Precomputed Active-Set LP Control for Spacecraft Thrusters
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Solution Overview
Problem
Existing linear programming problem solving systems, such as interior point methods and simplex methods, struggle with estimating the time to converge to an optimal solution, which can compromise optimality or violate constraints, especially in real-time control applications like spacecraft thruster control.
Innovation Solution
A linear programming problem solving system that includes a solution candidate calculation device and an optimal solution calculation device, which precalculates dual solution candidates and active sets offline, allowing for rapid determination of the optimal solution within a control cycle by selecting the optimal active set based on inner products of constraint vectors and stored dual solution candidates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If interior point methods or simplex methods are used to solve linear programming problems, then the optimal solution can be found, but the time to converge cannot be reliably estimated and may fail to meet control cycle requirements
Solution Approach 1:
The patent pre-calculates and stores solution candidates and their corresponding active sets before the control cycle begins. During the control cycle, the system only needs to select from pre-computed candidates based on the current constraint vector, eliminating the need for iterative convergence and ensuring the solution is obtained within the control cycle time limit while maintaining optimality.
2Measurement precision
If iterative methods are used to solve linear programming problems, then the solution can be refined, but the control cycle time cannot be guaranteed
Solution Approach 1:
The system performs comprehensive solution calculations in advance, generating multiple solution candidates with their associated active sets stored in memory. During real-time control, the system immediately selects the appropriate pre-computed solution based on the current constraint vector, ensuring both high solution accuracy and adherence to control cycle timing requirements without performing iterative refinements during the control cycle.
3Productivity
If precalculated solutions are stored and used, then the control cycle time is reduced, but the solution may not satisfy optimality or constraints
Solution Approach 1:
The system pre-calculates multiple solution candidates, each associated with specific active sets that define which constraints are binding. During the control cycle, the system selects the appropriate solution candidate by matching the current constraint vector with the pre-stored active sets, ensuring that the selected solution satisfies both optimality conditions and all constraints while achieving rapid control response.
Data Source
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AI summary
Known linear programming problem solving systems use interior point methods and simplex methods with iterations and have difficulty in estimating the time taken to find the optimal solution and reliably finding the optimal solution within a control cycle. A dual solution candidate searcher (22) receives an input of information about a constraint coefficient matrix and a cost vector, determines a dual problem of a linear programming problem being a primal problem and all active sets representing combinations of active formulas in constraints of the dual problem, finds, for each of the active sets, a feasible dual solution candidate meeting constraints, and stores the dual solution candidate into a storage (4) in a manner associated with a corresponding one of the active sets. An optimal solution calculation device (3) receives an input of a constraint vector as, selects an optimal one of the active sets as an optimal active set based on an inner product of the constraint vector and the dual solution candidate stored in the storage (4), and finds and outputs a basic feasible solution corresponding to the selected active set as an optimal solution.