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Feedback Refinement Relations for the Synthesis of Symbolic Controllers (1503.03715v3)

Published 12 Mar 2015 in math.OC, cs.LO, and cs.SY

Abstract: We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples.

Citations (230)

Summary

  • The paper presents a novel methodology using Feedback Refinement Relations to systematically bridge the abstraction and the plant in controller design.
  • It employs set-valued dynamics to handle uncertainties, enabling symbolic controller synthesis without needing detailed state information.
  • The approach is validated through practical demonstrations on autonomous vehicle path planning and aircraft landing maneuvers.

Feedback Refinement Relations: A Methodology for Automated Controller Synthesis

The paper "Feedback Refinement Relations" by Gunther Reissig, Alexander Weber, and Matthias Rungger introduces a new methodology for the automated synthesis of controllers to enforce predefined specifications on systems. The distinctive feature of this approach is the use of Feedback Refinement Relations (FRRs), which form the core concept, providing a structured way to relate a system and its abstraction. This is integral to overcoming common obstacles in controller design, such as those requiring exact state information and the refinement complexity of abstract controllers.

Core Concepts and Methodology

The authors propose a framework that effectively bridges the gap between a complex system (referred to as the plant) and its simplified model (an abstraction), ensuring that the designed controller for the abstraction can be straightforwardly adapted to control the plant itself. This is achieved through the FRRs, which demand that for each transition allowed by the controller in the abstraction, a corresponding feasible transition exists in the plant. This requirement is crucial in maintaining the controller's compatibility with the plant's constraints without needing detailed state information from the plant.

The abstraction is constructed using set-valued dynamics, accounting for uncertainties and disturbances in the plant's environment. This generalizes the approach, allowing it to be applicable to systems described with various types of perturbations.

Implications and Numerical Results

The implications of this research are significant for both theoretical and practical aspects of automated control. Theoretically, it proposes a notion of system relation that simplifies the control synthesis problem into manageable parts while maintaining rigorous guarantees on controller performance. Practically, it paves the way for implementing controllers in real-world applications efficiently, using symbolic state information that is much easier to obtain.

The paper substantiates its claims with practical demonstrations on examples like a path planning problem for autonomous vehicles and aircraft landing maneuvers. This showcases the flexibility and robustness of the approach when dealing with systems that include continuous and discrete dynamics intertwined with uncertainties.

Future Directions in AI

The framework's ability to interface symbolic controllers with systems via static quantizers opens potential avenues for advancements in artificial intelligence, where simplifying complex system behaviors can lead to more efficient learning and decision-making processes. Given the explosion of interest in multi-agent systems and autonomous robotics, such robust methods that handle uncertainty while ensuring reliable behavior are paramount.

In conclusion, this paper provides a comprehensive methodology that introduces feedback refinement relations as a tool for automated controller synthesis, offering a clear path towards creating controllers that are not only correct by design but also robust to the realities of practical implementation. Future research may expand this methodology to encompass more complex systems and explore its integration with other AI paradigms, potentially simplifying and enhancing intelligent decision-making in uncertain environments.