Abstract: Publication date: December 2018Source: Automatica, Volume 98Author(s): Marco F. Huber, Marc-André Zöller, Marcus BaumAbstractMany technical systems like manufacturing plants or software applications generate large event sequences. Knowing the temporal relationship between events is important for gaining insights into the status and behavior of the system. This paper proposes a novel approach for identifying the time lag between different event types. This identification task is formulated as a binary integer optimization problem that can be solved efficiently and close to optimality by means of a linear programming approximation. The performance of the proposed approach is demonstrated on synthetic and real-world event sequences.

Abstract: Publication date: Available online 14 September 2018Source: AutomaticaAuthor(s): Dilshad Raihan, Suman ChakravortyAbstractIn this paper, we propose a particle based Gaussian mixture filtering approach for nonlinear estimation that is free of the particle depletion problem inherent to most particle filters. We employ an ensemble of possible state realizations for the propagation of state probability density. A Gaussian mixture model (GMM) of the propagated uncertainty is then recovered by clustering the ensemble. The posterior density is obtained subsequently through a Kalman measurement update of the mixture modes. We prove the convergence in probability of the resultant density to the true filter density assuming exponential forgetting of initial conditions. The performance of the proposed filtering approach is demonstrated through several test cases and is extensively compared to other nonlinear filters.

Abstract: Publication date: December 2018Source: Automatica, Volume 98Author(s): Yuan Zhou, Hesuan Hu, Yang Liu, Shang-Wei Lin, Zuohua DingAbstractMotion planning of multi-robot systems has been extensively investigated. Many proposed approaches assume that all robots are reliable. However, robots with priori known levels of reliability may be used in applications to account for: (1) the cost in terms of unit price per robot type, and (2) the cost in terms of robot wear in long term deployment. In the former case, higher reliability comes at a higher price, while in the latter replacement may cost more than periodic repairs, e.g., buses, trams, and subways. In this study, we investigate robust control of multi-robot systems, such that the number of robots affected by the failed ones is minimized. It should mandate that the failure of a robot can only affect the motion of robots that collide directly with the failed one. We assume that the robots in a system are divided into reliable and unreliable ones, and each robot has a predetermined and closed path to execute persistent tasks. By modeling each robot’s motion as a labeled transition system, we propose two distributed robust control algorithms: one for reliable robots and the other for unreliable ones. The algorithms guarantee that wherever an unreliable robot fails, only the robots whose state spaces contain the failed state are blocked. Theoretical analysis shows that the proposed algorithms are practically operative. Simulations with seven robots are carried out and the results show the effectiveness of our algorithms.

Abstract: Publication date: Available online 13 September 2018Source: AutomaticaAuthor(s): Dilshad Raihan, Suman ChakravortyAbstractIn our previous work, we proposed a particle Gaussian mixture (PGM-I) filter for nonlinear estimation. The PGM-I filter uses the transition kernel of the state Markov chain to sample from the propagated prior. It constructs a Gaussian mixture representation of the propagated prior density by clustering the samples. The measurement data are incorporated by updating individual mixture modes using the Kalman measurement update. However, the Kalman measurement update is inexact when the measurement function is nonlinear and leads to the restrictive assumption that the number of modes remains fixed during the measurement update. In this paper, we introduce an alternate PGM-II filter that employs parallelized Markov Chain Monte Carlo (MCMC) sampling to perform the measurement update. The PGM-II filter update is asymptotically exact and does not enforce any assumptions on the number of Gaussian modes. The PGM-II filter is employed in the estimation of two test case systems. The results indicate that the PGM-II filter is suitable for handling nonlinear/non-Gaussian measurement update.

Abstract: Publication date: November 2018Source: Automatica, Volume 97Author(s): Ai-Guo Wu, Hui-Jie Sun, Ying ZhangAbstractA novel implicit iterative algorithm is presented via successive over relaxation (SOR) iterations in this paper for solving the coupled Lyapunov matrix equation related to continuous-time Markovian jump linear systems. This algorithm contains a relaxation parameter, which can be appropriately chosen to improve the convergence performance of the algorithm. It has been shown that the sequence generated by the proposed algorithm with zero initial conditions monotonically converges to the unique positive definite solution of the considered equation. Moreover, some convergence results of the presented SOR implicit iterative algorithm with arbitrary initial conditions are established, and a method to choose the optimal relaxation parameter for this algorithm is given. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithm.

Abstract: Publication date: November 2018Source: Automatica, Volume 97Author(s): Kun Lin, Cheng Jie, Steven I. MarcusAbstractHistorically, the study of risk-sensitive criteria has focused on their normative applications — i.e., what should be done. The classic example is expected utility functions which produce deterministic policies. More recently, the literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. However, coherent risk measures must be convex. This paper presents an alternative to both the expected utility and coherent risk measure approaches. This new approach, inspired by cumulative prospect theory (CPT), is nonconvex and has substantial empirical evidence supporting its descriptive power for human decisions, i.e., what is actually done. A key unique feature of the CPT-based approach, essential for modeling human decisions, is probabilistic distortion. Hence, CPT should be used instead of both expected utility and coherent risk measures when modeling human decisions, which requires a higher level of expressiveness than allowed by previous work. In addition, although both coherent risk measures and CPT produce randomized policies, which are more robust against inaccurate probabilistic descriptions of systems, CPT generates policies that are significantly different from those of coherent risk measures.

Abstract: Publication date: November 2018Source: Automatica, Volume 97Author(s): Saptarshi Bandyopadhyay, Soon-Jo ChungAbstractThe discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent’s estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.

Abstract: Publication date: November 2018Source: Automatica, Volume 97Author(s): Nilanjan Roy Chowdhury, Srikant Sukumar, Debasish ChatterjeeAbstractWe investigate asymptotic consensus of linear systems under a class of switching communication graphs. We significantly relax several reciprocity and connectivity assumptions prevalent in the consensus literature by employing switched-systems techniques to establish consensus. Our results rely solely on asymptotic properties of the switching communication graphs in contrast to classical average dwell-time conditions. A bound on the uniform rate of convergence to consensus is also established as part of this work.