An approximate solution to optimal Lp state estimation problems

نویسندگان

  • A. Alessandri
  • M. Sanguineti
چکیده

We consider optimal estimation problems characterized by a state vector with i) dynamics described via a differential equation with Lipschitz nonlinearities, ii) partial information provided via a Lipschitz nonlinear mapping, and iii) an Lp norm measure of the estimation error to be minimized. An approximate solution of such optimal estimation problem is searched for by restricting the optimization to parameterized nonlinear approximators such as feedforward neural networks. The parameters of a feedforward neural network are the neural weights. This approach entails a constrained nonlinear programming problem, whose constraints are given by the dynamic and measurement equations, and the conditions guaranteeing the stability of the estimation error. To optimize the parameters values of neural networks an algorithm is developed that is based on appropriate sampling of the state and error spaces. Choices of the sample points are devised based on the notion of dispersion, which allow one to obtain an approximate solution of the optimal estimation problem by a small sample complexity.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Optimal Estimation Problems for Nonlinear Systems and Their Approximate Solution

An approach based on optimization is described to construct state estimators that provide a stable dynamics of the estimation error and minimize a Lp measure of the estimation error. The state estimator depends on an innovation function made up of two terms: a linear gain and a feedforward neural network. The gain and the weights of the neural network can be chosen in such way to ensure the con...

متن کامل

Solution of Fractional Optimal Control Problems with Noise Function Using the Bernstein Functions

This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method‎. ‎The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions‎. ‎By substituting these estimated functions into the cost functional‎, ‎an unconstrained nonlinear optimizat...

متن کامل

Approximate Pareto Optimal Solutions of Multi objective Optimal Control Problems by Evolutionary Algorithms

In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced‎. ‎In this approach‎, ‎first a discretized form of the time-control space is considered and then‎, ‎a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...

متن کامل

LP problems constrained with D-FRIs

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of ...

متن کامل

Numerical solution of optimal control problems by using a new second kind Chebyshev wavelet

The main purpose of this paper is to propose a new numerical method for solving the optimal control problems based on state parameterization. Here, the boundary conditions and the performance index are first converted into an algebraic equation or in other words into an optimization problem. In this case, state variables will be approximated by a new hybrid technique based on new second kind Ch...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005