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

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

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

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

Robustness analysis for identification and control of nonlinear systems

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.Cataloged from PDF version of thesis.Includes bibliographical references (pages 119-131).This thesis concerns two problems of robustness in the modeling and control of nonlinear dynamical systems. First, I examine the problem of selecting a stable nonlinear state-space model whose open-loop simulations are to match experimental data. I provide a family of techniques for addressing this problem based on minimizing convex upper bounds for simulation error over convex sets of stable nonlinear models. I unify and extend existing convex parameterizations of stable models and convex upper bounds. I then provide a detailed analysis which demonstrates that existing methods based on these principles lead to significantly biased model estimates in the presence of output noise. This thesis contains two algorithmic advances to overcome these difficulties. First, I propose a bias removal algorithm based on techniques from the instrumental-variables literature. Second, for the class of state-affine dynamical models, I introduce a family of tighter convex upper bounds for simulation error which naturally lead to an iterative identification scheme. The performance of this scheme is demonstrated on several benchmark experimental data sets from the system identification literature. The second portion of this thesis addresses robustness analysis for trajectory-tracking feedback control applied to nonlinear systems. I introduce a family of numerical methods for computing regions of finite-time invariance (funnels) around solutions of polynomial differential equations. These methods naturally apply to non-autonomous differential equations that arise in closed-loop trajectory-tracking control. The performance of these techniques is analyzed through simulated examples.by Mark M. Tobenkin.Ph. D