Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Hide-and-Seek with Directional Sensing

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level.Comment: A short version of this paper (without proofs) will be presented at the 18th IFAC World Congress (IFAC 2011), Milan (Italy), August 28-September 2, 201

Estimation over Communication Networks: Performance Bounds and Achievability Results

This paper considers the problem of estimation over communication networks. Suppose a sensor is taking measurements of a dynamic process. However the process needs to be estimated at a remote location connected to the sensor through a network of communication links that drop packets stochastically. We provide a framework for computing the optimal performance in the sense of expected error covariance. Using this framework we characterize the dependency of the performance on the topology of the network and the packet dropping process. For independent and memoryless packet dropping processes we find the steady-state error for some classes of networks and obtain lower and upper bounds for the performance of a general network. Finally we find a necessary and sufficient condition for the stability of the estimate error covariance for general networks with spatially correlated and Markov type dropping process. This interesting condition has a max-cut interpretation

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

Event-triggered control cannot improve the ℓ2\ell_2 gain of h∞h_\infty optimal periodic control and transmit at a smaller average rate

We consider a standard discrete-time event-triggered control setting by which a scheduler collocated with the plant's sensors decides when to transmit sensor data to a remote controller collocated with the plant's actuators. When the scheduler transmits periodically with period larger than or equal to one, the $h_\infty$ optimal controller guarantees an optimal attenuation bound ($\ell_2$ gain) from any square-summable disturbance input to a plant's output. We show that, under mild assumptions, there does not exist a controller and scheduler pair that strictly improves the optimal attenuation bound of periodic control with a smaller average transmission rate. Equivalently, given any controller and scheduler pair, there exists a square-summable disturbance such that either the attenuation bound or the average transmission rate are larger than or equal to those of optimal periodic control

Optimal sampling schedules for h2h_2 and h∞h_\infty state-feedback control

We consider a discrete-time linear system for which the control input is updated at every sampling time, but the state is measured at a slower rate. We allow the state to be sampled according to a periodic schedule, which dictates when the state should be sampled along a period. Given a desired average sampling interval, our goal is to determine sampling schedules that are optimal in the sense that they minimize the $h_2$ or the $h_\infty$ closed-loop norm, under an optimal state-feedback control law. Our results show that, when the desired average sampling interval is an integer, the optimal state sampling turns out to be evenly spaced. This result indicates that, for the $h_2$ and $h_\infty$ performance metrics, there is relatively little benefit to go beyond constant-period sampling