Safety-Critical Distributed Optimization with Input Constraints and Unknown Second-Order Dynamics

This paper investigates the distributed safe optimization problem for uncertain second-order nonlinear multi-agent systems subject to inequality and input constraints. The primary goal is to collaboratively minimize the sum of local objective functions, with agents having access only to their own local information and the states of neighboring agents. To address this challenge, we introduce a desired distributed optimization algorithm that incorporates a Control Lyapunov Function (CLF) based condition. For handling inequality and input constraints, a high-order Control Barrier Function (CBF) based method is utilized. Additionally, quadratic programming is employed to determine the control inputs. When the desired optimization trajectory conflicts with the constraints, a relaxed CLF-based condition is adopted. The practical applicability of the theoretical findings is demonstrated through a series of numerical examples.