Linear Inequalities Solver for Air Traffic Analysis
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Solution Overview
Problem
Conventional methods for solving systems of linear inequalities, such as those used in air traffic analysis and control, become impractical due to their runtime growing as the cube of the number of aircraft, making it difficult to manage large airspaces efficiently.
Innovation Solution
A computer-implemented method and system that configures a homogeneous system of linear inequalities to reduce maximum and sum infeasibility, using techniques like recursive infeasibility reduction, zero-crossing, and de-grouping, to efficiently solve large systems of linear inequalities for air traffic control and analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional methods of solving systems of linear inequalities are used, then accuracy of air traffic control analysis is maintained, but runtime grows as the cube of the number of aircraft making it impractical for large airspace
Solution Approach 1:
The patent divides the large system of linear inequalities into smaller subsystems by partitioning aircraft groups and solving them separately. The airspace is divided into sectors, and aircraft are grouped by sector, allowing parallel processing of multiple smaller systems rather than solving one large system, thus reducing overall computation time while maintaining solution accuracy
Solution Approach 2:
The patent transforms the problem from solving a single large system of linear inequalities to solving multiple smaller systems in parallel by introducing a dimensional decomposition based on airspace sectors and aircraft groups. This dimensional change allows the computational problem to be distributed across multiple processing dimensions simultaneously
2Quantity of substance
If the number of aircraft increases, then air traffic control coverage area increases, but the number of variables and constraints grows making the problem impractical to solve
Solution Approach 1:
The patent segments the air traffic control system into multiple independent or loosely-coupled subsystems based on geographical sectors and aircraft groups. Each subsystem handles a subset of aircraft with its own set of variables and constraints, preventing the exponential growth of system complexity even as total aircraft numbers increase
Solution Approach 2:
The patent solves for a predetermined future time horizon rather than continuously solving for all future times, and focuses on resolving infeasibility at each time step rather than guaranteeing complete feasibility throughout the entire horizon. This partial action approach makes the problem tractable for large numbers of aircraft
3Measurement precision
If homogeneous system of linear inequalities is used to reduce infeasibility, then solution accuracy improves, but computational complexity increases
Solution Approach 1:
The patent applies homogeneous system solving techniques to each segmented subsystem rather than to the entire system, reducing the computational complexity of each individual homogeneous system while maintaining overall solution accuracy through the coordinated solution of multiple subsystems
Solution Approach 2:
The patent transforms the original system into a homogeneous system of linear inequalities before solving, which allows for more accurate detection and resolution of infeasibility. This preliminary transformation prepares the system in advance to handle infeasibility systematically through the homogeneous formulation
Data Source
AI summary
Computer-implemented methods, systems, and computer readable mediums for solving large systems of linear equations, such as for aircraft traffic control and analysis, are disclosed. A method for aircraft traffic control, includes receiving as input, airspace sector information and aircraft traffic information, configuring a homogeneous system of linear inequalities comprising a plurality of linear inequalities based upon the airspace sector information and the aircraft traffic information, and resolving the homogeneous linear system to determine a second airspace sector information and a second aircraft traffic information, wherein the second airspace sector information and the second aircraft traffic information are based upon a predetermined future point of time, and wherein the resolving includes at least one of reducing a maximum infeasibility of the homogeneous linear system and reducing a sum infeasibility of the homogeneous linear system.