We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design. 1

abstract: Overload management policies avoid network congestion by actively dropping packets. This paper studies the effect that such data dropouts have on the performance of spatially distributed control systems. We formally relate the spatially-distributed system’s performance (as measured by the average output signal power) to the data dropout rate. This relationship is used to pose an optimization problem whose solution is a Markov chain characterizing a dropout process that maximizes control system performance subject to a specified lower bound on the dropout rate. We then use this Markov chain to formulate an overload management policy that enables nodes to enforce the ”optimal ” dropout process identified in our optimization problem. Simulation experiments are used to verify the paper’s claims. 1

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 LQG controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network mentioned above. 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 more commonly used 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. I.

In this paper, we consider a discrete-time stochastic system, where sensor measurements are sent over a network to the controller. The design objective is a non-classical multicriterion optimization problem for finite horizon, where the cost function consists of the linear quadratic cost reflecting the control performance and a communication cost penalizing information exchange between sensor and controller. It is shown that the joint optimization of scheduling and control can be separated into three subproblems: an optimal regulator problem, an estimation problem and an optimal scheduling problem. The obtained results are extended to TCP-like networks with random packet loss. In the proposed framework, we classify three classes of schedulers, a purely randomized, a deterministic and a state-dependent scheme, and compare their performance by a numerical example.

Abstract: The stability and performance of a networked control system (NCS) strongly depends on the transmission delay. However, the randomness of the transmission delay is an intrinsic property in the network communication, e.g. Ethernet. Aiming at NCS with random transmission delay, a novel control approach is proposed. The transmission delays from sensorto-controller (SC) and controller-to-actuator (CA) are modelled by two independent Markovian processes. A controller, which is able to monitor the SC delay and synchronously switches according to it, is considered. The resulting closed-loop system is a Markovian jump linear system with randomly piecewise continuous delay. The exponential mean square stability for the given model is established by using a Lyapunov-Krasovskii functional. The performance benefits of the proposed approach are demonstrated in a numerical example. 1.

It is well known that the stability and performance of a networked control system (NCS) are strongly affected by the transmission delay, which is usually random in communication networks such as Ethernet. In order to cope with the random transmission delay and increase the control performance, a novel switching control approach for NCS is proposed. The random transmission delay is modelled by a Markov process. A controller able to monitor the transmission delay and synchronously switches with the delay is considered. The resulting closed-loop system is a Markovian jump linear system (MJLS) with time-varying random delay. In this paper a delaydependent stability condition for stochastic exponential mean square stability is derived by using a Lyapunov-Krasovskii functional. The controller design algorithm for a switching controller is proposed. Experiments with the 3 degree-of-freedom (DoF) robotic manipulator ViSHaRD3 validate the proposed approach. A benchmark non-switching approach with buffering strategy at the controller side is implemented for comparison. The experimental results demonstrate significant performance improvements by the proposed switching control approach.

iii To my parents, my brother, and my dear wife Acknowledgements iv First of all, I would like to express my heartfelt gratitude to my advisor, Prof. Richard M. Murray, for his guidance that is so conducive to the work I have undertaken. His broad knowledge, deep insights, outstanding leadership, and great personality make him a mentor that every student dreams of having. I am grateful to my committee members: Prof. John C. Doyle, Prof. Joel W. Burdick, Prof. Babak Hassibi, and Prof. Tracey Ho, for inspiring discussions and detailed comments on my thesis. I also appreciate the help from Prof. Michelle Effros, Prof. Leonard Schulman and Prof. Steven Low. There are many other people I would like to acknowledge with thankfulness for the help given to me in the last five years. Thanks to Dr. Alcherio Martinoli for the unforgettable support during my first year at Caltech. Thanks to Dr. Reza Olfati-Saber for showing me his wonderful work on coordinated control. Thanks to Dr. Eric Klavins, Dr. Lars Cremean, David van Gogh, and Steve Waydo for helping me conduct experiments on the testbed. Also, thanks to Vijay Gupta, Ling Shi, Abhishek Tiwari, and other group members for collaborations and brainstorming. Because of them, my research became much easier and more fruitful. Also thanks to staff members at Caltech for making my administrative life easy.

Abstract — It is well known that the stability and performance of a networked control system (NCS) are strongly affected by the transmission delay, which is usually random in communication networks such as Ethernet. In order to cope with the random transmission delay and increase the control performance, a novel switching control approach for NCS is proposed. The random transmission delay is modelled by a Markov process. A controller, which is able to monitor the transmission delay and synchronously switches with the delay, is considered. The resulting closed-loop system is a Markovian jump linear system (MJLS) with random delay. In this paper a delay-dependent stability condition for stochastic exponential mean square stability is derived by using a Lyapunov-Krasovskii functional. The controller design algorithm for a switching controller is proposed. Experiments with the 3 degree-of-freedom (DoF) robotic manipulator ViSHaRD3 1 show the validity of the proposed approach. An alternative nonswitching approach with buffering strategy at the controller side is considered. The experimental comparison with the nonswitching counterpart indicates performance benefits for the proposed switching control approach. I.

Abstract — The communication quality has a strong effect on the stability and control performance of a networked control system (NCS). To achieve superior control performance, better communication quality is desired. However, high network cost is induced. This paper aims at finding an optimal trade-off between control performance and network cost. A Quality-of-Service (QoS) communication network is introduced, where the statistical properties of the transmission delay can be controlled by adjusting its transition generator. The QoS concept enables a conjoint control of communication network and control system itself, which results in a Markovian jump linear system (MJLS) with mode-dependent delays. A delay-dependent stability condition ensuring stochastic mean-square stability is derived by using the Lyapunov-Krasovskii functional. A guaranteed cost of state evolutions is determined and the perturbation upper bound on Markov process transition generator is obtained. A performance-cost trade-off is achieved by optimizing the Markov process transition generator within the perturbation upper bound. The performance benefit of the proposed control concept is demonstrated in a numerical example. I.

This paper deals with the design of control systems over communication channels that stochastically drop packets. To deal with the data loss in the channel between the controller and the actuator, the use of actuation buffers and a receding horizon control strategy is proposed for the Linear Quadratic Control (LQG) problem. Optimal control inputs are designed via a separation principle and the stability and performance is analyzed. The theoretical results are illustrated with the help of simulations that show the improvement in overall performance as the actuator buffer length is increased. 1