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Nonlinear analysis of vehicle control actuations based on controlled invariant sets

Balázs Németh, Péter Gáspár, Tamás Péni (2016)

International Journal of Applied Mathematics and Computer Science

In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant...

Nonlinear model predictive control of a boiler unit: A fault tolerant control study

Krzysztof Patan, Józef Korbicz (2012)

International Journal of Applied Mathematics and Computer Science

This paper deals with a nonlinear model predictive control designed for a boiler unit. The predictive controller is realized by means of a recurrent neural network which acts as a one-step ahead predictor. Then, based on the neural predictor, the control law is derived solving an optimization problem. Fault tolerant properties of the proposed control system are also investigated. A set of eight faulty scenarios is prepared to verify the quality of the fault tolerant control. Based of different faulty...

Nonlinear predictive control based on neural multi-models

Maciej Ławryńczuk, Piotr Tatjewski (2010)

International Journal of Applied Mathematics and Computer Science

This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to...

Novel fault detection criteria based on linear quadratic control performances

Dušan Krokavec, Anna Filasová (2012)

International Journal of Applied Mathematics and Computer Science

This paper proposes a new approach to designing a relatively simple algorithmic fault detection system that is potentially applicable in embedded diagnostic structures. The method blends the LQ control principle with checking and evaluating unavoidable degradation in the sequence of discrete-time LQ control performance index values due to faults in actuators, sensors or system dynamics. Design conditions are derived, and direct computational forms of the algorithms are given. A simulation example...

NTGsim: a graphical user interface and a 3D simulator for nonlinear trajectory generation methodology

Lyall Jonathan Di Trapani, Tamer Inanc (2010)

International Journal of Applied Mathematics and Computer Science

Nonlinear Trajectory Generation (NTG), developed by Mark Milam, is a software algorithm used to generate trajectories of constrained nonlinear systems in real-time. The goal of this paper is to present an approach to make NTG more userfriendly. To accomplish this, we have programmed a Graphical User Interface (GUI) in Java, using object oriented design, which wraps the NTG software and allows the user to quickly and efficiently alter the parameters of NTG. This new program, called NTGsim, eliminates...

Numerical analysis and systems theory

Stephen Campbell (2001)

International Journal of Applied Mathematics and Computer Science

The area of numerical analysis interacts with the area of control and systems theory in a number of ways, some of which are widely recognized and some of which are not fully appreciated or understood. This paper will briefly discuss some of these areas of interaction and place the papers in this volume in context.

Numerical controllability of the wave equation through primal methods and Carleman estimates

Nicolae Cîndea, Enrique Fernández-Cara, Arnaud Münch (2013)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null...

Numerical operations among rational matrices: standard techniques and interpolation

Petr Hušek, Michael Šebek, Jan Štecha (1999)

Kybernetika

Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the...

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