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This article investigates distributed optimization of high‐order nonlinear multi‐agent systems (MASs) with disturbance under switching topologies. First, we propose a class of new distributed control algorithms for high‐order MASs under switching topologies, such that all agents asymptotically reach consensus at the unique minimizer of the sum of cost functions. Then, by constructing disturbance observer, the proposed algorithms are extended to address distributed optimization problems for high‐order nonlinear MASs with disturbance under switching topologies. In particular, both of new presented methods do not require optimal reference signal generator, which can save the computational resources of systems. In final, simulations are conducted to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This article proposes a new distributed finite‐time optimization algorithm for agents under directed graphs. By employing the nonsmooth technique and graph theory, a distributed discontinuous algorithm for continuous‐time agents subject to strongly convex local cost functions is first designed with a finite‐time distributed estimator, where the gradients of the local cost functions are estimated in finite time. It is shown that for a strongly connected graph and arbitrary initial conditions, the proposed algorithms can achieve consensus, and the systems can converge to the optimal point in finite time. Then, a two‐step approach is proposed to achieve finite‐time optimization of high‐order agents with disturbances under directed graphs. Finally, the validity of the proposed finite‐time optimization algorithm is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

Existing distributed finite‐time optimization algorithms for continuous‐time multi‐agent systems require either undirected graphs or weight balanced digraphs, and distributed finite‐time optimization problems for weight unbalanced digraphs are still great challenging. Thus, the distributed finite‐time optimization problems for continuous‐time multi‐agent systems with strongly convex local cost functions are investigated under directed graphs in this article. First, a distributed finite‐time gradient estimator is constructed by using non‐smooth analysis and algebraic graph theory, then distributed finite‐time optimization algorithms and piecewise distributed finite‐time optimization algorithms are proposed based on the designed gradient estimator. The new proposed distributed finite‐time optimization algorithms which only require strongly connected graphs relax the balanced requirement. Furthermore, the communication bandwidth of systems could be saved by deploying the proposed piecewise distributed finite‐time optimization algorithms since the information exchange in the optimization process is reduced. Finally, simulation examples are given to verify the effectiveness of proposed distributed optimization algorithms. [ABSTRACT FROM AUTHOR]

Distributed primal-dual methods have been widely used for solving large-scale constrained optimization problems. The majority of existing results focus on the problems with decoupled constraints. Some recent works have studied the problems subject to separable globally coupled constraints. This paper considers the distributed optimization problems with globally coupled constraints over networks without requiring the separability of the globally coupled constraints. This is made possible by the local estimates of the constraint violations. For solving such a problem, we propose a primal-dual algorithm in the augmented Lagrangian framework, combining the average consensus technique. We first establish a non-ergodic convergence rate of $\mathcal {O}(1/k)$ in terms of the objective residual for solving a distributed constrained convex optimization problem, where $k$ is the iteration counter. Specifically, the global objective function is the aggregate of the local convex and possibly non-smooth costs, and the coupled constraint is the sum of the local linear equality constraints. The numerical results illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we explore the possibility of designing a continuous control algorithm for time‐varying networks of high‐order nonlinear agents with input saturation. A class of neural network‐based (NN) distributed control algorithms are proposed for the consensus of nonlinear agents with input saturation and nonidentical unknown control directions (UCDs) under uniformly quasi‐strongly δ‐connected graphs. An NN is used to cancel the unknown part of agent dynamics due to the well known NN function approximation property. Also, an adaptive smooth term is employed to compensate for the bounded disturbance, the approximation error. Moreover, an auxiliary system is designed to counteract the effect of input saturation. Furthermore, the control law is augmented with the Nussbaum‐type function to obtain an estimation of the UCDs. It is proven rigorously that the consensus of nonlinear agents with input saturation and nonidentical UCDs can be guaranteed, and the boundedness of all signals of closed‐loop systems is ensured. Finally, simulation examples are given to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the optimal consensus problem of high‐order nonlinear agents under digraphs by PI regulation. A new type of adaptive PI variables is proposed for the first time, which is independent of the global information of graphs and complex dynamics. With the proposed variables, a key lemma is derived to transform the optimal consensus problem into a regulation problem, such that classical control techniques are used to regulate the adaptive PI variables for more complex dynamics. We also develop a new kind of distributed control algorithms based on the adaptive PI variables, Nussbaum‐type functions, and neural networks (NN). The proposed algorithms achieve the optimal consensus for high‐order nonlinear agents with nonidentical unknown control directions, bounded disturbances, and input saturation over weight‐unbalanced directed networks. Finally, a simulation example is provided to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Existing results for cooperative control of high-order agents mainly employ the Nussbaum-type function to cope with unknown control directions and mostly require an assumption that the control directions are identical and unknown. This paper proposes a class of algorithms with nonlinear PI functions to relax such an assumption and make them suitable for nonidentical unknown control directions. It is proven that if the distributed nonlinear PI functions are suitably selected, the proposed algorithms can achieve consensus for high-order agents under strongly connected topologies and switching topologies with a jointly strongly connected basis (JSCB). Furthermore, we extend the consensus results to the case of time-varying topologies described by $\delta $ -connected, continuous graphs. As a special case, the consensus of high-order agents under the directed graph having a spanning tree is also investigated. Finally, illustrative simulations are presented to indicate the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]