Robust Control Policy Under Uncertain Dynamics and Safety Constraints
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Solution Overview
Problem
Existing systems face challenges in controlling dynamics with uncertainties due to non-stationarity, wear-and-tear, and environmental factors, leading to difficulties in designing optimal controllers that satisfy safety constraints.
Innovation Solution
A robust and constraint Markov decision process (RCMDP) framework is developed, incorporating ambiguity sets to unify performance and safety costs, using Lyapunov descent to simplify computation, and enforcing constraints through a joint optimization of performance and safety costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a traditional controller is designed for a system with uncertain dynamics, then the controller structure becomes complex to handle all uncertainties, but the control performance and safety guarantee deteriorate
Solution Approach 1:
The patent transforms the control problem from optimizing control inputs directly to optimizing the parameters of a Lyapunov function. By changing the optimization variables from control parameters to Lyapunov function parameters, the method simplifies the controller structure while maintaining safety guarantees through the Lyapunov stability framework.
Solution Approach 2:
The patent introduces a Lyapunov function as an intermediary between the system dynamics and the control objective. This Lyapunov function serves as a certificate of safety, mediating the relationship between uncertain system dynamics and control performance, thereby simplifying the overall control architecture.
2Productivity
If reinforcement learning is used to optimize control policies, then the control performance improves, but the sample efficiency deteriorates requiring large amounts of data
Solution Approach 1:
The patent performs preliminary action by pre-defining a Lyapunov function with specific stability properties before optimization. This preliminary structure ensures safety constraints are satisfied from the outset, allowing the optimization to focus solely on performance improvement without requiring extensive sampling to discover safe regions.
Solution Approach 2:
The Lyapunov function serves multiple functions simultaneously: it certifies safety, guides optimization, and structures the control policy. This multi-functionality reduces the sample efficiency problem by consolidating multiple control objectives into a single unified framework rather than requiring separate learning processes for safety and performance.
3Reliability
If safety constraints are enforced strictly in constrained Markov decision processes, then the safety guarantee improves, but the performance cost increases due to conservative control
Solution Approach 1:
The patent changes the optimization parameters from control inputs to Lyapunov function parameters, which inherently encode safety information. This parameter transformation allows the optimizer to find solutions that satisfy safety constraints without the conservatism typical of direct constraint enforcement, as the Lyapunov structure naturally balances safety and performance.
Solution Approach 2:
Instead of enforcing safety constraints directly on control inputs (the conventional approach), the patent inverts the approach by ensuring safety through the Lyapunov function structure and optimizing performance through the same function's parameters. This inversion allows simultaneous optimization of both safety and performance without the trade-off.
Data Source
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AI summary
A controller for controlling a system having uncertainties in its dynamics subject to constraints on an operation of the system is provided. The controller is configured to acquire historical data of the operation of the system, and determine, for the system in a current state, a current control action transitioning a state of the system from the current state to a next state. The current control action is determined according to a robust and constraint Markov decision process (RCMDP) that uses the historical data to optimize a performance cost of the operation of the system subject to an optimization of a safety cost enforcing the constraints on the operation, wherein a state transition for each of state and action pairs in the performance cost and the safety cost is represented by a plurality of state transitions capturing the uncertainties of the dynamics of the system.