30,327 research outputs found
Fixed-time Distributed Optimization under Time-Varying Communication Topology
This paper presents a method to solve distributed optimization problem within
a fixed time over a time-varying communication topology. Each agent in the
network can access its private objective function, while exchange of local
information is permitted between the neighbors. This study investigates first
nonlinear protocol for achieving distributed optimization for time-varying
communication topology within a fixed time independent of the initial
conditions. For the case when the global objective function is strictly convex,
a second-order Hessian based approach is developed for achieving fixed-time
convergence. In the special case of strongly convex global objective function,
it is shown that the requirement to transmit Hessians can be relaxed and an
equivalent first-order method is developed for achieving fixed-time convergence
to global optimum. Results are further extended to the case where the
underlying team objective function, possibly non-convex, satisfies only the
Polyak-\L ojasiewicz (PL) inequality, which is a relaxation of strong
convexity.Comment: 25 page
Random Finite Set Theory and Optimal Control of Large Collaborative Swarms
Controlling large swarms of robotic agents has many challenges including, but
not limited to, computational complexity due to the number of agents,
uncertainty in the functionality of each agent in the swarm, and uncertainty in
the swarm's configuration. This work generalizes the swarm state using Random
Finite Set (RFS) theory and solves the control problem using Model Predictive
Control (MPC) to overcome the aforementioned challenges. Computationally
efficient solutions are obtained via the Iterative Linear Quadratic Regulator
(ILQR). Information divergence is used to define the distance between the swarm
RFS and the desired swarm configuration. Then, a stochastic optimal control
problem is formulated using a modified L2^2 distance. Simulation results using
MPC and ILQR show that swarm intensities converge to a target destination, and
the RFS control formulation can vary in the number of target destinations. ILQR
also provides a more computationally efficient solution to the RFS swarm
problem when compared to the MPC solution. Lastly, the RFS control solution is
applied to a spacecraft relative motion problem showing the viability for this
real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731
Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey
Wireless sensor networks (WSNs) consist of autonomous and resource-limited
devices. The devices cooperate to monitor one or more physical phenomena within
an area of interest. WSNs operate as stochastic systems because of randomness
in the monitored environments. For long service time and low maintenance cost,
WSNs require adaptive and robust methods to address data exchange, topology
formulation, resource and power optimization, sensing coverage and object
detection, and security challenges. In these problems, sensor nodes are to make
optimized decisions from a set of accessible strategies to achieve design
goals. This survey reviews numerous applications of the Markov decision process
(MDP) framework, a powerful decision-making tool to develop adaptive algorithms
and protocols for WSNs. Furthermore, various solution methods are discussed and
compared to serve as a guide for using MDPs in WSNs
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