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Efficient nonlinear predictive control based on structured neural models

Maciej Ławryńczuk (2009)

International Journal of Applied Mathematics and Computer Science

This paper describes structured neural models and a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm based on such models. The structured neural model has the ability to make future predictions of the process without being used recursively. Thanks to the nature of the model, the prediction error is not propagated. This is particularly important in the case of noise and underparameterisation. Structured models have much better long-range prediction accuracy...

Efficient numerical algorithms for balanced stochastic truncation

Peter Benner, Enrique Quintana-Ortí, Gregorio Quintana-Ortí (2001)

International Journal of Applied Mathematics and Computer Science

We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation of...

Ensemble neural network approach for accurate load forecasting in a power system

Krzysztof Siwek, Stanisław Osowski, Ryszard Szupiluk (2009)

International Journal of Applied Mathematics and Computer Science

The paper presents an improved method for 1-24 hours load forecasting in the power system, integrating and combining different neural forecasting results by an ensemble system. We will integrate the results of partial predictions made by three solutions, out of which one relies on a multilayer perceptron and two others on self-organizing networks of the competitive type. As the expert system we will apply different integration methods: simple averaging, SVD based weighted averaging, principal component...

Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form

Przemysław Orłowski (2007)

International Journal of Applied Mathematics and Computer Science

Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems...

Extension of first order Predictive Functional Controllers to handle higher order internal models

Mohamed Tarek Khadir, John V. Ringwood (2008)

International Journal of Applied Mathematics and Computer Science

Predictive Functional Control (PFC), belonging to the family of predictive control techniques, has been demonstrated as a powerful algorithm for controlling process plants. The input/output PFC formulation has been a particularly attractive paradigm for industrial processes, with a combination of simplicity and effectiveness. Though its use of a lag plus delay ARX/ARMAX model is justified in many applications, there exists a range of process types which may present difficulties, leading to chattering...

Fault tolerant control for uncertain time-delay systems based on sliding mode control

Jun Sheng Wu, Zhengxin Weng, Zuo Hua Tian, Song Jiao Shi (2008)

Kybernetika

Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some linear matrix inequalities (LMIs), delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can...

Fault tolerant control using Gaussian processes and model predictive control

Xiaoke Yang, Jan M. Maciejowski (2015)

International Journal of Applied Mathematics and Computer Science

Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably...

Finite horizon nonlinear predictive control by the Taylor approximation application to robot tracking trajectory

Ramdane Hedjar, Redouane Toumi, Patrick Boucher, Didier Dumur (2005)

International Journal of Applied Mathematics and Computer Science

In industrial control systems, practical interest is driven by the fact that today's processes need to be operated under tighter performance specifications. Often these demands can only be met when process nonlinearities are explicitly considered in the controller. Nonlinear predictive control, the extension of well-established linear predictive control to nonlinear systems, appears to be a well-suited approach for this kind of problems. In this paper, an optimal nonlinear predictive control structure,...

Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions

Antonios Armaou, Panagiotis Christofides (2001)

International Journal of Applied Mathematics and Computer Science

This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initial conditions and input perturbations) ensemble of solutions of the resulting time-varying PDE system is...

Genetic algorithm based method of elimination of residual oscillation in mechatronic systems

Peter Hubinský, Ladislav Jurišica, Branislav Vranka (2005)

Kybernetika

The paper presents control signals generation methods, preventing the excitation of residual vibration in slightly damped oscillational systems. It is focused on the feedforward methods, as most of the vibrations in examined processes are induced by the control, while the influence of disturbances is mostly negligible. Application of these methods involves ensuring of the insensitivity to natural frequency change, which can be reached in classical approach only by considerable increase of transient...

Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

Nathalie Verdiere, Lilianne Denis-Vidal, Ghislaine Joly-Blanchard, Dominique Domurado (2005)

International Journal of Applied Mathematics and Computer Science

The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it...

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