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This brief addresses distributed continuous-time optimization problems with time-varying objective functions. The goal is for multiple agents to cooperatively minimize the sum of local time-varying objective functions with only local interaction and information while explicitly taking into account distributed adaptive gain design. Here, the optimal point is time varying and creates an optimal trajectory. First, for the unconstrained case, a distributed nonsmooth algorithm coupled with a state-dependent gain is proposed. It is shown that the interaction gain for each agent can be computed according to the variation of the Hessian and gradient information of the convex local objective functions so that the algorithm can solve the time-varying optimization problem without imposing a bound on any information about the local objective functions. Second, for the case where there exist common time-varying linear equality constraints, an extended algorithm is presented, where local Lagrangian functions are introduced to address the equality constraints. The asymptotic convergence of both algorithms to the optimal solution is proved. Numerical simulations are presented to illustrate the theoretical results. In addition, the one proposed algorithm is experimentally implemented and validated on a multi-Crazyflie platform. [ABSTRACT FROM AUTHOR]

This paper studies a containment problem with communication delays and switching topologies. A nonlinear projection containment control algorithm for followers with single-integrator discrete-time dynamics is proposed. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to show the nonincreasing monotonicity of the largest distance from the agents to the convex hull. It is shown that the nonlinear projection containment control algorithm is robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed average tracking (DAT) problem for a group of agents to track the average of multiple time-varying reference signals, each of which is available to only one agent, under local interaction with neighbors and an undirected graph. We consider three cases: 1) DAT for single-integrator dynamics with a chain of integrators in algorithm design; 2) DAT with swarm behavior for single-integrator dynamics; and 3) DAT with swarm behavior for double-integrator dynamics. First, a continuous distributed algorithm with a chain of two integrators is proposed for single-integrator dynamics, where each agent needs its own and its neighbors’ filter outputs obtained through communication besides its absolute position, local relative positions, reference signal, and reference velocity. The introduced algorithm can deal with a wide class of reference signals with steady deviations among reference velocities. Then, two swarm-based DAT algorithms for, respectively, single- and double-integrator dynamics are presented. In the first swarm-based algorithm for single-integrator dynamics, each agent needs to measure the relative positions between itself and its neighbors, while in the second swarm-based algorithm for double-integrator dynamics, relative velocity information is required too. In both cases, the information can be obtained through local sensing. If correct initialization constraints can be achieved, the center of the agents will track the average of the reference signals and the agents will maintain connectivity and avoid interagent collision. Numerical simulations are also presented to illustrate the theoretical results. Finally, the algorithms presented in this paper are experimentally implemented and validated on a multirobot platform. [ABSTRACT FROM AUTHOR]

This paper studies the inherent connection between dynamic region-following formation control (DRFFC) and distributed average tracking (DAT). We propose a fixed-gain DAT algorithm with robustness to initialization errors for linear multiagent systems, which is capable of achieving DAT with a zero tracking error for a large class of reference signals. In the case that the fixed gain cannot be chosen properly, we present an adaptive control gain design, under which each agent simply chooses its own gain and the restriction on knowing the upper bounds on the reference signals and their inputs is removed. We show that the proposed DAT algorithms can be employed to solve the DRFFC problem. This is an attempt on the applications of DAT algorithms to achieve distributed control; existing works most use DAT as distributed estimation algorithms. For single-integrator, double-integrator, higher-order linear dynamics, we derive the corresponding DRFFC algorithms from the DAT algorithm. Compared with existing DRFFC algorithms, the DAT-based DRFFC algorithms do not require the desired region to have a regular shape and is capable of generating a much richer formation behavior. Numerical examples are also included to show the validity of the derived results. [ABSTRACT FROM PUBLISHER]

This brief studies distributed containment control for double-integrator dynamics in the presence of both stationary and dynamic leaders. In the case of stationary leaders, we propose a distributed containment control algorithm and study conditions on the network topology and the control gains to guarantee asymptotic containment control in any dimensional space. In the case of dynamic leaders, we study two cases: leaders with an identical velocity and leaders with nonidentical velocities. For the first case, we propose two distributed containment control algorithms to solve, respectively, asymptotic containment control under a switching directed network topology and finite-time containment control under a fixed directed network topology. In particular, asymptotic containment control can be achieved for any dimensional space if the network topology is fixed and for only the 1-D space if the network topology is switching. For the second case, we propose a distributed containment control algorithm under a fixed network topology where the communication patterns among the followers are undirected and derive conditions on the network topology and the control gains to guarantee asymptotic containment control for any dimensional space. Both simulation results and experimental results on a multi-robot platform are provided to validate some theoretical results. [ABSTRACT FROM AUTHOR]