1. B. DasGupta, J.P. Hespanha, J. Riehl, and E.D. Sontag. Honey-pot constrained searching with local sensory information. Nonlinear Analysis, 65:1773-1793, 2006. [PDF] Keyword(s): search problems, algorithms, computational complexity. Abstract:

   This paper investigates the problem of searching for a hidden target in a bounded region of the plane by an autonomous robot which is only able to use limited local sensory information. It proposes an aggregation-based approach to solve this problem, in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem and a solution to the original problem is obtained through a refinement procedure that lifts the discrete path into a continuous one. The resulting solution is in general not optimal but one can construct bounds to gauge the cost penalty incurred. The discrete version is formalized and an optimization problem is stated as a `reward-collecting' bounded-length path problem. NP-completeness and efficient approximation algorithms for various cases of this problem are discussed.




2. J.P. Hespanha, D. Liberzon, D. Angeli, and E.D. Sontag. Nonlinear norm-observability notions and stability of switched systems. IEEE Trans. Automat. Control, 50(2):154-168, 2005. [PDF] Keyword(s): observability, input to state stability, observability, invariance principle. Abstract:

   This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.

1. B. DasGupta, J.P. Hespanha, and E.D. Sontag. Aggregation-based approaches to honey-pot searching with local sensory information. In Proceedings American Control Conf., Boston, June 2004, 2004. Note: (CD-ROM WeM17.4, IEEE Publications, Piscataway). [PDF] Abstract:

   We investigate the problem of searching for a hidden target in a bounded region by an autonomous agent that is only able to use limited local sensory information. We propose an aggregation-based approach to solve this problem, in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem. A solution to the original problem is then obtained through a refinement procedure that lifts the discrete path into a continuous one. The resulting solution is in general not optimal but one can construct bounds to gauge the cost penalty incurred.




2. B. DasGupta, J.P. Hespanha, and E.D. Sontag. Computational complexities of honey-pot searching with local sensory information. In Proceedings American Control Conf., Boston, June 2004, CD-ROM, ThA06.1, IEEE Publications, Piscataway, 2004. [PDF] Abstract:

   In this paper we investigate the problem of searching for a hidden target in a bounded region of the plane, by an autonomous robot which is only able to use limited local sensory information. We formalize a discrete version of the problem as a "reward-collecting" path problem and provide efficient approximation algorithms for various cases.




3. J.P. Hespanha, D. Liberzon, and E.D. Sontag. Nonlinear observability and an invariance principle for switched systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 4300-4305, 2002. [PDF] Keyword(s): observability.

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