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  • [ September 27, 2018]

    Continuous Finite- and Fixed-Time High-Order Regulators

  • Speaker:
    Michael Basin
    Thursday, September 27, 2018
    Room 314, Mechanics Building
    Ying Yang
  • Abstract
  • It is well known that a state of a controllable linear system of an arbitrary dimension can be asymptotically driven as close to zero as necessary by means of a linear scalar feedback control. Using a continuous nonlinear scalar control law, a chain of integrators of an arbitrary dimension can be driven to the origin in finite time. Given that an arbitrary minimum phase linear system can be transformed into a chain of integrators form by using an appropriate change of variables, finite-time high-order regulators are applicable to an arbitrary minimum phase multi-dimensional linear system. A relevant problem consists in estimating the convergence (settling) time for the finite-time convergent control laws Another challenging problem is to design a fixed-time continuous control law such that a system state converges to the origin for a pre-established or fixed settling time, independently of a magnitude of initial conditions.

    The contribution of this study is twofold. First, an upper estimate of the convergence (settling) time is calculated for the finite-time convergent control algorithm that drives the state of a series of integrators to the origin. To the best of the authors’ knowledge, such an estimate is obtained for the first time. Second, a novel fixed-time continuous control law is proposed for a chain of integrators of an arbitrary dimension. Its fixed-time convergence is established and the uniform upper bound of the settling time is computed. The theoretical developments are applied to a case study of controlling a DC motor.

    Finally, an extension of the developed approach to design fixed-time observers for integrator chain systems (differentiators) is discussed and compared to a built-in Simulink differentiation technique.
  • Biography
  • Michael V. Basin (SM’07, M’95) received his Ph.D. degree in Physical and Mathematical Sciences with major in Automatic Control and System Analysis from the Moscow Aviation University (MAI) in 1992. He is currently Full Professor with the Autonomous University of Nuevo Leon, Mexico, and Leading Researcher with ITMO University, St. Petersburg, Russia. Starting from 1992, Dr. Basin published more than 300 research papers in international referred journals and conference proceedings. He is the author of the monograph “New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems,” published by Springer.  His works are cited more than 3500 times (h index = 32).  Dr. Basin has supervised 14 doctoral and 7 master's theses. He has served as the Editor-in-Chief and serves as the Co-Editor-in-Chief of Journal of The Franklin Institute, a Technical Editor of IEEE/ASME Transactions on Mechatronics, an Associate Editor of Automatica, IEEE Transactions on Systems, Man and Cybernetics: Systems, IET-Control Theory and Applications, International Journal of Systems Science, Neural Networks. Dr. Basin was awarded a title of Highly Cited Researcher by Thomson Reuters, the publisher of Science Citation Index, in 2009; he is a regular member of the Mexican Academy of Sciences. His research interests include optimal filtering and control problems, stochastic systems, time-delay systems, identification, sliding mode control and variable structure systems.