The Experts below are selected from a list of 37404 Experts worldwide ranked by ideXlab platform
J. Klamka - One of the best experts on this subject based on the ideXlab platform.
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CONSTRALNED CON~OLLABILITY OF Semilinear SYSTEMS
2020Co-Authors: J. KlamkaAbstract:In the paper infinite-dimensional dynamical control systems described by Semilinear abstract differential equations are considered. Using a generalized open mapping theorem, sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local controllability of Semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local controllability problem for Semilinear hyperbolic type distributed parameters dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented. Keyd:ords: Controllability. Nonlinear systems. Abstract systeiiis. Constrained controls. Second-order systems.
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Constrained exact controllability of Semilinear systems with delay in control
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004Co-Authors: J. KlamkaAbstract:In the paper infinite-dimensional dynamical control systems with constant point delay in the control described by Semilinear abstract differential equations are considered. Using a generalized open mapping theorem, sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local relative controllability of Semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local relative controllability problem for Semilinear hyperbolic type distributed parameters dynamical system is solved in details.
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Constrained exact controllability of Semilinear systems
Systems & Control Letters, 2002Co-Authors: J. KlamkaAbstract:In the paper infinite-dimensional dynamical control systems described by Semilinear abstract differential equations are considered. Using a generalized open-mapping theorem, sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local controllability of Semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local controllability problem for Semilinear hyperbolic type distributed parameters dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
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Constrained controllability of Semilinear systems
Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002Co-Authors: J. KlamkaAbstract:In the paper infinite-dimensional dynamical control systems described by Semilinear abstract differential equations are considered. Using a generalized open mapping theorem, sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local controllability of Semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local controllability problem for a Semilinear hyperbolic type distributed parameter dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
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Controllability of Semilinear systems with delays in control
IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems Man and Cybernetics (Cat. No.99CH37028), 1999Co-Authors: J. KlamkaAbstract:The relative controllability of a Semilinear infinite delay dynamical system with time varying multiple lumped delays in control and state variables is considered. Using Schauder's fixed point theorem a sufficient condition for relative controllability in a given time interval is formulated and proved. Namely, if the linear part of the system is asymptotically stable and relatively controllable, then the Semilinear system is also relative controllable.
Rohit Patel - One of the best experts on this subject based on the ideXlab platform.
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Controllability results for fractional Semilinear delay control systems
Journal of Applied Mathematics and Computing, 2020Co-Authors: Anurag Shukla, Rohit PatelAbstract:In this article, we have presented the controllability relationship between the Semilinear control system of fractional order (1, 2] with delay and that of the Semilinear control system without delay. Suppose X and U be Hilbert spaces which are separable and $$Z=L_2[0,b;X],\;Z_h=L_2[-h,b;X],\;0\le h\le b$$ Z = L 2 [ 0 , b ; X ] , Z h = L 2 [ - h , b ; X ] , 0 ≤ h ≤ b and $$Y=L_2[0,b;U]$$ Y = L 2 [ 0 , b ; U ] be the function spaces. Let the Semilinear control system of fractional order with delay as $$\begin{aligned} ^CD_\tau ^\alpha z(\tau )= & {} Az(\tau )+Bv(\tau )+g(\tau ,z(\tau -h)),\;0\le \tau \le b;\\ z_0(\theta )= & {} \phi (\theta ),\;\;\;\; \theta \in [-h,0]\\ z'(0)= & {} z_0. \end{aligned}$$ C D τ α z ( τ ) = A z ( τ ) + B v ( τ ) + g ( τ , z ( τ - h ) ) , 0 ≤ τ ≤ b ; z 0 ( θ ) = ϕ ( θ ) , θ ∈ [ - h , 0 ] z ′ ( 0 ) = z 0 . where $$1
Thomas Meurer - One of the best experts on this subject based on the ideXlab platform.
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On the Extended Luenberger-Type Observer for Semilinear Distributed-Parameter Systems
IEEE Transactions on Automatic Control, 2013Co-Authors: Thomas MeurerAbstract:The design of an extended Luenberger observer is considered to solve the state observation problem for Semilinear distributed-parameter systems. For this, a backstepping-based technique is proposed for the design of the output injection weights by making use of the (extended) linearization of the Semilinear observer error system with respect to the observer state. Stability of both the linearized and the Semilinear observer error dynamics is analyzed theoretically. Moreover, an efficient sample-and-hold implementation is considered to improve the computational efficiency of the observer design. Simulation examples are provided for a bistable Semilinear partial differential equation and the simplified model of a bioreactor with Monod kinetics.
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Flatness of Semilinear Parabolic PDEs—A Generalized Cauchy–Kowalevski Approach
IEEE Transactions on Automatic Control, 2013Co-Authors: Birgit Schörkhuber, Thomas Meurer, Ansgar JüngelAbstract:A generalized Cauchy-Kowalevski approach is proposed for flatness-based trajectory planning for boundary controlled Semilinear systems of partial differential equations (PDEs) in a one-dimensional spatial domain. For this, the ansatz presented in “Trajectory planning for boundary controlled parabolic PDEs with varying parameters on higher-dimensional spatial domains” (T. Meurer and A. Kugi, IEEE Trans. Autom. Control, vol. 54, no, 8, pp. 1854-1868, Aug. 2009) using formal integration is generalized towards a unified design framework, which covers linear and Semilinear PDEs including rather broad classes of nonlinearities arising in applications. In addition, an efficient semi-numerical solution of the implicit state and input parametrizations is developed and evaluated in different scenarios. Simulation results for various types of nonlinearities and a tubular reactor model described by a system of Semilinear reaction-diffusion-convection equations illustrate the applicability of the proposed method.
Hiroyuki Takamura - One of the best experts on this subject based on the ideXlab platform.
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nonexistence of global solutions for a weakly coupled system of Semilinear damped wave equations of derivative type in the scattering case
Mediterranean Journal of Mathematics, 2020Co-Authors: Alessandro Palmieri, Hiroyuki TakamuraAbstract:In this paper, we consider the blow-up for solutions to a weakly coupled system of Semilinear damped wave equations of derivative type in the scattering case. The assumption on the time-dependent coefficients for the damping terms means that these coefficients are summable and nonnegative. After introducing suitable functionals proposed by Lai-Takamura for the corresponding single Semilinear equation, we employ Kato’s lemma to derive the blow-up result in the subcritical case. On the other hand, in the critical case, an iteration procedure based on the slicing method is employed. Let us point out that we find as critical curve in the p - q plane for the pair of exponents (p, q) in the nonlinear terms the same one as for the weakly coupled system of Semilinear not-damped wave equations with the same kind of nonlinearities.
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nonexistence of global solutions for a weakly coupled system of Semilinear damped wave equations of derivative type in the scattering case
arXiv: Analysis of PDEs, 2018Co-Authors: Alessandro Palmieri, Hiroyuki TakamuraAbstract:In this paper we consider the blow-up for solutions to a weakly coupled system of Semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the corresponding single Semilinear equation, we employ Kato's lemma to derive the blow-up result in the subcritical case. On the other hand, in the critical case an iteration procedure based on the slicing method is employed. Let us point out that we find as critical curve in the p-q plane for the pair of exponents (p, q) in the nonlinear terms the same one as for the weakly coupled system of Semilinear not-damped wave equations with the same kind of nonlinearities.
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blow up for Semilinear damped wave equations with subcritical exponent in the scattering case
Nonlinear Analysis-theory Methods & Applications, 2018Co-Authors: Hiroyuki TakamuraAbstract:Abstract It is well-known that the critical exponent for Semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in 2017 have obtained a blow-up result not only for super-Fujita exponent but also for the one closely related to Strauss exponent when the damping is scaling invariant and its constant is relatively small, which has been recently extended by Ikeda and Sobajima. Introducing a multiplier for the time-derivative of the spatial integral of unknown functions, we succeed in employing the techniques on the analysis for Semilinear wave equations and proving a blow-up result for Semilinear damped wave equations with sub-Strauss exponent when the damping is in the scattering range.
Anurag Shukla - One of the best experts on this subject based on the ideXlab platform.
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Controllability results for fractional Semilinear delay control systems
Journal of Applied Mathematics and Computing, 2020Co-Authors: Anurag Shukla, Rohit PatelAbstract:In this article, we have presented the controllability relationship between the Semilinear control system of fractional order (1, 2] with delay and that of the Semilinear control system without delay. Suppose X and U be Hilbert spaces which are separable and $$Z=L_2[0,b;X],\;Z_h=L_2[-h,b;X],\;0\le h\le b$$ Z = L 2 [ 0 , b ; X ] , Z h = L 2 [ - h , b ; X ] , 0 ≤ h ≤ b and $$Y=L_2[0,b;U]$$ Y = L 2 [ 0 , b ; U ] be the function spaces. Let the Semilinear control system of fractional order with delay as $$\begin{aligned} ^CD_\tau ^\alpha z(\tau )= & {} Az(\tau )+Bv(\tau )+g(\tau ,z(\tau -h)),\;0\le \tau \le b;\\ z_0(\theta )= & {} \phi (\theta ),\;\;\;\; \theta \in [-h,0]\\ z'(0)= & {} z_0. \end{aligned}$$ C D τ α z ( τ ) = A z ( τ ) + B v ( τ ) + g ( τ , z ( τ - h ) ) , 0 ≤ τ ≤ b ; z 0 ( θ ) = ϕ ( θ ) , θ ∈ [ - h , 0 ] z ′ ( 0 ) = z 0 . where $$1
