Miguel Hernández-González

Discrete-time filtering for nonlinear polynomial systems over linear observations

This paper designs a discrete-time filter for nonlinear polynomial systems driven by additive white Gaussian noises over linear observations. The solution is obtained by computing the time-update and measurement-update equations for the state estimate and the error covariance matrix. A closed form of this filter is obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and the error covariance. As a particular case, a third-degree polynomial is considered to obtain the finite-dimensional filtering equations. Numerical simulations are performed for a third-degree polynomial system and an induction motor model. Performance of the designed filter is compared with the extended Kalman one to verify its effectiveness.

Joint state and parameter estimation for uncertain stochastic nonlinear polynomial systems

This article presents the joint state filtering and parameter identification problem for uncertain stochastic nonlinear polynomial systems with unknown parameters in the state equation over nonlinear polynomial observations, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The obtained mean-square filter for the extended state vector also serves as the mean-square identifier for the unknown parameters. Performance of the designed mean-square state filter and parameter identifier is verified for both, positive and negative, parameter values.

Mean-square filtering for uncertain linear stochastic systems

This paper presents the mean-square joint filtering and parameter identification problem for uncertain linear stochastic systems with unknown parameters in both, state and observation, equations, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The resulting filtering system is polynomial in state and linear in observations. The obtained mean-square filter for the extended state vector also serves as the mean-square identifier for the unknown parameters. A simulation example is included to show convergence of the designed mean-square state filter and parameter identifier for both, positive and negative, parameter values.

Discrete-time optimal control for stochastic nonlinear polynomial systems

This paper presents a solution to the discrete-time optimal control problem for stochastic nonlinear polynomial systems over linear observations and a quadratic criterion. The solution is obtained in two steps: the optimal control algorithm is developed for nonlinear polynomial systems by considering complete information when generating a control law. Then, the state estimate equations for discrete-time stochastic nonlinear polynomial system over linear observations are employed. The closed-form solution is finally obtained substituting the state estimates into the obtained control law. The designed optimal control algorithm can be applied to both distributed and lumped systems. To show effectiveness of the proposed controller, an illustrative example is presented for a second degree polynomial system. The obtained results are compared to the optimal control for the linearized system.

Discrete-time Neural Network Control for a Linear Induction Motor

This paper presents a discrete-time control for a linear induction motor (LIM). First, an identifier is proposed with a nonlinear block controllable form (NBC) structure. This identifier is based on a discrete-time high order neural network trained on-line with an extended Kalman filter (EKF)-based algorithm. Then, a sliding mode control is used to achieve the purpose of tracking velocity and magnitude flux. The neural control performance is illustrated via simulations.

Optimal Controller for Stochastic Polynomial Systems with State-Dependent Polynomial Input

This paper presents an optimal quadratic-Gaussian controller for stochastic polynomial systems with a state-dependent polynomial control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for polynomial systems with a state-dependent polynomial control input and a quadratic criterion. Performance of the obtained optimal controller is verified in an illustrative example against a conventional linear-quadratic-Gaussian (LQG) controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.

Discrete-time filtering for nonlinear polynomial systems

This paper presents a suboptimal filtering problem solution for a class of discrete-time nonlinear polynomial systems over linear observations. The solution is obtained splitting the whole problem into finding a-priori and a-posteriori equations for state estimates and gain matrices. The closed-form filtering equations for the state estimate and gain matrix are obtained in case of a third-degree polynomial system. Numerical simulations are carried out to show effectiveness of the proposed filter. The obtained filter is compared to the extended Kalman-like filter.

Discrete-time reduced order neural observer for Linear Induction Motors

This paper focusses on a discrete-time reduced order neural observer applied to a Linear Induction Motor (LIM) model, whose model is assumed to be unknown. This neural observer is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF)-based algorithm, using a parallel configuration. Simulation results are included in order to illustrate the applicability of the proposed scheme.

Mean-square joint state and noise intensity estimation for linear stochastic systems

This paper presents the mean-square joint state and diffusion coefficient (noise intensity) estimator for linear stochastic systems with unknown noise intensity over linear observations, where unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. Since the noise intensities cannot be observable in the original linear system, the new quadratic vector variable formed by the diagonal of the matrix square of the system state is introduced. The obtained mean-square filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed mean-square state filter and parameter identifier is verified in an illustrative example.

Real-time discrete neural identifier for a linear induction motor using a dSPACE DS1104 board

This paper presents a real-time discrete nonlinear neural identifier for a Linear Induction Motor (LIM). This identifier is based on a discrete-time recurrent high order neural network (RHONN) trained on-line with an extended Kalman filter (EKF)-based algorithm. A reduced order observer is used to estimate the secondary fluxes. The real-time implementation of the neural identifier is implemented by using dSPACE DS1104 controller board on MATLAB/Simulink with dSPACE RTI library and its performance is shown by graphs.