In this paper, we study an optimal output consensus problem for a multiagent network with agents in the form of multi-input multioutput minimum-phase dynamics. Optimal output consensus can be taken as an extended version of the existing output consensus problem for higher-order agents with an optimization requirement, where the output variables of agents are driven to achieve a consensus on the optimal solution of a global cost function. To solve this problem, we first construct an optimal signal generator, and then propose an embedded control scheme by embedding the generator in the feedback loop. We give two kinds of algorithms based on different available information along with both state feedback and output feedback, and prove that these algorithms with the embedded technique can guarantee the solvability of the problem for high-order multiagent systems under standard assumptions.

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In this paper, two aggregative games over weight-balanced digraphs are studied, where the cost functions of all players depend on not only their own decisions but also the aggregate of all decisions. In the first problem, the cost functions of players are differentiable with Lipschitz gradients, and the decisions of all players are coupled by linear coupling constraints. In the second problem, the cost functions are nonsmooth, and the decisions of all players are constrained by local feasibility constraints as well as linear coupling constraints. In order to seek the variational generalized Nash equilibrium (GNE) of the differentiable aggregative games, a continuous-time distributed algorithm is developed via gradient descent and dynamic average consensus, and its exponential convergence to the variational GNE is proven with the help of Lyapunov stability theory. Then, another continuous-time distributed projection-based algorithm is proposed for the nonsmooth aggregative games based on differential inclusions and differentiated projection operations. Moreover, the convergence of the algorithm to the variational GNE is analyzed by utilizing singular perturbation analysis. Finally, simulation examples are presented to illustrate the effectiveness of our methods.

In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms.