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Displaying similar documents to “Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation”

Design of a model following control system for nonlinear descriptor system in discrete time

Shujing Wu, Shigenori Okubo, Dazhong Wang (2008)

Kybernetika

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A model following control system (MFCS) can output general signals following the desired ones. In this paper, a method of nonlinear MFCS will be extended to be a nonlinear descriptor system in discrete time. The nonlinear system studied in this paper has the property of norm constraint | | f ( v ( k ) ) | | ≤ α + β | | v ( k ) | | γ , where α ≥ 0 , β ≥ 0 , 0 ≤ γ < 1 . In this case, a new criterion is proposed to ensure the internal states be stable.

Protector control: Extension to a class of nonlinear distributed systems

Youssef Qaraai, Abdes Samed Bernoussi (2010)

International Journal of Applied Mathematics and Computer Science

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We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we...

Tracking with prescribed transient behaviour

Achim Ilchmann, E. P. Ryan, C. J. Sangwin (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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Universal tracking control is investigated in the context of a class 𝒮 of M -input, M -output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary ℝ M -valued reference signal r of class...

Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion

Juan González-Hernández, Raquiel R. López-Martínez, J. Adolfo Minjárez-Sosa (2009)

Kybernetika

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The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process x t and the discount process α t evolve according to the coupled difference equations x t + 1 = F ( x t , α t , a t , ξ t ) , α t + 1 = G ( α t , η t ) where the state and discount disturbance processes { ξ t } and { η t } are sequences of i.i.d. random variables with densities ρ ξ and ρ η respectively. The main objective is to introduce approximation algorithms...

Optimal control of a rotating body beam

Weijiu Liu (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose...

On some optimal control problems governed by a state equation with memory

Guillaume Carlier, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to study problems of the form: i n f ( u ∈ V ) J ( u ) with J ( u ) : = ∫ 0 1 L ( s , y u ( s ) , u ( s ) ) d s + g ( y u ( 1 ) ) where is a set of admissible controls and is the solution of the Cauchy problem: x ˙ ( t ) = 〈 f ( . , x ( . ) ) , ν t 〉 + u ( t ) , t ∈ ( 0 , 1 ) , x ( 0 ) = x 0 and each ν t is a nonnegative measure with support in . After studying the Cauchy problem, we establish existence of minimizers, optimality conditions (in particular in the form of a nonlocal version of the Pontryagin principle) and prove some regularity results. We also consider the more general case where the control...

Feedback in state constrained optimal control

Francis H. Clarke, Ludovic Rifford, R. J. Stern (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem is studied, in which the state is required to remain in a compact set S . A control feedback law is constructed which, for given ε &gt; 0 , produces ε -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of S and a related trajectory tracking result. The control feedback is shown to possess...