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This technical paper presents a distributed continuous-time algorithm to solve multi-agent optimization problem with the team objective being the sum of all local convex objective functions while subject to an equality constraint. The optimal solutions are achieved within fixed time which is independent of the initial conditions of agents. This advantage makes it possible to off-line preassign the settling time according to task requirements. The fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization and fixed-time Lyapunov theory. Finally, the algorithm is valuated via an example. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a state-space solution to weight optimization problem in loop-shaping control. A pointwise-in-frequency weight optimization framework is transformed into convex optimization searches that are independent of frequency. The introduced optimization problem therefore avoids gridding of the frequency space and consequently, the inaccuracies attributed to fitting transfer functions to magnitude data. In this optimization problem, the order of the weight is specified ‘a priori’, thus facilitating the synthesis of low-order controllers, which is desirable from an implementation perspective. The proposed solution algorithm simultaneously synthesizes a robust stabilizing controller and a loop-shaping weight (pre-compensator) that maximize the robust stability margin subject to constraints on the performance and the singular values of the weight. Three numerical examples are given to illustrate the effectiveness of the technique. [Copyright &y& Elsevier]

This paper presents two distributed event-triggered algorithms under directed communication networks to solve a class of convex optimization problems such as the economic dispatch problem (EDP) with equality constraint, while the objective of optimization is the sum of all locally convex functions. One is distributed continuous-time event-triggered optimization algorithm, and the other is discrete-time algorithm based on iteration scheme. Continuous communication is not required by adopting event-triggered communication strategy. It means that the communication cost can be reduced and unnecessary waste of network resources can be avoided. Moreover, the convergence for the proposed algorithms are rigorously proved with the aid of Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, four numerical simulations show the effectiveness and advantages of the two novel distributed event-triggered optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we exploit the possibility of combining nonsmooth control jointly with projected gradient approaches to solve convex optimization problems with linear equality constraints. Our development gives rise to a sign projected gradient method employing only "coarse" information, which has finite-time convergence capability and preserves the simplicity and elegance of gradient descent. Our primary objective is to understand the design principle of the projection matrix in the nonsmooth setting and to investigate some key features of the method, such as convergence time. Specifically, we offer a set of convergence results via nonsmooth analysis, revealing that the algorithm guarantees finite-time convergence for a wide range of cost functions, including strongly convex, strictly convex, and convex functions, provided that the proposed design criteria and conditions are satisfied. The results suggest that the choice of the projection matrix might not be unique, which motivates the optimal design issue of the projection matrix to minimize convergence time. We show that the problem can be formulated as a convex optimization problem, which can be solved readily by existing optimization tools. We discuss the possibility of employing the proposed method to solve unconstrained optimization problems, which in turn gives an initial feasible solution to the sign projected gradient flow. We apply the algorithm to solve a formation control problem, and the numerical results show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]