Distributed Controller Synthesis for Real-Time Correctness
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Solution Overview
Problem
Current methods for synthesizing correct-by-construction controllers are limited by exponential complexity, making them unsuitable for control systems with many state variables and input parameters, and are not capable of real-time processing.
Innovation Solution
A method that distributes the comparison of successor states with initial target sets over multiple processing elements, utilizing available processing resources to reduce computation time and facilitate parallel computing, enabling the synthesis of controllers for complex systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If symbolic controller synthesis is performed using traditional methods, then correctness of the controller is guaranteed, but computation time becomes prohibitively long for systems with many state variables and input parameters
Solution Approach 1:
The patent divides the computation of the updated target set into multiple independent comparison operations that can be performed in parallel. Each processing element handles a subset of successor states, comparing them against the initial target set independently. This segmentation transforms the exponential complexity into a parallelizable structure, maintaining correctness while reducing overall computation time.
Solution Approach 2:
The patent introduces a parallel computation dimension by distributing the comparison task across multiple processing elements. Instead of sequentially processing successor states, the system utilizes parallel processing to simultaneously evaluate multiple states, effectively adding a temporal dimension to the computation and reducing the time required for controller synthesis.
2Adaptability or versatility
If the number of state variables and input parameters increases, then the control system becomes more capable of handling complex applications, but the complexity of controller synthesis increases exponentially
Solution Approach 1:
The patent segments the synthesis complexity by dividing the comparison operation into independent parallel tasks. Each processing element handles a portion of the state space, allowing the system to scale with increased numbers of state variables and parameters without experiencing exponential complexity growth in the synthesis process.
Solution Approach 2:
The patent creates multiple copies of the comparison operation, one for each processing element. Instead of performing a single complex sequential comparison, the system replicates the comparison logic across multiple parallel instances, each handling a subset of the state space, thereby managing complexity through replication rather than sequential processing.
3Ease of manufacture
If traditional sequential methods are used for target set computation, then implementation is simple, but real-time processing capability is lost
Solution Approach 1:
The patent segments the target set computation into parallel comparison operations that can be executed simultaneously across multiple processing elements. This segmentation enables real-time processing by reducing the overall computation time while maintaining a relatively simple implementation structure based on independent parallel tasks.
Solution Approach 2:
The patent performs preliminary discretization of the state space and identification of available processing elements before executing the parallel comparison operations. This preliminary preparation enables the subsequent parallel computation to proceed efficiently, achieving real-time processing capability while keeping the overall implementation straightforward.
Data Source
AI summary
A method includes: receiving a mathematical model of a control system, with state variables and control parameters; discretizing at least a part of a space to obtain a set of tuples; determining for each tuple at least one successor state; obtaining an initial winning set of tuples; determining an updated winning set of tuples, including comparing the at least one successor state with the initial winning set of tuples, where the comparison is distributed over available processing elements by choosing one processing element from the available processing elements for each tuple to perform the comparison and where the available processing elements are used simultaneously at least in part; repeating the determination of the updated winning set of tuples to obtain a new updated winning set of tuples if a convergence measure does not meet a criterion, and constructing a controller for the control system from the new updated winning set.