Online Receding Horizon Safe-Critical Control for Complex Nonlinear System Under Uncertainty: A Biological Brain-Inspired Dual Learning Approach

This research introduces a real-time, computationally efficient receding horizon control (RHC) framework with adaptive safety mechanisms under uncertainty. Achieving real-time optimal performance and safety with uncertain nonlinear systems and environments is a challenging task due to the heavy computational complexity involved in learning optimal solutions and managing system uncertainties. To address this, a novel RHC-based safe critical mechanism is designed, enhancing the classical RHC by integrating performance with a real-time safety framework that adapts to environmental uncertainties. Particularly, a human brain-inspired dual-learning algorithm is developed with a slow learning phase that gradually learns the system and environmental uncertainties and further achieves the optimal RHC solution by employing a situation-aware physics-informed neural network (SA-PINN). A fast-learning mechanism is then developed to maintain system safety with quick decision-making capabilities, utilizing a fast-learned adaptive control barrier (FLA-CBF) function that incorporates an adaptive bound relaxation. This approach enables the slow-learning phase to gradually learn the optimal solutions and adapt to uncertainties, thus enhancing the fast-learning phase, which supports real-time control execution with guaranteed safety. In addition, Lyapunov stability analysis and a series of experimental results have been provided to showcase the efficacy of the developed algorithm. Note to Practitioners—This paper investigates the critical challenge of ensuring safety and performance in real-time control of complex nonlinear systems with uncertainties, emphasizing the need to balance control effectiveness and safety in dynamic real-world environments. The approach detailed in the paper has potential applications across various fields that involve dynamic systems needing robust safe control and performance under uncertainty, like robotics, autonomous vehicles, and aerospace engineering. A key potential of this research lies in its novel dual-learning algorithm, which mimics human cognitive processes to balance safety and performance dynamically. This is particularly advantageous in environments where fast safety decisions are needed, and system responsiveness is critical. Here, the optimal control and model learning from the slow learning part are transferred to the fast learning phase, which quickly adapts to environmental changes using a modified CBF, known as FLA-CBF, with an initial strict safety threshold that is gradually relaxed. However, the selection of this bound threshold depends on the environment and requires further exploration. Also, the computation intensity of the algorithm needs to be improved for real-time application, especially in scenarios involving multiple agents.