Chithrupa Ramesh

Design of State-Based Schedulers for a Network of Control Loops

For a closed-loop system with a contention-based multiple access network on its sensor link, the medium access controller (MAC) may discard some packets when the traffic on the link is high. We use a local state-based scheduler to select a few critical data packets to send to the MAC. In this paper, we analyze the impact of such a scheduler on the closed-loop system in the presence of traffic, and show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of an innovations-based scheduler with a certainty equivalent controller. However, this controller is not an equivalent design for the optimal controller, in the sense of Witsenhausen. The computation of the estimate can be simplified by introducing a symmetry constraint on the scheduler. Based on these findings, we propose a dual predictor architecture for the closed-loop system, which ensures separation between scheduler, observer and controller. We present an example of this architecture, which illustrates a network-aware event-triggering mechanism.

On the dual effect in state-based scheduling of networked control systems

In this paper, we show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of a sub-optimal scheduler with a certainty equivalent controller. Furthermore, we show that a mapping of the state-based scheduler into one which fulfills this condition, and consequently has an optimal certainty equivalent controller, does not result in an equivalent class of design in the sense of Witsenhausen. Computing the estimate remains hard, but can be simplified by introducing a symmetry constraint on the scheduler.

Steady state performance analysis of multiple state-based schedulers with CSMA

In this paper, we analyze the performance of multiple event-based systems that share access to the same network. Transmissions are attempted only when a local state-based scheduler generates an event, and access to the network is determined using a Carrier Sensing Multiple Access (CSMA) protocol. In general, the interactions in such a multiple access network introduce correlations between the system variables of the various loops, and the respective traffic contributions as well. Hence, analyzing the performance of this network is difficult. However, a class of state-based schedulers, introduced in the paper, permits a joint analysis of the scheduler and the Contention Resolution Mechanism (CRM). The analysis is based on a Markov model, which is validated through simulations. The resulting steady-state model makes it possible to characterize the statistics of packet arrivals in this network.

LQG and Medium Access Control

The communication channel is a shared resource in networked control systems, and channel access at every instant cannot be guaranteed. In this paper, we propose a novel architecture for control over wireless networks with integrated medium access control (MAC).We evaluate the impact of constrained channel access on the cost of controlling a single plant over a network and establish that the separation principle holds under certain conditions on the MAC. We arrive at a classification of random access methods for networked control systems and identify a structure for each method. Then, by evaluating the increase in cost compared to a conventional setup, we identify an adaptive random access method which uses a threshold-based decision criteria on the current data to determine channel access. Finally, we give stability criteria for control applications using these medium access methods.

Stability analysis of multiple state-based schedulers with CSMA

In this paper, we identify sufficient conditions for Lyapunov Mean Square Stability (LMSS) of a contention-based network of first-order systems, with state-based schedulers. The stability analysis helps us to choose policies for adapting the scheduler threshold to the delay from the network and scheduler. We show that three scheduling laws can result in LMSS: constant-probability laws and additively increasing or decreasing probability laws. Our results counter the notions that increasing probability scheduling laws alone can guarantee stability of the closed-loop system, or that decreasing probability scheduling laws are required to mitigate congestion in the network.

Network Estimation and Packet Delivery Prediction for Control over Wireless Mesh Networks

Much of the current theory of networked control systems uses simple point-to-point communication models as an abstraction of the underlying network. As a result, the controller has very limited inf ...

Separated Design of Encoder and Controller for Networked Linear Quadratic Optimal Control

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising of a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. We consider three basic formats for encoder outputs: quantized samples, real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop system. We also show that this separated design need not be optimal when the controller or encoder are to be chosen from within restricted classes.

TrACS: transceiver architecture and wireless channel simulator

This paper presents the design of a system-level simulator for radio receivers, including receiver circuits, in Matlab. The system level outlook offers a better characterization of circuit design, as the signal processing in the digital receiver is asymmetric across topologies. Also, circuit models in the simulator make it more precise and realistic compared to baseband models, which assume a single-step error-free down conversion. This interpretation is especially relevant in the design of energy-constrained wireless sensor network solutions. The simulator results for binary FSK in AWGN confirm the importance of system level simulation.

Reducing packet loss bursts in a wireless mesh network for stochastic bounds on estimation error

A big challenge for wireless networked control systems is how to design the underlying networking algorithms and protocols to provide high reliability, defined as the end-to-end probability of packet delivery, despite the high packet loss rates of individual wireless links. This paper formulates the problem of jointly designing a set of packet forwarding policies on a multipath mesh network to meet control application requirements. We derive several results to help understand the problem space. First, we demonstrate that some common approaches, like applying a single forwarding policy to all packets or always routing packets on disjoint paths, are not optimal for the application when the links are bursty. Second, we introduce the notion of dominance to give a partial ordering to sets of forwarding policies, used to prove that an optimal policy schedules all outgoing links at each node and that an upper bound on the performance attained by unicast forwarding policies on the network graph can be computed assuming a flooding policy. Third, we demonstrate how to convert application performance metrics to packet forwarding policy objectives, using the probability that the error covariance of a Kalman filter stays within a bound as our application metric. Fourth, we provide an algorithm to compute the joint probability mass function that a sequence of packets are delivered, given a set of policies and a network graph. Finally, we describe how to obtain optimal policies via an exhaustive search, motivating future research for more computationally efficient solutions.