Ladislav Král

Performance analysis of derivative-free filters

Nonlinear state estimation by the derivative-free Sigma Point Kalman Filters is treated. Particularly, impact of the derivative-free Kalman filters on estimation quality of the Sigma Point Gaussian Sum Filters is discussed. New relations between the Unscented Kalman Filter and the Divided Difference Filters are derived. The main stress is laid on the covariance matrixes which have crucial role for the behaviour explanation of the Sigma Point Gaussian Sum Filters. The theoretical results are illustrated in some numerical examples.

NEURAL NETWORK BASED BICRITERIAL DUAL CONTROL OF NONLINEAR SYSTEMS

Abstract A bicriterial dual controller for nonlinear stochastic systems is suggested. Two separate criterions are designed and used to introduce one of opposing aspects between estimation and control; caution and probing. A system is modelled using a multilayer perceptron network. Parameters of the network are estimated by the Gaussian sum method which allows to determine conditional probability density functions of the network weights. The proposed approach is compared with inovation dual control and the quality of the estimator and the regulator is analyzed by simulation and Monte Carlo analysis.

Identification of nonlinear non-gaussian systems by neural networks

Abstract Application of neural networks in identification of non linear nonGaussian systems is treated. Stress is laid on a parameter estimation of the networks. They are trained by the Gaussian sum method which is a global filtering method allowing to determine conditional probability density functions of network weights. Proposed approach to estimation of network weights (parameters) based on Gaussian sum filtering method overcomes commonly used prediction error methods and it is an interesting alternative to sequential Monte Carlo methods. The considered training approach is demonstrated by an illustration example.

Functional Adaptive Control for Multi-Input Multi-Output Systems

A functional adaptive control for nonlinear stochastic systems with Multi-Input Multi-Output is suggested. The systems are modelled using a multilayer perceptron networks. Parameters of the model are estimated by the Gaussian sum method which allows to determine conditional probability density functions of the network weights. Control design is based on bicriterial dual approach that use two separate criterions to introduce one of opposing aspects between estimation and control; caution and probing. The proposed approach is compared with two adaptive non-dual controllers. The quality of the proposed functional adaptive controller is illustrated in a numerical example.

Predictive dual control for nonlinear stochastic systems modelled by neural networks

A predictive dual control for a nonlinear system with functional uncertainty based on the bicriterial approach is proposed and discussed. The nonlinear functions of the system are approximated by multi-layered perceptron neural networks where the unknown parameters are found in real time without a necessity of any off-line training process. These nonlinear predictors based on the affine structure in inputs together with the certainty equivalence principle utilization allow to obtain an analytical solution to the predictive control. Behavior of the system based on the certainty equivalence assumption can negatively be affected, especially in a presence of disturbances and functional uncertainties. For that, the obtained predictive control is enhanced about dual property based on the bicriterial approach that uses two separate criteria to introduce one of the opposing aspects between estimation and control. The quality of the proposed predictive dual controller is illustrated in a numerical example.

Dual adaptive control for non-minimum phase systems with functional uncertainties

Abstract A dual control for a nonlinear system with non-minimum phase based on the bicriterial approach is proposed and discussed. A particular class of the nonlinear input/output recursive model is composed of linear and nonlinear blocks, the latter being implemented with a multi-layered perceptron neural network. The unknown parameters of the model are estimated in real-time by the extended Kalman filter. The chosen nonlinear model with the affine structure in inputs together with the certainty equivalence principle utilization allow to obtain an analytical solution to control based on generalised minimum variance method. Behaviour of the system based on the enforcement of the certainty equivalence can negatively be affected, especially in a presence of disturbances and functional uncertainties. For that, the control action is enhanced about dual property based on the bicriterial approach that uses two separate criteria to introduce one of the opposing aspects between estimation and control.

Gaussian process based dual adaptive control of nonlinear stochastic systems

The paper proposes a suboptimal adaptive control for a nonlinear stochastic system subject to functional uncertainty. The problem of a real-time identification of the unknown nonlinear system is tackled by using the Gaussian process based non-parametric model. The covariance function of the Gaussian process is chosen in such a way that allows deriving the control law in a closed form. The control action stems from the bicriterial dual approach that uses two separate criteria to introduce both of the mutually opposing aspects between estimation and control. Properties of the novel dual controller are tested and validated in a numerical example by Monte Carlo analysis.

Neural Network Based Bicriterial Dual Control with Multiple Linearization

Abstract A suboptimal dual controller for discrete nonlinear stochastic systems based on the bicriterial approach is proposed and discussed.Two individual criteria are designed and used to introduce one of the conflicting efforts between estimation and control; caution and probing. parametersof the network are estimated by a global estimation method, the Gaussian sum method (GSM), which allows to determine conditional probability density function (pdf) of the NNs parameters.The GSM in association with an idea of multiple linearization is chosen and utilized in the bicriterial dual control (BDC) approach. The probing component of the control law is determined for each local mode of estimated pdf separately and respects accuracy of each local estimate inherent in the estimated pdf.A comparison of the proposed modified BDC and the BDC which uses a global point estimate only is shown inanumerical example.

Functional Adaptive Control for Nonlinear Stochastic Systems in Presence of Outliers

Abstract This paper presents an enhancement of a functional adaptive control of nonlinear stochastic systems that renders it to be robust with respect to the occurrence of outliers in the plant measured output. Outliers are considered to be large deviations of a signal being measured, only occurring in a few percent of the observations. Therefore, although rare, the outliers cause poor parameter estimates and, consequently, heavily degrade control performance due to their large amplitude. A system is modelled using a multi-layer perceptron network and the measurement noise is modelled by a mixture of Gaussian distributions. One component of the mixture describes uncorrupted process data, while the others describe various types of outliers. Parameters of the network together with output prediction of the uncorrupted data component are estimated by an estimation method based on the mixture of Gaussian distributions. Control design is based on a bicriterial dual approach. The advantages of the proposed controller are illustrated in an example by simulation and Monte Carlo analysis.

Functional Dual Adaptive Control with Recursive Gaussian Process Model

The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded.