Data-Driven Control Model Adaptation for Nonlinear System Stability
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Solution Overview
Problem
Current data-driven control methods for dynamical systems struggle to capture the physical dynamics of systems, leading to suboptimal control policies and instability, especially in nonlinear systems where model-based design is challenging and computationally expensive.
Innovation Solution
A method using reinforcement learning to update a closure model, combining ordinary differential equations (ODEs) with a closure model to mimic the pattern of system behavior, allowing for efficient control policy design that accounts for physical dynamics and constraints, while reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If model-based control techniques are used to control nonlinear dynamical systems, then control stability and optimality can be achieved, but the computational complexity and difficulty of solving Hamilton-Jacobi-Bellman equations increase significantly
Solution Approach 1:
The patent introduces a neural network as an intermediary component that approximates the value function and control policy. Instead of directly solving the complex Hamilton-Jacobi-Bellman equations, the neural network learns to map system states to control actions through reinforcement learning, serving as a mediator between the system dynamics and the control objective. This approach maintains control stability while significantly reducing computational complexity during operation.
Solution Approach 2:
The patent replaces the traditional analytical mechanics-based control approach (solving PDEs) with a data-driven reinforcement learning approach. The neural network is trained offline using simulated or real operational data to learn optimal control policies, substituting the need for real-time solving of complex differential equations with efficient neural network inference.
2Ease of operation
If data-driven control methods are used to avoid complex modeling, then ease of implementation improves, but the ability to capture physical dynamics and ensure control stability deteriorates
Solution Approach 1:
The patent incorporates feedback mechanisms where the neural network's control policies are continuously refined based on actual system performance. Through reinforcement learning, the agent receives rewards or penalties based on control outcomes, allowing the system to learn from experience and adapt its control strategy. This feedback loop ensures that the data-driven approach progressively captures physical dynamics while maintaining ease of implementation.
Solution Approach 2:
The patent performs preliminary training of the neural network offline using extensive simulated or real operational data before deployment. This preliminary action allows the system to learn optimal control policies and capture physical dynamics in advance, so that during actual operation, the pre-trained network can provide stable control decisions without requiring complex real-time computations or extensive online data collection.
3Measurement precision
If indirect data-driven control methods are used to construct system models, then model accuracy can be improved, but the quantity of data required and computational resources increase
Solution Approach 1:
The patent employs partial action by focusing the neural network training on the most critical aspects of system dynamics and control policies rather than attempting to model all system behaviors with exhaustive precision. The reinforcement learning agent learns to prioritize actions and states that have the greatest impact on control objectives, achieving sufficient model accuracy for effective control without requiring exhaustive datasets covering all possible system conditions.
Data Source
AI summary
An apparatus for controlling an operation of a system is provided. The apparatus comprises an input interface configured to receive a state trajectory of the system, and a memory configured to store a model of dynamics of the system including a combination of at least one differential equation and a closure model. The apparatus further comprises a processor configured to update the closure model using reinforcement learning (RL) having a value function reducing a difference between a shape of the received state trajectory and a shape of state trajectory estimated using the model with the updated closure model, and determine a control command based on the model with the updated closure model. Further, the apparatus comprises an output interface configured to transmit the control command to an actuator of the system to control the operation of the system.