Stable Nonlinear Identification From Noisy Repeated Experiments via Convex Optimization

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small set of repeated experiments with suitably independent measurement noise is available. Stability of the estimated models is guaranteed without any assumptions on the input-output data. We first present a convex optimization scheme for identifying stable state-space models from empirical moments. Next, we provide a method for using repeated experiments to remove the effect of noise on these moment and model estimates. The technique is demonstrated on a simple simulated example

Constraint and Restoring Force

Long-lived sensor network applications must be able to self-repair and adapt to changing demands. We introduce a new approach for doing so: Constraint and Restoring Force. CRF is a physics-inspired framework for computing scalar fields across a sensor network with occasional changes. We illustrate CRFs usefulness by applying it to gradients, a common building block for sensor network systems. The resulting algorithm, CRF-Gradient, determines locally when to self-repair and when to stop and save energy. CRF-Gradient is self-stabilizing, converges in O(diameter) time, and has been verified experimentally in simulation and on a network of Mica2 motes. Finally we show how CRF can be applied to other algorithms as well, such as the calculation of probability fields

Convex Optimization In Identification Of Stable Non-Linear State Space Models

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron.Comment: 9 pages, 2 figure, elaboration of same-title paper in 49th IEEE Conference on Decision and Contro

Nonlinear filtering for narrow-band time delay estimation

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 101-103).This thesis presents a method for improving passive acoustic tracking. A large family of acoustic tracking systems combine estimates of the time difference of arrival (TDoA) between pairs of spatially separated sensors - this work improves those estimates by independently tracking each TDoA using a Bayesian filter. This tracking is particularly useful for overcoming spatial aliasing, which results from tracking narrowband, high frequency sources. I develop a theoretical model for the evolution of each TDoA from a bound placed on the velocity of the target being tracked. This model enables an efficient form of exact marginalization. I then present simulation and experimental results demonstrating improved performance over a simpler nonlinear preprocessor and Kalman filtering, so long as this bound is chosen appropriately.by Mark M. Tobenkin.M.Eng

Fast Self-Healing Gradients

We present CRF-Gradient, a self-healing gradient algorithm that provably reconfigures in O(diameter) time. Self-healing gradients are a frequently used building block for distributed self-healing systems, but previous algorithms either have a healing rate limited by the shortest link in the network or must rebuild invalid regions from scratch. We have verified CRF-Gradient in simulation and on a network of Mica2 motes. Our approach can also be generalized and applied to create other self-healing calculations, such as cumulative probability fields

Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures

In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS. In contrast to traditional Lyapunov based approaches, which are non-convex and require feasible initialization, our approach is convex and does not require any form of initialization. The resulting time-varying controllers and approximated backwards reachable sets are well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on four nonlinear systems.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051)National Science Foundation (U.S.) (Contract IIS-1161679)Thomas and Stacey Siebel Foundatio