Data Transmission Over Networks for Estimation and Control

We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network

Optimal capacity reliability design of networks based on genetic algorithm

The cost, capacity and reliability of components vary in different component types, and the optimal component combination is determined by minimizing the total cost under the constraint of network capacity reliability requirement. To solve the problem that the gradient method can only be applied for networks whose capacity and reliability of components monotonically increase with the cost, a general optimization model is presented, and a Genetic Algorithm (GA) method using the minimal path sets to calculate the network capacity reliability is proposed to solve this optimal capacity reliability design problem. The optimal types of both nodes and links can be obtained using our optimization method. Our case study on ARPA network shows that our algorithm is efficient for the problem with good convergence and search performance

Improved inclusion-exclusion identities via closure operators

Let (A_v)_v ∈ V be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure operator on the power set of V having the unique base property. The result generalizes three improvements of the inclusion-exclusion principle as well as Whitney's broken circuit theorem on the chromatic polynomial of a graph

Application of the Jaya algorithm to solve the optimal reliability allocation for reduction oxygen supply system of a spacecraft

In this paper the reliability of reduction oxygen supply system (ROSS) of a spacecraft which was calculated as a complex system using minimal cut method. The reliability of each component of system was calculated as well as the reliability importance of the system. The cost of each component of the system was possible approaches of the allocation values of reliability based the minimization of the overall cost in this system. The advantage of this algorithm can be used to allocate the optimization of reliability for simple or complex system. This optimization is achieved using the Jaya algorithm. The proposed technique is based on the notion that a conclusion reached on a particular problem should pass near the best results and avoid the worst outcomes. The original findings of this paper are: I) the system used in this paper is a spacecraft's reduced oxygen supply system with the logarithmic cost function; and ii) the results obtained were by using the Jaya algorithm to solve specific system reliability optimization problems

Inclusion-Exclusion and Network Reliability

Based on a recent improvement of the inclusion-exclusion principle, we present a new approach to network reliability problems. In particular, we give a new proof of a result of Shier, which expresses the reliability of a network as an alternating sum over chains in a semilattice, and a new proof of a result of Provan and Ball, which provides an algorithm for computing network reliability in pseudopolynomial time. Moreover, some results on k-out-of-n systems are established. 1. Introduction to network reliability We consider both directed and undirected networks in which nodes are perfectly reliable and edges fail randomly and independently with known probabilities. For such networks, a large variety of reliability measures exists. The two-terminal reliability , for instance, is the probability that a message can pass from a distinguished source node s to a distinguished terminal node t along a path of operating edges. More generally, the source-to-T -terminal reliability is the..