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

The computational complexity of PEPS

We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to solve PP problems, the latter two tasks are both proven to be #P-complete. We further show how PEPS can be used to approximate ground states of gapped Hamiltonians, and that creating them is easier than creating arbitrary PEPS. The main tool for our proofs is a duality between PEPS and postselection which allows to use existing results from quantum compexity.Comment: 5 pages, 1 figure. Published version, plus a few extra

Revealing Student Thinking about Experimental Design and the Roles of Control Experiments

Well-designed “controls” distinguish experimental from non-experimental studies. Surprisingly, we found that a high percentage of students had difficulty identifying control experiments even after completing three university-level laboratory courses. To address this issue, we designed and ran a revised cell biology lab course in which students participated in weekly “experimental control exercises.” To measure student understanding of control experiments, we developed a set of assessment questions; these were given to students prior to and following completion of either a standard cell biology lab course or the revised cell biology lab course. Not unexpectedly, the results indicate that the revised course led to greater improvements in students’ ability to identify and explain the purpose of control experiments. Based on these observations, we recommend that explicit and detailed discussions designed to identify the design and purpose behind control experiments become a standard component of all laboratory courses

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