Distributed min-projection control: A switching consensus protocol for switched affine multi-agent systems

In this study, a distributed control problem is addressed for switched affine multi-agent systems. In dynamical systems with an affine control input, the use of error feedback is essential for the realization of consensus protocols, but different from most existing results with affine control multi-agent systems, switched affine multi-agent systems face additional difficulties in the analysis and control; meanwhile, affine diffusive coupling consensus algorithms are not applicable. For this reason, a switching signal is considered as a control mechanism. We study switched networks in which the leader’s state is accessible only for a portion of agents, and the Lyapunov matrix-based min-projection control strategy is proposed to determine the active mode for each agent based on the state information of the neighbors. Using parameter-dependent stability analysis, a range of different reference points can be tracked by distributed min-projection switching without any redesigning. Also, benefiting from the hybrid dynamical system, min-projection switch is modified such that a periodic time-triggered sampled control is introduced to obtain finite switching frequency. Finally, a multi-motor system fed by DC–DC buck–boost converters is simulated for a stepwise changing of leader signal and different dwell-time switching, and the effectiveness of proposed method is assessed.

A Distributed Control Problem for a Fractional Tumor Growth Model

In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three self-adjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a Cahn–Hilliard type phase field system modeling tumor growth that has been proposed by Hawkins–Daarud, van der Zee and Oden. The aim of the control process, which could be realized by either administering a drug or monitoring the nutrition, is to keep the tumor cell fraction under control while avoiding possible harm for the patient. In contrast to previous studies, in which the occurring unbounded operators governing the diffusional regimes were all given by the Laplacian with zero Neumann boundary conditions, the operators may in our case be different; more generally, we consider systems with fractional powers of the type that were studied in a recent work by the present authors. In our analysis, we show the Fréchet differentiability of the associated control-to-state operator, establish the existence of solutions to the associated adjoint system, and derive the first-order necessary conditions of optimality for a cost functional of tracking type.

Distributed tracking control of multiple nonholonomic mobile agents with input delay

This paper considers the distributed control problem of nonholonomic mobile agents with input delay to track a target. In contrast to the existing works in which some controllers have been designed for ideal conditions, the destructive factor of input delay is considered in the dynamics of the agents in this work. At first, a distributed controller is suggested for each agent to track the target in the absence of input delay. In this case, each nonholonomic mobile agent is divided into two subsystems and two terminal sliding mode controllers are designed for the two subsystems. Based on the proposed controllers, a switching control strategy is obtained to guarantee the finite time tracking control of nonholonomic mobile agents. Then, this controller is extended based on a future state estimator for tracking control in the presence of input delay. The stability analysis of distributed controllers and estimator is also provided. Simulation results illustrate the effectiveness of the suggested algorithms.