The Experts below are selected from a list of 258 Experts worldwide ranked by ideXlab platform
K. J. Adebayo - One of the best experts on this subject based on the ideXlab platform.
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On Application of a Control Operator to ECGM Algorithm for Solving Discrete-Time Linear Control Systems with Delay-II
Applied mathematical sciences, 2016Co-Authors: R. B. Ogunride, K. J. AdebayoAbstract:In this paper, we constructed a Control Operator sequel to an earlier constructed Control Operator in one of our papers which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving discrete time linear quadratic regulator problems with delay parameter in the state variable. The construction of the Control Operator places scalar linear delay problems of the type within the class of problems that can be solved with the ECGM and it is aimed at reducing the rigours faced in using the classical methods in solving this of class of problem. More so, the authors of this paper desire that the application of this Control Operator will further improve the results of the ECGM as well as increasing the variant approaches used in solving the said class of optimal Control problem.
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Numerical experiment with the construction of a Control Operator applied in ECGM algorithm
American Journal of Applied Mathematics, 2015Co-Authors: F. M. Aderibigbe, B. Ojo, K. J. AdebayoAbstract:In this paper, we constructed a Control Operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal Control and trajectories of continuous time linear regulator problems. Similar Operators constructed in the past by various authors have limited application. This call for the construction of the Control Operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the Operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal Control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the Operator.
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On Construction of A Control Operator Applied To Conjugate Gradient Method in Solving Continuous Time Linear Regulator Problems with Delay-I
IOSR Journal of Mathematics, 2014Co-Authors: F. M. Aderibigbe, K. J. AdebayoAbstract:In this paper, we constructed a Control Operator, G, which enables a Conjugate Gradient Method (CGM) to be employed in solving continuous time linear regulator problems with delay parameter in the state variable. The Control Operator takes care of any of Mayer's, Lagrange's and Bolza's cost form of linear regulator problems. It is the desire of the authors of this paper that the application of this Control Operator will further improve on the result of the Conjugate Gradient Method in solving this class of optimal Control problem.
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On Construction of a Control Operator Applied In ECGM Algorithm
IOSR Journal of Mathematics, 2014Co-Authors: F. M. Aderibigbe, K. J. Adebayo, B. OjoAbstract:In this paper, we constructed a Control Operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal Control and trajectories of continuous time linear regulator problems. Similar Operators constructed in the past by various authors have limited application. This call for the construction of the Control Operator that is aimed at taking care of any of the Mayer's, Lagrange's and Bolza's cost form of linear regulator problems. The authors of this paper desire that, with the construction of the Operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal Control problem.
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On Construction of A Control Operator Introduced To ECGM Algorithm for Solving Discrete-Time Linear Quadratic Regulator Control Systems with Delay-I
IOSR Journal of Mathematics, 2014Co-Authors: K. J. Adebayo, F. M. AderibigbeAbstract:In this paper, we constructed a Control Operator sequel to an earlier constructed Control Operator in one of our papers which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving discrete time linear quadratic regulator problems with delay parameter in the state variable. The construction of the Control Operator places scalar linear delay problems of the type within the class of problems that can be solved with the ECGM and it is aimed at reducing the rigours faced in using the classical methods in solving this class of problem. More so, the authors of this paper desire that, the application of this Control Operator will further improve the results of the ECGM as well as increasing the variant approaches used in solving the said class of optimal Control problem.
F. M. Aderibigbe - One of the best experts on this subject based on the ideXlab platform.
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Numerical experiment with the construction of a Control Operator applied in ECGM algorithm
American Journal of Applied Mathematics, 2015Co-Authors: F. M. Aderibigbe, B. Ojo, K. J. AdebayoAbstract:In this paper, we constructed a Control Operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal Control and trajectories of continuous time linear regulator problems. Similar Operators constructed in the past by various authors have limited application. This call for the construction of the Control Operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the Operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal Control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the Operator.
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On Construction of A Control Operator Applied To Conjugate Gradient Method in Solving Continuous Time Linear Regulator Problems with Delay-I
IOSR Journal of Mathematics, 2014Co-Authors: F. M. Aderibigbe, K. J. AdebayoAbstract:In this paper, we constructed a Control Operator, G, which enables a Conjugate Gradient Method (CGM) to be employed in solving continuous time linear regulator problems with delay parameter in the state variable. The Control Operator takes care of any of Mayer's, Lagrange's and Bolza's cost form of linear regulator problems. It is the desire of the authors of this paper that the application of this Control Operator will further improve on the result of the Conjugate Gradient Method in solving this class of optimal Control problem.
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On Construction of a Control Operator Applied In ECGM Algorithm
IOSR Journal of Mathematics, 2014Co-Authors: F. M. Aderibigbe, K. J. Adebayo, B. OjoAbstract:In this paper, we constructed a Control Operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal Control and trajectories of continuous time linear regulator problems. Similar Operators constructed in the past by various authors have limited application. This call for the construction of the Control Operator that is aimed at taking care of any of the Mayer's, Lagrange's and Bolza's cost form of linear regulator problems. The authors of this paper desire that, with the construction of the Operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal Control problem.
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On Construction of A Control Operator Introduced To ECGM Algorithm for Solving Discrete-Time Linear Quadratic Regulator Control Systems with Delay-I
IOSR Journal of Mathematics, 2014Co-Authors: K. J. Adebayo, F. M. AderibigbeAbstract:In this paper, we constructed a Control Operator sequel to an earlier constructed Control Operator in one of our papers which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving discrete time linear quadratic regulator problems with delay parameter in the state variable. The construction of the Control Operator places scalar linear delay problems of the type within the class of problems that can be solved with the ECGM and it is aimed at reducing the rigours faced in using the classical methods in solving this class of problem. More so, the authors of this paper desire that, the application of this Control Operator will further improve the results of the ECGM as well as increasing the variant approaches used in solving the said class of optimal Control problem.
Emmanuel Trélat - One of the best experts on this subject based on the ideXlab platform.
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Characterization by observability inequalities of Controllability and stabilization properties
Pure and Applied Analysis, 2020Co-Authors: Emmanuel Trélat, Gengsheng WangAbstract:Given a linear Control system in a Hilbert space with a bounded Control Operator, we establish a characterization of exponential stabilizability in terms of an observability inequality. Such dual characterizations are well known for exact (null) Controllability. Our approach exploits classical Fenchel duality arguments and, in turn, leads to characterizations in terms of observability inequalities of approximately null Controllability and of α-null Controllability. We comment on the relationships between those various concepts, at the light of the observability inequalities that characterize them.
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Optimal location of Controllers for the one-dimensional wave equation
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 2013Co-Authors: Yannick Privat, Emmanuel Trélat, Enrique ZuazuaAbstract:In this paper, we consider the homogeneous one-dimensional wave equation defined on $(0,\pi)$. For every subset $\omega\subset [0,\pi]$ of positive measure, every $T \geq 2\pi$, and all initial data, there exists a unique Control of minimal norm in $L^2(0,T;L^2(\omega))$ steering the system exactly to zero. In this article we consider two optimal design problems. Let $L\in(0,1)$. The first problem is to determine the optimal shape and position of $\omega$ in order to minimize the norm of the Control for given initial data, over all possible measurable subsets $\omega$ of $[0,\pi]$ of Lebesgue measure $L\pi$. The second problem is to minimize the norm of the Control Operator, over all such subsets. Considering a relaxed version of these optimal design problems, we show and characterize the emergence of different phenomena for the first problem depending on the choice of the initial data: existence of optimal sets having a finite or an infinite number of connected components, or nonexistence of an optimal set (relaxation phenomenon). The second problem does not admit any optimal solution except for $L=1/2$. Moreover, we provide an interpretation of these problems in terms of a classical optimal Control problem for an infinite number of Controlled ordinary differential equations. This new interpretation permits in turn to study modal approximations of the two problems and leads to new numerical algorithms. Their efficiency will be exhibited by several experiments and simulations.
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Uniform Controllability of semidiscrete approximations of parabolic Control systems
Systems and Control Letters, 2006Co-Authors: Stéphane Labbé, Emmanuel TrélatAbstract:Controlling an approximation model of a Controllable infinite dimensional linear Control system does not necessarily yield a good approximation of the Control needed for the continuous model. In the present paper, under the main assumptions that the discretized semigroup is uniformly analytic, and that the Control Operator is mildly unbounded, we prove that the semidiscrete approximation models are uniformly Controllable. Moreover, we provide a computationally efficient way to compute the approximation Controls. An example of application is implemented for the one- and two-dimensional heat equation with Neumann boundary Control.
Ahmet Ozkan Ozer - One of the best experts on this subject based on the ideXlab platform.
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Stabilization Results for Well-Posed Potential Formulations of a Current-Controlled Piezoelectric Beam and Their Approximations
Applied Mathematics & Optimization, 2020Co-Authors: Ahmet Ozkan OzerAbstract:Hysteresis is highly undesired for the vibration Control of piezoelectric beams especially in high-precision applications. Current-Controlled piezoelectric beams cope with hysteresis substantially in comparison to the voltage-Controlled counterparts. However, the existing low fidelity current-Controlled beam models are finite dimensional, and they are either heuristic or mathematically over-simplified differential equations. In this paper, novel infinite-dimensional models, by a thorough variational approach, are introduced to describe vibrations on a piezoelectric beam. Electro-magnetic effects due to Maxwell’s equations factor in the models via the electric and magnetic potentials. Both models are written in the standard state-space formulation ( A , B , C ), and are shown to be well-posed in the energy space by fixing the so-called Coulomb and Lorenz gauges. Different from the voltage-actuated counterparts, the Control Operator B is compact in the energy space, i.e. the exponential stabilizability is not possible. Considering the compact $$C=B^*-$$ C = B ∗ - type state feedback Controller (induced voltage), both models fail to be asymptotically stable if the material parameters satisfy certain conditions. To achieve at least asymptotic stability, we propose an additional Controller. Finally, the stabilizability of infinite-dimensional electrostatic/quasi-static model (no magnetic effects) is analyzed for comparison. The biggest contrast is that the asymptotic stability is achieved by an electro-mechanical state feedback Controller for all material parameters. Our findings are simulated by the filtered semi-discrete Finite Difference Method.
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ACC - Semigroup well-posedness of a voltage Controlled active constrained layered (ACL) beam with magnetic effects
2016 American Control Conference (ACC), 2016Co-Authors: Ahmet Ozkan OzerAbstract:The layered smart composites involving a piezoelectric layer are traditionally activated by a voltage source, and the magnetic effects are totally ignored since these effects are relatively smaller in comparison to electrical and mechanical effects. However, recent results for even a single piezoelectric beam show that ignoring these effects may cause unControllable and unstabilizable systems. In this paper, a variational approach is used to derive a voltage-Controlled Rao-Nakra type active constrained layer model. All magnetic effects due to the full set of Maxwell's equations are included. It is shown that the proposed model can be put into the semigroup formulation, i.e. ẋ = Ax + Bu; and is well-posed in the corresponding energy space. Moreover, the observed quantity due to the observation Operator B* (corresponding to the Control Operator B with the voltage Control) is totally electrical.
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Modeling and related results for current-actuated piezoelectric beams by including magnetic effects
arXiv: Analysis of PDEs, 2016Co-Authors: K Morris, Ahmet Ozkan OzerAbstract:Piezo-electric material can be Controlled with current as the electrical variable, instead of voltage. The main purpose of this paper is to derive the governing equations for a current-Controlled piezo-electric beam and to investigate stabilizability. Besides the consideration of current Control, there are several new aspects to the model here. Most significantly, magnetic effects are included. For the electromagnetic part of the model, electrical potential and magnetic vector potential are chosen to be quadratic-through thickness to include the induced effects of the electromagnetic field. Two sets of decoupled system of partial differential equations are obtained; one for stretching motion and another one for bending motion. Hamilton's principle is used to derive a boundary value problem that models a single piezo-electric beam actuated by a charge (or current) source at the electrodes. Current or charge Controllers at the electrodes can only Control the stretching motion. Attention is therefore focused on Control of the stretching equations in this paper. It is shown that the Lagrangian of the beam is invariant under certain transformations. A Coulomb-type gauge condition which is widely used in the electromagnetic theory is used here. This gauge condition decouples the electrical potential equation from the equations of the magnetic potential. A semigroup approach is used to prove that the Cauchy problem is well-posed. Unlike the voltage or charge actuation, a bounded Control Operator in the natural energy space is obtained in the current actuation case. The paper concludes with analysis of stabilizability and comparison with other actuation approaches and models.
George Weiss - One of the best experts on this subject based on the ideXlab platform.
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Well-posedness, regularity and exact Controllability of the SCOLE model
Mathematics of Control Signals and Systems, 2010Co-Authors: Xiaowei Zhao, George WeissAbstract:The SCOLE model is a coupled system consisting of a flexible beam (modelled as an Euler–Bernoulli equation) with one end clamped and the other end linked to a rigid body. Its inputs are the force and the torque acting on the rigid body. It is well-known that the SCOLE model is not exactly Controllable with L ^2 input signals in the natural energy state space H ^ c , because the Control Operator is bounded from the input space $${\mathbb{C}^2}$$ to H ^ c , and hence compact. We regard the velocity and the angular velocity of the rigid body as the output signals of this system. Using the theory of coupled linear systems (one infinite-dimensional and one finite-dimensional) developed by us recently in another paper, we show that the SCOLE model is well-posed, regular and exactly Controllable in arbitrarily short time when using a certain smoother state space $${\mathcal{X}\subset H^c}$$ .
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The Operator Carleson measure criterion for admissibility of Control Operators for diagonal semigroups on 1 2
Systems & Control Letters, 1991Co-Authors: Scott W. Hansen, George WeissAbstract:Abstract Suppose a Control system is described by a diagonal semigroup on the state space l 2 and by an unbounded Control Operator B defined on the input space l 2 . We formulate a condition called the Operator Carleson measure criterion, and show that this condition is necessary for the admissibility of B . If the semigroup is analytic or invertible, then the condition is sufficient as well. Our results extend the ones of Ho, Russell and Weiss concerning the case where the input space is one dimensional.
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Two conjectures on the admissibility of Control Operators
International Series of Numerical Mathematics Internationale Schriftenreihe zur Numerischen Mathematik Série Internationale d’Analyse Numérique, 1991Co-Authors: George WeissAbstract:We are searching for necessary and/or sufficient conditions for the admissibility of unbounded Control Operators for semigroups on Hilbert spaces, with respect to input functions of class L 2. Our first conjecture is that admissibility of an unbounded input element 6 for a semigroup with generator A is equivalent to a certain decay rate of ∥(sI - A)-1 b∥ as Re s → ∞. The second conjecture states that a Control Operator B defined on a Hilbert space U is admissible if and only if, for any v ∈ U, Bv is an admissible input element. It is proved that both conjectures hold in many important particular cases (e.g., the first conjecture is true if the semigroup is normal).