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Number of results: 27
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Abstract

This research presents a 3D FE method for the simulation of the variable reluctance stepper motor dynamics. The proposed model is used to obtain the optimal minimum energy control law that minimizes the energy injected by the controller. The method is based on the strong coupling of field - circuit equations and extended to eddy current, motion and nonlinearity problem. The linearization technique for the coupled problem is presented. Also the lamination of the motor core is considered. In the paper the open - loop control problem is analyzed. The proposed model is validated by the comparison with measurements. Next, to demonstrate the effectiveness of the proposed optimal minimum energy control method is applied. In both cases, the examination of the variable reluctance stepper motor dynamics and the steel loss in the core is presented and compared.

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Authors and Affiliations

Jakub Bernat
Jakub Kołota
Sławomir Stępień
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Abstract

This article presents the time optimal control system adopted to control double winding VCM motor. This kind of control is widely used in hard disk drive servo for head positioning. Mathematical model of double winding VCM motor is presented, and its implementation in MATLAB/Simulink is shown. The extended time optimal control algorithm is implemented on dSpace DS1104 board. The results obtained from simulation and real measurements are compared and discussed.

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Authors and Affiliations

Wojciech Kołton
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Abstract

This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.

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Authors and Affiliations

A. Świerniak
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Abstract

The paper concerns development of original method of optimal control at energy performance index and its application to dynamic processes surveillance of some mechatronic systems. The latter concerns chatter vibration surveillance during highspeed slender milling of rigid details, as well as motion control of two-wheeled mobile platform. Results of on-line computer simulations and real performance on the target objects reflect a great efficiency of the processes surveillance.

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Authors and Affiliations

Krzysztof Kaliński
Marek Galewski
Michał Mazur
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Abstract

The paper reports on investigation and development of a flywheel device intended for an energy storage prototype. The goal was to design and experimentally verify the concept of self-integrated flywheel with smart control of energy flow and accumulation. The Flywheel Energy Storage System (FESS) must has high energy efficiency and structural robustness. Investigation on structural dynamics of the composite flywheel connected with outer type rotor was carried out using Finite Element Method. The FESS is designed to run in vacuum and is supported on low-energy, controlled, active magnetic bearings (AMBs). The flywheel device of 10 MJ energy density and a weight of 150 kg with two integrated rotors/generators of 50 kW power density each is intended to operate up to 40 000 rpm.

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Authors and Affiliations

Arkadiusz Mystkowski
Artur Rowiński
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Abstract

We consider in this work a class of finite dimensional time-varying linear disturbed systems. The main objective of this work is to studied the optimal control which ensures the remediability of a disturbance of time-varying disturbed systems. The remediability concept consist to find a convenient control which bringing back the corresponding observation of disturbed system to the normal one at the final time. We give firstly some characterisations of compensation and in second party we find a control which annul the output of the system and we show also that the Hilbert Uniqueness Method can be used to solve the optimal control which ensure the remediability.Ageneral approachwas given to minimize the linear quadratic problem. Examples and numerical simulations are given.
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Authors and Affiliations

El Mostafa Magri
1
Chadi Amissi
1
Larbi Afifi
1
Mustapha Lhous
1

  1. Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P.5366-Maârif, Casablanca, Morocco
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Abstract

Current drive control systems tend to push control loops to the limits of their performance. One of the ways of doing so is to use advanced optimization algorithms, usually related to model-based off-line calculations, such as genetic algorithms, the particle swarmoptimisation or the others. There is, however, a simpler way, namely to use predictive control formalism and by formulation of a simple linear programming problem which is easy to solve using powerful solvers, without excessive computational burden, what is a reliable solution, as whenever the optimization problem has a feasible solution, a global minimizer can be efficiently found. This approach has been deployed for a servo drive system operated by a real-time sampled-data controller, verified between model-in-the-loop and hardwarein- the-loop configurations, for a range of prediction horizons, as an attractive alternative to classical quadratic programming-related formulation of predictive control task.
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Authors and Affiliations

Dariusz Horla
1
ORCID: ORCID
Piotr Pinczewski
2

  1. Institute of Robotics and Machine Intelligence, Poznan University of Technology, Piotrowo 3a Str., 60-965 Poznan, Poland
  2. IT.integro sp. z o.o. Zabkowicka 12 Str., 60-166 Poznan, Poland
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Abstract

The human environment consists of a large variety of mechanical and biomechanical systems in which different types of contact can occur. In this work, we consider a monopedal jumper modelled as a three-dimensional rigid multibody system with contact and simulate its dynamics using a structure preserving method. The applied mechanical integrator is based on a constrained version of the Lagrange-d’Alembert principle. The resulting variational integrator preserves the symplecticity and momentum maps of the multibody dynamics. To ensure the structure preservation and the geometric correctness, we solve the non-smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non-smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a constrained optimisation problem, see [14].

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Authors and Affiliations

Michael W. Koch
Sigrid Leyendecker
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Abstract

A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
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Bibliography

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[2] K.J. Arrow: Applications of control theory of economic growth. Mathematics of Decision Sciences, 2, AMS, 1968.
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[4] R. Bellmann: Adaptive control processes: a guided tour. Princeton Univ. Press: Princeton, 1972.
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[6] R. Brocket: Lie algebras and Lie groups in control theory. In: Mayne D.Q., Brockett R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series (Series C – Mathematical and Physical Sciences), vol. 3. Springer, Dordrecht, 1973, 43–82, DOI: 10.1007/978-94-010-2675-8_2.
[7] M. Caputo: Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications. Cambridge Univ. Press, 2005, DOI: 10.1017/CBO9780511806827.
[8] M. Danahe, A. Chelbi, and N. Rezg: Optimal production plan for a multiproducts manufacturing system with production rate dependent failure rate. International Journal of Production Research, 50(13), (2012), 3517–3528, DOI: 10.1080/00207543.2012.671585.
[9] G. Feichtinger and R. Hartl: Optimal pricing and production in an inventory model. European Journal of Operational Research, 19 (1985), 45–56, DOI: 10.1016/0377-2217(85)90307-8.
[10] C. Gaimon: Simultaneous and dynamic price, production, inventory and capacity decisions. European Journal of Operational Research, 35 (1988), 426–441.
[11] J.P. Gayon, S. Vercraene, and S.D. Flapper: Optimal control of a production-inventory system with product returns and two disposal options. European Journal of Operational Research, 262(2), (2017), 499–508, DOI: 10.1016/j.ejor.2017.03.018.
[12] C. Hermosilla, R. Vinter, and H. Zidani: Hamilton–Jacobi–Bellman equations for optimal control processes with convex state constraints. Systems & Control Letters, 109 (2017), 30–36, DOI: 10.1016/j.sysconle.2017.09.004.
[13] V. Jurdjevic: Geometric Control Theory. Cambridge Studies in Advanced Mathematics, 52, Cambridge Univ. Press, 1997, DOI: 10.1017/CBO9780511530036.
[14] M.I. Kamien and N.L. Schwartz: Dynamic optimization: The Calculus of Variations and Optimal Control in Economics and Management, 31 Elsevier, 1991.
[15] K. Kogan and E. Khmelnitsky: An optimal control model for continuous time production and setup scheduling. International Journal of Production Research, 34(3), (1996), 715–725.
[16] Y. Qiu, J. Qiao, and P. Pardalos: Optimal production, replenishment, delivery, routing and inventory management policies for products with perishable inventory. Omega-International Journal of Management Science, 82 (2019), 193–204, DOI: 10.1016/j.omega.2018.01.006.
[17] S.M. LaValle: Planning Algorithms. Cambridge University Press, 2006.
[18] M. Li and Z. Wang: An integrated replenishment and production control policy under inventory inaccuracy and time-delay. Computers&Operations Research, 88 (2017), 137–149, DOI: 10.1016/j.cor.2017.06.014.
[19] B. Li and A. Arreola-Risa: Optimizing a production-inventory system under a cost target. Computers&Operations Research, 123 (2020), 105015, DOI: 10.1016/j.cor.2020.105015.
[20] M. Ortega and L. Lin: Control theory applications to the productioninventory problem: a review. International Journal of Production Research, 42(11), (2004), 2303–2322, DOI: 10.1080/00207540410001666260.
[21] V. Pando and J. Sicilia: A new approach to maximize the profit/cost ratio in a stock-dependent demand inventory model. Computers & Operations Research, 120 (2020), 104940, DOI: 10.1016/j.cor.2020.104940.
[22] L. Popescu: Applications of driftles control affine sytems to a problem of inventory and production. Studies in Informatics and Control, 28(1), (2019), 25–34, DOI: 10.24846/v28i1y201903.
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[24] L. Popescu, D. Militaru, and O. Mituca: Optimal control applications in the study of production management. International Journal of Computers, Communications & Control, 15(2), (2020), 3859, DOI: 10.15837/ijccc.2020.2.3859.
[25] A. Seierstad and K. Sydsater: Optimal Control Theory with Economic Applications. North-Holland, Amsterdam, NL, 1987.
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[27] S.P. Sethi and G.L.Thompson: Optimal Control Theory: Applications to Management Science and Economics. Springer, New York, 2000.
[28] J.D. Schwartz and D.E. Rivera: A process control approach to tactical inventory management in production-inventory systems. International Journal of Production Economics, 125(1), (2010), 111–124, DOI: 10.1016/j.ijpe.2010.01.011.
[29] D.R. Towill, G.N. Evans, and P. Cheema: Analysis and design of an adaptive minimum reasonable inventory control system. Production Planning & Control, 8(6), (1997), 545–557, DOI: 10.1080/095372897234885.
[30] T.A. Weber, Optimal control theory with applications in economics. MIT Press, 2011.
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Authors and Affiliations

Liviu Popescu
1
Ramona Dimitrov
1

  1. University of Craiova, Faculty of Economics and Business Administration, Department of Statistics and Economic Informatics, Al. I. Cuza st., No. 13, Craiova 200585, Romania
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Abstract

The problem of optimally controlling a Wiener process until it leaves an interval (a; b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = ��1, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.

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Authors and Affiliations

Mario Lefebvre
Abderrazak Moutassim
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Abstract

This paper addresses the nonlinear Cucker–Smale optimal control problem under the interplay of memory effect. The aforementioned effect is included by employing the Caputo fractional derivative in the equation representing the velocity of agents. Sufficient conditions for the existence of solutions to the considered problem are proved and the analysis of some particular problems is illustrated by two numerical examples.

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Authors and Affiliations

Ricardo Almeida
Rafał Kamocki
Agnieszka B. Malinowska
Tatiana Odzijewicz
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Abstract

The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

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Authors and Affiliations

Zumrud R. Safarova
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Abstract

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre- Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.
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Authors and Affiliations

Shakir Sh. Yusubov
1
Elimhan N. MahmudoV
2 3
ORCID: ORCID

  1. Department of Mechanics and Mathematics, Baku State University, Baku, Azerbaijan
  2. Department of Mathematics, Istanbul Technical University, Istanbul, Turkey
  3. Azerbaijan National Aviation Academy, Baku, Azerbaijan
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Abstract

In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.
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Authors and Affiliations

Rafał Kamocki
1

  1. Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Łódz, Poland
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Abstract

This paper proposes a finite-time horizon suboptimal control strategy based on statedependent Riccati equation (SDRE) to control of F16 multirole aircraft. Flight stabilizer control of super maneuverable aircraft is modelled and simulated. For aircraft modelling purpose a full 6 DOF model is considered and described by nonlinear state-space approach. Also a stable state-dependent parametrization (SDP) necessary for solution of the SDRE control problem is proposed. Solution of the SDRE control problem with adequate defined weighting matrices in performance index shows possibility of fast and optimal aircraft control in finite-time. The method in this form can be used for stabilization of aircraft flight and aerodynamics.
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Authors and Affiliations

Marcin Chodnicki
1
Paweł Pietruszewski
1
Mariusz Wesołowski
1
Sławomir Stępień
2

  1. Air Force Institute of Technology, Ksiecia Bolesława 6, 01-494 Warsaw, Poland
  2. Poznan University of Technology, Institute of Automatic Control and Robotics, Piotrowo 3a, 60-965 Poznan, Poland
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Abstract

The paper introduces Extended Identification-Based Predictive Control (EIPC), which is a novel control method developed for the problem of adaptive impact mitigation. The model-based approach utilizing the paradigm of Model Predictive Control is combined with sequential identification of selected system parameters and process disturbances. The elaborated method is implemented in the shock-absorber control system and tested under impact loading conditions. The presented numerical study proves the successful and efficient adaptation of the absorber to unknown excitation conditions as well as to unknown force and leakage disturbances appearing during the process. The EIPC is used for both semi-active and active control of the impact mitigation process, which are compared in detail. In addition, the influence of selected control parameters and disturbance identification on the efficiency of the impact absorption process is assessed. As a result, it can be concluded that an efficient and robust control method was developed and successfully applied to the problem of adaptive impact mitigation.
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Authors and Affiliations

Cezary Graczykowski
1
ORCID: ORCID
Rami Faraj
1
ORCID: ORCID

  1. Institute of Fundamental Technological Research PAS, Pawi´nskiego 5B, 02-106 Warszawa, Poland
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Abstract

In this paper two different update schemes for the recently developed plug-in direct particle swarm repetitive controller (PDPSRC) are investigated and compared. The proposed approach employs the particle swarm optimizer (PSO) to solve in on-line mode a dynamic optimization problem (DOP) related to the control task in the constant-amplitude constant-frequency voltage-source inverter (CACF VSI) with an LC output filter. The effectiveness of synchronous and asynchronous update rules, both commonly used in static optimization problems (SOPs), is assessed and compared in the case of PDPSRC. The performance of the controller, when synthesized using each of the update schemes, is studied numerically.
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Authors and Affiliations

Bartlomiej Ufnalski
Lech M. Grzesiak
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Abstract

Together with the dynamic development of modern computer systems, the possibilities of applying refined methods of nonparametric estimation to control engineering tasks have grown just as fast. This broad and complex theme is presented in this paper for the case of estimation of density of a random variable distribution. Nonparametric methods allow here the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. Following an illustratory description of the fundamental procedures used to this end, results will be generalized and synthetically presented of research on the application of kernel estimators, dominant here, in problems of Bayes parameter estimation with asymmetrical polynomial loss function, as well as for fault detection in dynamical systems as objects of automatic control, in the scope of detection, diagnosis and prognosis of malfunctions. To this aim the basics of data analysis and exploration tasks - recognition of outliers, clustering and classification - solved using uniform mathematical apparatus based on the kernel estimators methodology were also investigated

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Authors and Affiliations

P. Kulczycki
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Abstract

In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.
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Bibliography

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[4] T. Yuvapriya, P. Lakshmi, and S. Rajendiran: Vibration control and performance analysis of full car active suspension system using fractional order terminal sliding mode controller. Archives of Control Sciences, 30(2), (2020), 295–324, DOI: 10.24425/ACS.2020.133501.
[5] D.S. Naidu: Optimal Control Systems. 1st edition, CRC Press, 2018.
[6] O.P. Agrawal: A general formulation and solution scheme for fractional optimal Control problems. Nonlinear Dynamics, 38(1), (2004), 323–337, DOI: 10.1007/s11071-004-3764-6.
[7] T. Chiranjeevi and R.K. Biswas: Formulation of optimal control problems of fractional dynamic systems with control constraints. Journal of Advanced Research in Dynamical and Control Systems, 10(3), (2018), 201–212.
[8] R.K. Biswas and S. Sen: Fractional optimal control problems with specified final time. Journal of Computational and Nonlinear Dynamics, 6(021009), (2010), DOI: 10.1115/1.4002508.
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[10] R.K. Biswas and S. Sen: Numerical method for solving fractional optimal control problems. In: Proceedings of the ASME IDETC/CIE Conference, (2010), 1205–120, DOI: 10.1115/DETC2009-87008.
[11] C. Tricaud and Y. Chen: An approximate method for numerically solving fractional order optimal control problems of general form. Computers & Mathematics with Applications, 59(5), (2010), 1644–1655, DOI: 10.1016/j.camwa.2009.08.006.
[12] Y. Ding, Z. Wang, and H. Ye: Optimal control of a fractional-order HIVimmune system with memory. IEEE Transactions on Control Systems Technology, 20(3), (2012), 763–769, DOI: 10.1109/TCST.2011.2153203.
[13] T. Chiranjeevi and R.K. Biswas: Closed-form solution of optimal control problem of a fractional order system. Journal of King Saud University – Science, 31(4), (2019), 1042–1047, DOI: 10.1016/j.jksus.2019.02.010.
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[17] M. Gomoyunov: Optimal control problems with a fixed terminal time in linear fractional-order systems. Archives of Control Sciences, 30(2), (2019), 295–324, DOI: 10.24425/acs.2020.135849.
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[20] T. Chiranjeevi, R.K. Biswas, and N.R. Babu: Effect of initialization on optimal control problem of fractional order discrete-time system. Journal of Interdisciplinary Mathematics, 23(1), (2020), 293–302, DOI: 10.1080/09720502.2020.1721924.
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[26] R.K. Biswas and S. Sen: Fractional optimal control within Caputo’s derivative. In: Proceedings of the ASME IDETC/CIE Conference, (2012), 353– 360, DOI: 10.1115/DETC2011-48045.
[27] T. Chiranjeevi, R.K. Biswas, and C. Sethi: Optimal control of fractional order singular system. The International Journal of Electrical Engineering & Education, p. 0020720919833031, (2019), DOI: 10.1177/0020720919833031.
[28] T. Chiranjeevi and R.K. Biswas: Numerical approach to the fractional optimal control problem of continuous-time singular system. In: Advances in Electrical Control and Signal Systems, Singapore, (2020), 239–248, DOI: 10.1007/978-981-15-5262-5_16.
[29] T. Chiranjeevi and R.K. Biswas: Linear quadratic optimal control problem of fractional order continuous-time singular system. Procedia Computer Science, 171 (2020), 1261–1268, DOI: 10.1016/j.procs.2020.04.134.
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[32] Muhafzan, A. Nazra, L. Yulianti, Zulakmal, and R. Revina: On LQ optimization problem subject to fractional order irregular singular systems. Archives of Control Sciences, 30(4), (2020), 745–756, DOI: 10.24425/acs.2020.135850.
[33] T. Chiranjeevi and R.K. Biswas: Computational method based on reflection operator for solving a class of fractional optimal control problem. Procedia Computer Science, 171 (2020), 2030–2039, DOI: 10.1016/j.procs.2020.04.218.
[34] T. Chiranjeevi and R.K. Biswas: Numerical simulation of fractional order optimal control problem. Journal of Statistics and Management Systems, 23(6), (2020), 1069–1077, DOI: 10.1080/09720510.2020.1800188.
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Authors and Affiliations

Tirumalasetty Chiranjeevi
1
Raj Kumar Biswas
2
Ramesh Devarapalli
3
ORCID: ORCID
Naladi Ram Babu
2
Fausto Pedro García Márquez
4

  1. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India
  2. Department of Electrical Engineering, National Institute of Technology, Silchar, India
  3. Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India
  4. Ingenium Research Group, University of Castilla-La Mancha, Spain
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Abstract

In this paper, model reference output feedback tracking control of an aircraft subject to additive, uncertain, nonlinear disturbances is considered. In order to present the design steps in a clear fashion: first, the aircraft dynamics is temporarily assumed as known with all the states of the system available. Then a feedback linearizing controller minimizing a performance index while only requiring the output measurements of the system is proposed. As the aircraft dynamics is uncertain and only the output is available, the proposed controller makes use of a novel uncertainty estimator. The stability of the closed loop system and global asymptotic tracking of the proposed method are ensured via Lyapunov based arguments, asymptotic convergence of the controller to an optimal controller is also established. Numerical simulations are presented in order to demonstrate the feasibility and performance of the proposed control strategy.
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Authors and Affiliations

Ilker Tanyer
1
Enver Tatlicioglu
2
Erkan Zergeroglu
3

  1. Gezgini Inc., Folkart Towers, BBuilding, Floor: 36, Office: 3608, Izmir, 35580, Turkey
  2. Department of Electrical and Electronics Engineering, Ege University, Izmir, 35100, Turkey
  3. Department of Computer Engineering, Gebze Technical University, Kocaeli, 41400, Turkey
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Abstract

Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in theNeumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
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Authors and Affiliations

Adam Kowalewski
1

  1. AGH University of Science and Technology, Institute of Automatic Control and Robotics, 30-059 Cracow, al. Mickiewicza 30, Poland
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Abstract

The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two terms: the first one evaluates the state of the system at a fixed terminal time, and the second one is an integral evaluation of the control on the whole time interval. In order to solve this problem, we propose to reduce it to some auxiliary optimal control problem in a dynamical system described by a first-order ordinary differential equation. The reduction is based on the representation formula for solutions to linear fractional differential equations and is performed by some linear transformation, which is called the informational image of a position of the original system and can be treated as a special prediction of a motion of this system at the terminal time. A connection between the original and auxiliary problems is established for both open-loop and feedback (closed-loop) controls. The results obtained in the paper are illustrated by examples.

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Authors and Affiliations

Mikhail I. Gomoyunov
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Abstract

In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholes equation can be mapped to one dimensional free Schrödinger equation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system.We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.

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Authors and Affiliations

Archana Tiwari
Debanjana Bhattacharyya
K.C. Pati
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Abstract

This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various �� values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
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Authors and Affiliations

Tirumalasetty Chiranjeevi
1
Ramesh Devarapalli
2
ORCID: ORCID
Naladi Ram Babu
3
Kiran Babu Vakkapatla
4
R. Gowri Sankara Rao
5
Fausto Pedro Garcìa Màrquez
6

  1. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U.P., India
  2. Department of EEE, Lendi Institute of Engineering and Technology, Vizianagaram-535005, India
  3. Department of EEE, Aditya Engineering College, Surampalem, Andhra Pradesh, India
  4. Lingayas Institute of Management and Technology Madalavarigudem, A.P., India
  5. Department of EEE, MVGR College of Engineering Vizianagaram, A.P., India
  6. Ingenium Research Group, University of Castilla-La Mancha, Spain

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