No Arabic abstract
This paper considers a remote state estimation problem with multiple sensors observing a dynamical process, where sensors transmit local state estimates over an independent and identically distributed (i.i.d.) packet dropping channel to a remote estimator. At every discrete time instant, the remote estimator decides whether each sensor should transmit or not, with each sensor transmission incurring a fixed energy cost. The channel is shared such that collisions will occur if more than one sensor transmits at a time. Performance is quantified via an optimization problem that minimizes a convex combination of the expected estimation error covariance at the remote estimator and expected energy usage across the sensors. For transmission schedules dependent only on the estimation error covariance at the remote estimator, this work establishes structural results on the optimal scheduling which show that 1) for unstable systems, if the error covariance is large then a sensor will always be scheduled to transmit, and 2) there is a threshold-type behaviour in switching from one sensor transmitting to another. Specializing to the single sensor case, these structural results demonstrate that a threshold policy (i.e. transmit if the error covariance exceeds a certain threshold and dont transmit otherwise) is optimal. We also consider the situation where sensors transmit measurements instead of state estimates, and establish structural results including the optimality of threshold policies for the single sensor, scalar case. These results provide a theoretical justification for the use of such threshold policies in variance based event triggered estimation. Numerical studies confirm the qualitative behaviour predicted by our structural results. An extension of the structural results to Markovian packet drops is also outlined.
In networked systems, state estimation is hampered by communication limits. Past approaches, which consider scheduling sensors through deterministic event-triggers, reduce communication and maintain estimation quality. However, these approaches destroy the Gaussian property of the state, making it computationally intractable to obtain an exact minimum mean squared error estimate. We propose a stochastic event-triggered sensor schedule for state estimation which preserves the Gaussianity of the system, extending previous results from the single-sensor to the multi-sensor case.
General nonlinear continuous-time systems are considered for which the state is to be estimated via a packet-based communication network. We assume that the system has multiple sensor nodes, affected by measurement noise, which can transmit output data at discrete (non-equidistant) and asynchronous points in time. For this general system setup, we develop a state estimation framework, where the transmission instances of the individual sensor nodes can be generated in both time-triggered and event-triggered fashions. In the latter case, we guarantee the absence of Zeno behavior by construction. It is shown that, under the provided design conditions, an input-to-state stability property is obtained for the estimation error and that the state is thus reconstructed asymptotically in the absence of noise. A numerical case study shows the strengths of the developed framework.
This paper considers the problem of sensory data scheduling of multiple processes. There are $n$ independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which sends its local state estimate to the remote estimator. The sizes of the packets are different due to different dimensions of each process, and thus it may take different lengths of time steps for the sensors to send their data. Because of bandwidth limitation, only a portion of all the sensors are allowed to transmit. Our goal is to minimize the average of estimation error covariance of the whole system at the remote estimator. The problem is formulated as a Markov decision process (MDP) with average cost over an infinite time horizon. We prove the existence of a deterministic and stationary policy for the problem. We also find that the optimal policy has a consistent behavior and threshold type structure. A numerical example is provided to illustrate our main results.
This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of scheduling strategy is to provide significant reductions in the usage of the sensor-to-controller communication and, in turn, improve energy expenditure in the network. In this paper, we aim to design an admissible control policy, which is a function of the observed output, to minimize a quadratic cost function while employing a stochastic event-triggered scheduler that preserves the Gaussian property of the plant state and the estimation error. For the infinite horizon case, we present analytical expressions that quantify the trade-off between the communication cost and control performance of such event-triggered control systems. This trade-off is confirmed quantitatively via numerical examples.
The paper proposes a novel event-triggered control scheme for nonlinear systems based on the input-delay method. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, a cyclic mapping forms from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggering law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. With this idea, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.