Displaying similar documents to “Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance”

Improving the performance of semiglobal output controllers for nonlinear systems

Abdallah Benabdallah, Walid Hdidi (2017)

Kybernetika

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For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers ( 𝒰 R ) R > 0 with increasing regions of attraction ( Ω R ) R > 0 is that, when the region of attraction Ω R is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is...

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 M -valued reference signal r of class...

Model following control system with time delays

Dazhong Wang, Shujing Wu, Wei Zhang, Guoqiang Wang, Fei Wu, Shigenori Okubo (2016)

Kybernetika

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Design of model following control system (MFCS) for nonlinear system with time delays and disturbances is discussed. In this paper, the method of MFCS will be extended to nonlinear system with time delays. We set the nonlinear part f ( v ( t ) ) of the controlled object as | | f ( v ( t ) ) | | α + β | | v ( t ) | | γ , and show the bounded of internal states by separating the nonlinear part into γ 0 . Some preliminary numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Linearization techniques for 𝕃 See PDF-control problems and dynamic programming principles in classical and 𝕃 See PDF-control problems

Dan Goreac, Oana-Silvia Serea (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of the paper is to provide a linearization approach to the 𝕃 See PDF-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the 𝕃 p See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating 𝕃 See PDF problems in continuous and...

Synthesis of optimal control for nonlinear third order systems

Wiesław Szwiec

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The paper is devoted to a certain problem in the theory of synthesis of optimal control. The fundamental results of research in the synthesis of optimal control for second order systems are given in [1], [2], [5], [10]. In particular, in [2] and [5] some specific nonlinear systems are investigated, namely the systems related with the differential equations of the forms̈ + F(s,ṡ) = u or s̈ + F(s,ṡ,u) = 0where u is a control parameter in the interval [—1,1]. Some results concerning third...

Distances to convex sets

Antonio S. Granero, Marcos Sánchez (2007)

Studia Mathematica

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If X is a Banach space and C a convex subset of X*, we investigate whether the distance d ̂ ( c o ¯ w * ( K ) , C ) : = s u p i n f | | k - c | | : c C : k c o ¯ w * ( K ) from c o ¯ w * ( K ) to C is M-controlled by the distance d̂(K,C) (that is, if d ̂ ( c o ¯ w * ( K ) , C ) M d ̂ ( K , C ) for some 1 ≤ M < ∞), when K is any weak*-compact subset of X*. We prove, for example, that: (i) C has 3-control if C contains no copy of the basis of ℓ₁(c); (ii) C has 1-control when C ⊂ Y ⊂ X* and Y is a subspace with weak*-angelic closed dual unit ball B(Y*); (iii) if C is a convex subset of X and X is considered canonically...

Stability and sensitivity analysis for optimal control problems with control-state constraints

Kazimierz Malanowski

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A family of parameter dependent optimal control problems ( O ) h with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of ( O ) h exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to ( O ) h and the associated Lagrange...

On approximation of stability radius for an infinite-dimensional feedback control system

Hideki Sano (2016)

Kybernetika

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In this paper, we discuss the problem of approximating stability radius appearing in the design procedure of finite-dimensional stabilizing controllers for an infinite-dimensional dynamical system. The calculation of stability radius needs the value of H -norm of a transfer function whose realization is described by infinite-dimensional operators in a Hilbert space. From the computational point of view, we need to prepare a family of approximate finite-dimensional operators and then to...

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. CHOUDHURY, Samir Kumar BHANDARI, Parbati SAHA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we introduce generalized cyclic contractions through r number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t -norm. In another theorem we use a control function with minimum t -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

Transportation flow problems with Radon measure variables

Marcus Wagner (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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For a multidimensional control problem ( P ) K involving controls u L , we construct a dual problem ( D ) K in which the variables ν to be paired with u are taken from the measure space rca (Ω,) instead of ( L ) * . For this purpose, we add to ( P ) K a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.

On the stabilization problem for nonholonomic distributions

Ludovic Rifford, Emmanuel Trélat (2009)

Journal of the European Mathematical Society

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Let M be a smooth connected complete manifold of dimension n , and Δ be a smooth nonholonomic distribution of rank m n on M . We prove that if there exists a smooth Riemannian metric on1for which no nontrivial singular path is minimizing, then there exists a smooth repulsive stabilizing section of Δ on M . Moreover, in dimension three, the assumption of the absence of singular minimizing horizontal paths can be dropped in the Martinet case. The proofs are based on the study, using specific...

On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters

Aldo Bressan (1988)

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

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In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control u ( ) . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control u = u ( ) , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system Σ , referred to a system χ of Lagrangian co-ordinates, and to try and write some handy...

The internal stabilization by noise of the linearized Navier-Stokes equation

Viorel Barbu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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One shows that the linearized Navier-Stokes equation in 𝒪 R d , d 2 , around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V ( t , ξ ) = i = 1 N V i ( t ) ψ i ( ξ ) β ˙ i ( t ) , ξ 𝒪 , where { β i } i = 1 N are independent Brownian motions in a probability space and { ψ i } i = 1 N is a system of functions on 𝒪 with support in an arbitrary open subset 𝒪 0 𝒪 . The stochastic control input { V i } i = 1 N is found in feedback form. One constructs also a tangential boundary noise controller which exponentially stabilizes in probability...

On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters

Aldo Bressan (1988)

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

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In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control u ( ) . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control u = u ( ) , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system Σ , referred to a system χ of Lagrangian co-ordinates, and to try and write some handy...

Control for Schrödinger operators on 2-tori: rough potentials

Jean Bourgain, Nicolas Burq, Maciej Zworski (2013)

Journal of the European Mathematical Society

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For the Schrödinger equation, ( i t + ) u = 0 on a torus, an arbitrary non-empty open set Ω provides control and observability of the solution: u t = 0 L 2 ( 𝕋 2 ) K T u L 2 ( [ 0 , T ] × Ω ) . We show that the same result remains true for ( i t + - V ) u = 0 where V L 2 ( 𝕋 2 ) , and 𝕋 2 is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for V C ( 𝕋 2 ) and conjectured for V L ( 𝕋 2 ) . The higher dimensional generalization remains open for V L ( 𝕋 n ) .

A note on control of the false discovery proportion

Marcin Dudziński, Konrad Furmańczyk (2009)

Applicationes Mathematicae

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We consider the problem of simultaneous testing of a finite number of null hypotheses H i , i=1,...,s. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number s, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned...

Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert, Onesimo Hernández-Lerma (2001)

Applicationes Mathematicae

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We consider a class of d -valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation x t + 1 = G ( x t , a t ) + ξ t (t = 0,1,... ), for each fixed n = 0,1,..., where the ξ t are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function G as n → ∞. Under suitable hypotheses, our main results state the existence of stationary control policies that are expected average cost (EAC) optimal and sample path average cost (SPAC)...

Systems of Bellman Equations to Stochastic Differential Games with Discount Control

Alain Bensoussan, Jens Frehse (2008)

Bollettino dell'Unione Matematica Italiana

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We consider two dimensional diagonal elliptic systems Δ u + a u = H ( x , u , u ) which arise from stochastic differential games with discount control. The Hamiltonians H have quadratic growth in u and a special structure which has notyet been covered by regularity theory. Without smallness condition on H , the existence of a regular solution is established.