Constrained computational hybrid controller for Input Affine Hybrid Dynamical Systems
Ali Taghavian, Ali Safi, Esmaeel Khanmirza
TL;DR
This paper tackles constrained control of input-affine hybrid dynamical systems by introducing the Computational Hybrid Controller (CHC). CHC partitions the state space into bounded rectangular elements, builds a Transition Graph via Rectangular Automata simulations, and uses a Reachability Sector to steer the system toward a set-point, aided by a Fine-tuner Section and a stabilizer for local convergence. The method is validated on a nonlinear pendulum with input saturation and a three-tank benchmark, with CHC compared to Model Predictive Control (MPC) to illustrate constraint handling and robustness. Offline construction of the Reachability Sector can be computationally intensive, increasing with the number of elements, but CHC offers a real-time implementable approach for certain classes of hybrid systems where safety and saturation constraints are critical.
Abstract
Hybrid dynamical systems are viewed as the most complicated systems with continuous and event-based behaviors. Since traditional controllers cannot handle these systems, some newly-developed controllers have been published in recent decades to deal with them. This paper presents a novel implementable constrained final-state controller based on partitioning the system's state-space, computational simulations, and graph theory. Experimental results and a comparison with Model Predictive Controller on the three tank benchmark and swing-up control of a pendulum show the effectiveness of the proposed Computational Hybrid Controller(CHC).