Decentralized Formation Control with A Quadratic Lyapunov Function

In this paper, we investigate a decentralized formation control algorithm for an undirected formation control model. Unlike other formation control problems where only the shape of a configuration counts, we emphasize here also its Euclidean embedding. By following this decentralized formation control law, the agents will converge to certain equilibrium of the control system. In particular, we show that there is a quadratic Lyapunov function associated with the formation control system whose unique local (global) minimum point is the target configuration. In view of the fact that there exist multiple equilibria (in fact, a continuum of equilibria) of the formation control system, and hence there are solutions of the system which converge to some equilibria other than the target configuration, we apply simulated annealing, as a heuristic method, to the formation control law to fix this problem. Simulation results show that sample paths of the modified stochastic system approach the target configuration

Decentralized formation control with connectivity maintenance and collision avoidance under limited and intermittent sensing

A decentralized switched controller is developed for dynamic agents to perform global formation configuration convergence while maintaining network connectivity and avoiding collision within agents and between stationary obstacles, using only local feedback under limited and intermittent sensing. Due to the intermittent sensing, constant position feedback may not be available for agents all the time. Intermittent sensing can also lead to a disconnected network or collisions between agents. Using a navigation function framework, a decentralized switched controller is developed to navigate the agents to the desired positions while ensuring network maintenance and collision avoidance.Comment: 8 pages, 2 figures, submitted to ACC 201

Transmit Power Minimization in Small Cell Networks Under Time Average QoS Constraints

We consider a small cell network (SCN) consisting of N cells, with the small cell base stations (SCBSs) equipped with Nt \geq 1 antennas each, serving K single antenna user terminals (UTs) per cell. Under this set up, we address the following question: given certain time average quality of service (QoS) targets for the UTs, what is the minimum transmit power expenditure with which they can be met? Our motivation to consider time average QoS constraint comes from the fact that modern wireless applications such as file sharing, multi-media etc. allow some flexibility in terms of their delay tolerance. Time average QoS constraints can lead to greater transmit power savings as compared to instantaneous QoS constraints since it provides the flexibility to dynamically allocate resources over the fading channel states. We formulate the problem as a stochastic optimization problem whose solution is the design of the downlink beamforming vectors during each time slot. We solve this problem using the approach of Lyapunov optimization and characterize the performance of the proposed algorithm. With this algorithm as the reference, we present two main contributions that incorporate practical design considerations in SCNs. First, we analyze the impact of delays incurred in information exchange between the SCBSs. Second, we impose channel state information (CSI) feedback constraints, and formulate a joint CSI feedback and beamforming strategy. In both cases, we provide performance bounds of the algorithm in terms of satisfying the QoS constraints and the time average power expenditure. Our simulation results show that solving the problem with time average QoS constraints provide greater savings in the transmit power as compared to the instantaneous QoS constraints.Comment: in Journal on Selected Areas of Communications (JSAC), 201

Distributed Receding Horizon Control with Application to Multi-Vehicle Formation Stabilization

We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen sufficiently fast. The theory is applied in simulation for stabilization of a formation of vehicles