Stochastic Stability of Event-triggered Anytime Control

We investigate control of a non-linear process when communication and processing capabilities are limited. The sensor communicates with a controller node through an erasure channel which introduces i.i.d. packet dropouts. Processor availability for control is random and, at times, insufficient to calculate plant inputs. To make efficient use of communication and processing resources, the sensor only transmits when the plant state lies outside a bounded target set. Control calculations are triggered by the received data. If a plant state measurement is successfully received and while the processor is available for control, the algorithm recursively calculates a sequence of tentative plant inputs, which are stored in a buffer for potential future use. This safeguards for time-steps when the processor is unavailable for control. We derive sufficient conditions on system parameters for stochastic stability of the closed loop and illustrate performance gains through numerical studies.Comment: IEEE Transactions on Automatic Control, under revie

Sequence-based Anytime Control

We present two related anytime algorithms for control of nonlinear systems when the processing resources available are time-varying. The basic idea is to calculate tentative control input sequences for as many time steps into the future as allowed by the available processing resources at every time step. This serves to compensate for the time steps when the processor is not available to perform any control calculations. Using a stochastic Lyapunov function based approach, we analyze the stability of the resulting closed loop system for the cases when the processor availability can be modeled as an independent and identically distributed sequence and via an underlying Markov chain. Numerical simulations indicate that the increase in performance due to the proposed algorithms can be significant.Comment: 14 page

Stability analysis of event-triggered anytime control with multiple control laws

To deal with time-varying processor availability and lossy communication channels in embedded and networked control systems, one can employ an event-triggered sequence-based anytime control (E-SAC) algorithm. The main idea of E-SAC is, when computing resources and measurements are available, to compute a sequence of tentative control inputs and store them in a buffer for potential future use. State-dependent Random-time Drift (SRD) approach is often used to analyse and establish stability properties of such E-SAC algorithms. However, using SRD, the analysis quickly becomes combinatoric and hence difficult to extend to more sophisticated E-SAC. In this technical note, we develop a general model and a new stability analysis for E-SAC based on Markov jump systems. Using the new stability analysis, stochastic stability conditions of existing E-SAC are also recovered. In addition, the proposed technique systematically extends to a more sophisticated E-SAC scheme for which, until now, no analytical expression had been obtained.Comment: Accepted for publication in IEEE Transactions on Automatic Contro

Anytime Control using Input Sequences with Markovian Processor Availability

We study an anytime control algorithm for situations where the processing resources available for control are time-varying in an a priori unknown fashion. Thus, at times, processing resources are insufficient to calculate control inputs. To address this issue, the algorithm calculates sequences of tentative future control inputs whenever possible, which are then buffered for possible future use. We assume that the processor availability is correlated so that the number of control inputs calculated at any time step is described by a Markov chain. Using a Lyapunov function based approach we derive sufficient conditions for stochastic stability of the closed loop.Comment: IEEE Transactions on Automatic Control, to be publishe

Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

Variable Annealing Length and Parallelism in Simulated Annealing

In this paper, we propose: (a) a restart schedule for an adaptive simulated annealer, and (b) parallel simulated annealing, with an adaptive and parameter-free annealing schedule. The foundation of our approach is the Modified Lam annealing schedule, which adaptively controls the temperature parameter to track a theoretically ideal rate of acceptance of neighboring states. A sequential implementation of Modified Lam simulated annealing is almost parameter-free. However, it requires prior knowledge of the annealing length. We eliminate this parameter using restarts, with an exponentially increasing schedule of annealing lengths. We then extend this restart schedule to parallel implementation, executing several Modified Lam simulated annealers in parallel, with varying initial annealing lengths, and our proposed parallel annealing length schedule. To validate our approach, we conduct experiments on an NP-Hard scheduling problem with sequence-dependent setup constraints. We compare our approach to fixed length restarts, both sequentially and in parallel. Our results show that our approach can achieve substantial performance gains, throughout the course of the run, demonstrating our approach to be an effective anytime algorithm.Comment: Tenth International Symposium on Combinatorial Search, pages 2-10. June 201