اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStable Nonlinear Identification From Noisy Repeated Experiments via Convex Optimization
170
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the robust identification error framework in which a convex
upper bound on simulation error is optimized to fit rational polynomial models with a strong stability guarantee. In this work, we relax the stability constraint using the concepts of transverse dynamics and orbital stability, thus allowing systems with autonomous oscillations to be identified. The resulting optimization problem is convex, and can be formulated as a semidefinite program. A simulation-error bound is proved without assuming that the true system is in the model class, or that the number of measurements goes to infinity. Conditions which guarantee existence of a unique limit cycle of the model are proved and related to the model class that we search over. The method is illustrated by identifying a high-fidelity model from experimental recordings of a live rat hippocampal neuron in culture.
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state
estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an off-line search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of detectable nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in the paper. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical and biochemical systems.
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.
We propose a framework to use Nesterovs accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously differentiable ex
act penalty function. This reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem by Lagrange multiplier functions. The expressions of these Lagrange multiplier functions, which depend upon the gradients of the objective function and the constraints, can make the unconstrained penalty function non-convex in general even if the original problem is convex. We establish sufficient conditions on the objective function and the constraints of the original problem under which the unconstrained penalty function is convex. This enables us to use Nesterovs accelerated gradient method for unconstrained convex optimization and achieve a guaranteed rate of convergence which is better than the state-of-the-art first-order algorithms for constrained convex optimization. Simulations illustrate our results.
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 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 five nonlinear systems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
