This paper is concerned with solving the distributed resource allocation optimization problem by multi-agent systems over undirected graphs. The optimization objective function is a sum of local cost functions associated to individual agents, and the optimization variable satisfies a global network resource constraint. The local cost function and the network resource are the private data for each agent, which are not shared with others. A novel gradient-based continuous-time algorithm is proposed to solve the distributed optimization problem. We take an event-triggered communication strategy and an event-triggered gradient measurement strategy into account in the algorithm. With strongly convex cost functions and locally Lipschitz gradients, we show that the agents can find the optimal solution by the proposed algorithm with exponential convergence rate, based on the construction of a suitable Lyapunov function. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed scheme.
This paper is concerned with the problem of global state regulation by output feedback for large-scale uncertain nonlinear systems with time delays in the states and inputs. The systems are assumed to be bounded by a more general form than a class of feedforward systems satisfying a linear growth condition in the unmeasurable states multiplying by unknown growth rates and continuous functions of the inputs or delayed inputs. Using the dynamic gain scaling technique and choosing the appropriate Lyapunov-Krasovskii functionals, we explicitly construct the universal output feedback controllers such that all the states of the closed-loop system are globally bounded and the states of large-scale uncertain systems converge to zero.