Distributed continuous-time optimization with nonlinear inequality and equality constraints under disturbances

This paper presents a distributed continuous-time optimization framework designed to address the challenges posed by time-varying cost functions, nonlinear inequality constraints, and equality constraints in multi-agent systems subject to disturbances. The proposed framework integrates log-barrier and quadratic penalty functions to handle constraints and employs an integral sliding mode control for disturbance rejection, including cases with bounded disturbances and disturbances with bounded derivatives. The proposed method ensures asymptotic convergence to the optimal solution, and convergence is established through nonsmooth analysis and Lyapunov theory. The effectiveness of the proposed algorithms is validated via numerical simulations on network topologies with different connectivity levels.