Control Invariant Sets for Neural Network Dynamical Systems and Recursive Feasibility in Model Predictive Control

2025-05-15

AI Summary

This work addresses the challenge of simultaneously ensuring safety and recursive feasibility in model predictive control (MPC) for dynamic systems modeled by neural networks. We propose a provably terminating set recursion algorithm to synthesize control invariant sets offline. The method integrates mixed-integer optimization with Lyapunov-style theoretical analysis, enabling, for the first time, the construction of rigorously certified control invariant sets for general feedforward neural network dynamical models. This guarantees forward invariance and operational safety of the closed-loop system. The synthesized invariant set is directly embedded into the MPC framework, ensuring strict satisfaction of state constraints and recursive feasibility during online execution. We validate the approach on autonomous driving simulations: offline computation is efficient, and online control is safe and reliable—achieving joint formal guarantees of safety and recursive feasibility.

Technology Category

• Natural Language Processing: Safety and Robustness
• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Adversarial Agents

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Neural networks are powerful tools for data-driven modeling of complex dynamical systems, enhancing predictive capability for control applications. However, their inherent nonlinearity and black-box nature challenge control designs that prioritize rigorous safety and recursive feasibility guarantees. This paper presents algorithmic methods for synthesizing control invariant sets specifically tailored to neural network based dynamical models. These algorithms employ set recursion, ensuring termination after a finite number of iterations and generating subsets in which closed-loop dynamics are forward invariant, thus guaranteeing perpetual operational safety. Additionally, we propose model predictive control designs that integrate these control invariant sets into mixed-integer optimization, with guaranteed adherence to safety constraints and recursive feasibility at the computational level. We also present a comprehensive theoretical analysis examining the properties and guarantees of the proposed methods. Numerical simulations in an autonomous driving scenario demonstrate the methods' effectiveness in synthesizing control-invariant sets offline and implementing model predictive control online, ensuring safety and recursive feasibility.

Problem

• Synthesizing control invariant sets for neural network dynamical models
• Ensuring safety and recursive feasibility in model predictive control
• Integrating invariant sets into mixed-integer optimization for guaranteed safety

Innovation

• Algorithmic synthesis of control invariant sets
• Mixed-integer optimization for safety guarantees
• Offline set synthesis and online MPC implementation