Constraint-Admissible Machine Control Using Lipschitz Bounds
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Solution Overview
Problem
Conventional reinforcement learning methods are unsuitable for data-driven control of constrained systems as they fail to guarantee state and input constraint satisfaction, leading to potential system instability and unsafe operation due to the lack of a mathematical model.
Innovation Solution
A data-driven control system that estimates Lipschitz constants from training data to design a feasible and safe control policy, allowing for constraint-admissible control policies to be initialized and iteratively updated, ensuring stability and safety without requiring a complete model of the system's dynamics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional reinforcement learning methods are used for data-driven control, then the system can learn control policies without a mathematical model, but the system cannot guarantee state and input constraint satisfaction leading to potential instability and unsafe operation
Solution Approach 1:
The patent applies preliminary action by pre-computing a control barrier function based on the partial system model before actual control execution. This pre-computed function establishes safety constraints that guide the reinforcement learning process, ensuring that exploration actions do not violate state or input constraints. The control barrier function is calculated in advance using available system dynamics information, creating a safety framework before data-driven learning begins.
Solution Approach 2:
The patent introduces a control barrier function as an intermediary between the reinforcement learning agent and the physical system. This intermediary layer translates the partial system model into safety constraints that the RL policy must satisfy. The control barrier function acts as a mediator that filters RL actions, allowing only those that maintain constraint satisfaction, thus bridging the gap between model-free learning and constraint-guaranteed operation.
2Device complexity
If a partial model of system dynamics is used, then the control design can proceed with limited information, but the controller cannot guarantee feasibility and safety due to unmodeled dynamics
Solution Approach 1:
The patent applies partial action by utilizing only the portion of system dynamics that is known and reliable. Instead of requiring a complete and accurate system model, the method uses the available partial model to construct a control barrier function that provides sufficient safety guarantees. The approach accepts that not all system dynamics need to be perfectly modeled to achieve safe and feasible control, focusing only on the critical dynamics that affect constraint satisfaction.
Solution Approach 2:
The patent transforms the partial system model into a control barrier function through parameterization. The control barrier function is expressed in terms of system states and parameters that can be bounded using the partial model information. By changing the representation from direct system dynamics to a barrier function framework, the method can guarantee safety using only partial model knowledge, converting incomplete information into reliable control constraints.
3Measurement precision
If reinforcement learning explores the system with different inputs to learn states, then the system can improve learning accuracy, but it may direct the system state outside the specified constraint set violating safety
Solution Approach 1:
The patent implements feedback by continuously evaluating candidate RL actions against the control barrier function before execution. The control barrier function provides real-time feedback on whether a proposed action would violate state or input constraints. This feedback mechanism guides the reinforcement learning exploration, allowing the system to learn from safe transitions only, thereby improving learning accuracy without compromising safety through constraint-violating explorations.
Data Source
AI summary
A control system for controlling a machine with partially modeled dynamics to perform a task estimates a Lipschitz constant bounding the unmodeled dynamics of the machine, initializes a constraint-admissible control policy using the Lipschitz constant for controlling the machine to perform a task, such that the constraint-admissible control policy satisfies stability constraint, safety and admissibility constraint including one or combination of a state constraint and an input constraint, and has a finite cost on the performance of the task, and jointly controls the machine and update the control policy to control an operation of the machine to perform the task according the control policy starting with the initialized constraint-admissible control policy and to update the control policy using data collected while performing the task. In such a manner, the updated control policy is constraint-admissible.