal control to design deep space missions. The related art cannot achieve the combined benefits of both parameter optimization and optimal control simultaneously. The following two subsections describe the parameter optimization and the optimal control methods presently in use.
A. Parameter Optimization Methods
The related art applies parameter optimization to the dynamic problem of spacecraft trajectory optimization by making several significant approximations. The physics of the trajectory problem is approximated by instantaneous impulses followed by ballistic coasts. The instantaneous impulses are intended to represent the effect of thrust on a spacecraft. A sequence of impulses and coasts can roughly approximate a continuously running engine. The ballistic coasts usually only account for the gravitational influence of a single central object (usually the sun.) All long range planetary gravitational effects are ignored. Since planetary gravitation is ignored, the ballistic coasts are perfect conic sections whose shape is always time independent. The time independence of the shape is a necessary assumption for the non-dynamic parameter optimization method.
Of particular interest is the ion propulsion engine. Ion propulsion engines are far more efficient than ordinary traditional chemical engines. Ion propulsion engines are expected to replace many applications of chemical engines in the near future. Ion propulsion engines have significantly different operating characteristics than chemical engines. In particular, ion engines typically operate continuously for days or even years at low thrust intensities. The impulse/ballistic coast approximation required by parameter optimization is a particularly poor approximation when applied to ion engines.
The parameter optimization method used in the related art requires prespecification of the sequence of planets that the spacecraft will pass by closely (“planetary flyby sequence”). Thus, the planetary flyby sequence is not susceptible to parameter optimization. Individual planetary flybys are prespecified by fixed constraints. Prespecification of flybys greatly reduces the likelihood of discovering the most efficient flyby sequence.
Parameter optimization typically requires the physics of planetary flybys to be approximated as a collision at a single point in space. The spacecraft trajectory is propagated to the center of the flyby body without accounting for the gravity of the body. Flybys are then modeled as an instantaneous change in velocity without a change in the spacecraft position. With parameter optimization, the true extended spatial and dynamic nature of flybys is not correctly represented. This approximation significantly reduces the precision of parameter optimization solutions.
Related art parameter optimization methods do not optimize spacecraft thrust sequences directly. Instead, related art methods optimize instantaneous changes to spacecraft velocity. Optimizing velocity changes neglects or only approximates the effect of the dynamic nature of the spacecraft mass. The spacecraft mass is a decreasing function of time because fuel is burned. Neglecting this fact reduces the precision of parameter optimization solutions.
B. Optimal Control Methods
The related art uses an optimal control method to calculate or fine tune navigation paths or trajectories for spacecraft. The optimal control method is known as the calculus of variations (“COV.”) The COV method is not capable of calculating optimal trajectories for spacecraft from scratch. An efficient trajectory and/or a prespecified flyby sequence must be supplied as input. The input trajectory, or trajectory associated with a prescribed flyby sequence, is not derived from a precise optimization procedure and is therefore not necessarily optimal. Similarly, the prespecified flyby sequence is not necessarily optimal.
Related art COV methods typically make several approximations similar to the approximations made by related art parameter optimization methods. For example, thrust is approximated as a sequence of impulses, spacecraft propagation only takes into account the Sun's gravity, and planetary flybys are treated as an instantaneous change in spacecraft velocity. As a result, the COV method is limited in precision in the same way that the parameter optimization method is limited in precision.
The COV method also suffers from extreme sensitivity to flyby parameters. The extreme sensitivity of COV results in a substantial reduction in the improvement that COV can potentially achieve when flybys are involved. The sensitivity problem limits the COV method to consider trajectories with only a small number of flybys.
The main advantage of the COV method is that it is a dynamic method. The dynamic aspect of the COV method could, in theory, permit the correct representation of the dynamics of space flight. Unfortunately, the COV method is not robust enough to solve the trajectory problem without relying on significant approximations or requir

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