Personal communications: An extension to the mobile satellite

As time progresses, customer demands become far more universal, involving integrated, simple to operate, cost effective services, with technology virtually transparent to the operator. Industry will be in a position of providing the necessary services to meet the subscribers' needs. Our resource based industries, transportation services, and utilities in the more rural and unserviced areas will require quality and affordable services that can only be supplied via satellite. One answer to these needs will be one- and two-way interoperable data messaging

Estimation Schemes for Networked Control Systems Using UDP-Like Communication

In this work we consider a class of networked control systems (NCS) when the control signal is sent to the plant via a UDP-like communication protocol, the controller sends a communication packet to the plant across a lossy network but the controller does not receive any acknowledgement signal indicating the status of reception/delivery of the control packet. Standard observer based estimators assume the estimator has knowledge of what control signal is applied to the plant, but under the UDP-like communication scheme the estimator does not know what control is applied. Continuing previous work, we present a simple estimation algorithm consisting of a state estimator and mode observer. For single input systems we can add an extra control signal that guarantees recovery of the fate of the control packet. Using a modified state feedback with the added input we can guarantee the estimation error is bounded as is the expected value of the state. This extra input is removed and sufficient conditions on the system properties are given to assure the estimation remain bounded. Comparisons are made between the algorithm presented and the method of unknown input observer. Simulations are provided to demonstrate the algorithm

Kalman Filtering Over A Packet Dropping Network: A Probabilistic Approach

We consider the problem of state estimation of a discrete time process over a packet dropping network. Previous pioneering work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M, and we derive lower and upper bounds on Pr[P_k ≤ M]. We are also able to recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper

Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective

We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[P_k ≤ M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[P_k ≤ M]. We also recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper

An Estimation Algorithm for a Class of Networked Control Systems Using UDP-Like Communication Schemes

In this work we consider a class of networked control systems (NCS) when the control signal is sent to the plant via a UDP-like communication protocol. In this case the controller sends a communication packet to the plant across a lossy network, but the controller does not receive any acknowledgement signal indicating the status of the control packet. Standard observer based estimators assume the estimator has knowledge of what control signal is applied to the plant. Under the UDP-like protocol the controller/estimator does not have explicit knowledge whether the control signals have been applied to the plant or not. We present a simple estimation and control algorithm that consists of a state and mode observer as well as a constraint on the control signal sent to the plant. For the class of systems considered, discrete time LTI plants where at least one of the states that is directly affected by the input is also part of the measurement vector, the estimator is able to recover the fate of the control packet from the measurement at the next timestep and exhibit better performance than other naive schemes. For single-input-single-output (SISO) systems we are able to show convergence properties of the estimation error and closed loop stability. Simulations are provided to demonstrate the algorithm and show its effectiveness

A context-free and a 1-counter geodesic language for a Baumslag-Solitar group

We give a language of unique geodesic normal forms for the Baumslag-Solitar group BS(1,2) that is context-free and 1-counter. We discuss the classes of context-free, 1-counter and counter languages, and explain how they are inter-related

Biologically Inspired Feedback Design for Drosophila Flight

We use a biologically motivated model of the Drosophila's flight mechanics and sensor processing to design a feedback control scheme to regulate forward flight. The model used for insect flight is the grand unified fly (GUF) [3] simulation consisting of rigid body kinematics, aerodynamic forces and moments, sensory systems, and a 3D environment model. We seek to design a control algorithm that will convert the sensory signals into proper wing beat commands to regulate forward flight. Modulating the wing beat frequency and mean stroke angle produces changes in the flight envelope. The sensory signals consist of estimates of rotational velocity from the haltere organs and translational velocity estimates from visual elementary motion detectors (EMD's) and matched retinal velocity filters. The controller is designed based on a longitudinal model of the flight dynamics. Feedforward commands are generated based on a desired forward velocity. The dynamics are linearized around this operating point and a feedback controller designed to correct deviations from the operating point. The control algorithm is implemented in the GUF simulator and achieves the desired tracking of the forward reference velocities and exhibits biologically realistic responses

Estimation of linear stochastic systems over a queueing network

In this paper, we consider the standard state estimation problem over a congested packet-based network. The network is modeled as a queue with a single server processing the packets. This provides a framework to consider the effect of packet drops, packet delays and bursty losses on state estimation. We use a modified Kalman Filter with buffer to cope with delayed packets. We analyze the stability of the estimates with varying buffer length and queue size. We use high order Markov chains for our analysis. Simulation examples are presented to illustrate the theory

Limit cycles in the presence of convection, a travelling wave analysis

We consider a diffusion model with limit cycle reaction functions, in the presence of convection. We select a set of functions derived from a realistic reaction model: the Schnakenberg equations. This resultant form is unsymmetrical. We find a transformation which maps the irregular equations into model form. Next we transform the dependent variables into polar form. From here, a travelling wave analysis is performed on the radial variable. Results are complex, but we make some simple estimates. We carry out numerical experiments to test our analysis. An initial `knock' starts the propagation of pattern. The speed of the travelling wave is not quite as expected. We investigate further. The system demonstrates distinctly different behaviour to the left and the right. We explain how this phenomenon occurs by examining the underlying behaviour.Comment: 20 pages, 5 figure