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Neural network-based MRAC control of dynamic nonlinear systems

Ghania Debbache, Abdelhak Bennia, Noureddine Golea (2006)

International Journal of Applied Mathematics and Computer Science

This paper presents direct model reference adaptive control for a class of nonlinear systems with unknown nonlinearities. The model following conditions are assured by using adaptive neural networks as the nonlinear state feedback controller. Both full state information and observer-based schemes are investigated. All the signals in the closed loop are guaranteed to be bounded and the system state is proven to converge to a small neighborhood of the reference model state. It is also shown that stability...

Nonlinear bounded control for time-delay systems

Germain Garcia, Sophie Tarbouriech (2001)

Kybernetika

A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an e -parameterized family of algebraic Riccati equations or on an e -parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov–Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance...

Nonlinear feedback stabilization of a two-dimensional Burgers equation

Laetitia Thevenet, Jean-Marie Buchot, Jean-Pierre Raymond (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of...

Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise

Viorel Barbu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier − Stokes equations with multiplicative noise. The exact controllability is also discussed.

Observer-based controller design of time-delay systems with an interval time-varying delay

Mai Viet Thuan, Vu Ngoc Phat, Hieu Trinh (2012)

International Journal of Applied Mathematics and Computer Science

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability...

On generalized Popov theory for delay systems

Silviu-Iulian Niculescu, Vlad Ionescu, Dan Ivanescu, Luc Dugard, Jean-Michel Dion (2000)

Kybernetika

This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an ℒ 2 norm bound constraint on disturbance attenuation. Note that the proposed results extend...

On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body

Bao-Zhu Guo, Qiong Zhang (2004)

ESAIM: Control, Optimisation and Calculus of Variations

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body

Bao-Zhu Guo, Qiong Zhang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

On motions with bursting characters for Lagrangian mechanical systems with a scalar control. I. Existence of a wide class of Lagrangian systems capable of motions with bursting characters

Aldo Bressan, Marco Favretti (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note (which will be followed by a second) we consider a Lagrangian system Σ (possibly without any Lagrangian function) referred to N + 1 coordinates q 1 ⁢ ⋯ , q N , u , with u to be used as a control, and precisely to add to Σ a frictionless constraint of the type u = u ⁢ t . Let Σ 's (frictionless) constraints be represented by the manifold V t generally moving in Hertz's space. We also consider an instant d (to be used for certain limit discontinuity-properties), a point q ¯ , u ¯ of V d , a value p ¯ for Σ 's momentum conjugate...

On one algorithm for solving the problem of source function reconstruction

Vyacheslav Maksimov (2010)

International Journal of Applied Mathematics and Computer Science

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations...

On periodic oscillations for a class of feedback control systems in Hilbert spaces

Nguyen Van Loi (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.

On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption

Volodymyr Lynnyk, Sergej Čelikovský (2010)

Kybernetika

In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...

On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi (2016)

Mathematics of Climate and Weather Forecasting

Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...

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