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Revisiting the LQR Problem of Singular Systems

IEEE/CAA Journal of Automatica Sinica 2024年第11期11卷 2236-2252页

作者： Komeil Nosrati Juri Belikov Aleksei Tepljakov eduard petlenkov IEEE the Department of Computer Systems Tallinn University of Technology the Department of Software Science Tallinn University of Technology

In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attributes are applicable only to transformed singular systems, and the efficiency of the regulator may be undermined if constraints are violated in nonsingular versions. To address this gap, we introduce a direct approach to the LQR problem for linear singular systems, avoiding the need for any transformations and eliminating the need for regularity assumptions. To achieve this goal, we begin by formulating a quadratic cost function to derive the LQR algorithm through a penalized and weighted regression framework and then connect it to a constrained minimization problem using the Bellman's criterion. Then, we employ a dynamic programming strategy in a backward approach within a finite horizon to develop an LQR algorithm for the original system. To accomplish this, we address the stability and convergence analysis under the reachability and observability assumptions of a hypothetical system constructed by the pencil of augmented matrices and connected using the Hamiltonian diagonalization technique.

关键词： DC motor optimal control penalized weighted regression power system quadratic regulator singular system

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Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

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IEEE/CAA Journal of Automatica Sinica 2023年第3期10卷 762-780页

作者： Majid Ghorbani Mahsan Tavakoli-Kakhki Aleksei Tepljakov eduard petlenkov Department of Computer Systems Tallinn University of TechnologyTallinn 12618Estonia Faculty of Electrical Engineering K.N.Toosi University of TechnologyTehran ***Iran IEEE

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this *** uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world ***,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)*** the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time *** three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise ***,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

关键词： Interval uncertainty FOPID controller fractional-order systems robust stability analysis smith predictor

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NN-ANARX Structure for Control of Nonlinear SISO and MIMO Systems: Neural Networks Based Approach

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第二十六届中国控制会议

作者： petlenkov eduard Belikov Juri Tallinn University of Technology Department of Computer control Institute of Cybernetics at Tallinn University of Technology

ISBN: (纸本)7900719229

An application of Neural Networks based Additive Nonlinear Autoregressive Exogenous （NN-ANARX） structure for modeling and control of nonlinear SISO and MIMO systems is presented in the paper.A novel neural network based ap- proach for calculation of control signals by using NN-ANARX based dynamic output linearization algorithm is proposed in the *** effectiveness of the approach proposed in the paper is demonstrated on example

关键词： nonlinear control systems nonlinear MIMO systems ANARX model dynamic output feedback linearization neural networks

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Time-domain identification of One Noninteger Order Plus Time Delay models from step response measurements

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第1期10卷 155-176页

作者： Baris Baykant Alagoz Aleksei Tepljakov Abdullah Ates eduard petlenkov Celaleddin Yeroglu Department of Computer Engineering Inonu University MalatyaTurkey Department of Computer Systems Tallinn University of Technology TallinnEstonia

Practical performances of controller design methods strongly depend on relevancy of identified *** order system models promise advantage of more accurate modeling of real *** study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole(NOPTD-I)*** identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response *** the study,step responses of NOPTD-I models are numerically calculated according to two fundamental methods,which are Mittag-Leffler(ML)function and Grunwald-Letnikov(GL)*** swarm optimization(PSO)algorithm is used to perform data *** examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test *** experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.

关键词： Model identification fractional-order systems Mittag-Leffler(ML)function Grunwald-Letnikov(GL)definition PSO

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