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On the Existence of Optimal Solutions for Infinite Horizon Optimal Control Problems: Nonconvex and Multicriteria Problems

Dean A. Carlson (1984)

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

In questa Nota si continua la discussione iniziata in [4] dell'esistenza di soluzioni ottimali per problemi di ottimo controllo in [ 0 + ∞ ] . Si definiscono problemi generalizzati, e si ottengono estensioni di risultati già presentati in [4]. Si dimostrano anche varie relazioni tra le soluzioni ottimali dei problemi generalizzati e i problemi originali e non convessi di ottimo controllo. Alla fine si considerano problemi lineari nelle variabili di stato anche nel caso di costi funzionali a valori vettoriali...

On the optimal continuous decentralized control of non-linear dynamical multivariable systems about the origin.

Manuel de la Sen Parte (1987)

Trabajos de Investigación Operativa

This paper deals with the local (around the equilibrium) optimal decentralized control of autonomous multivariable systems of nonlinearities and couplings between subsystems which can be expressed as power series in the state-space are allowed in the formulation. They only affect for the optimal performance integrals in cubic and higher terms in the norm of the initial conditions of the dynamical differential system. The basic hypothesis which is made is that the system is centrally-stabilizable...

On the Optimal Control of a Class of Time-Delay System

L. Boudjenah, M.F. Khelfi (2010)

Mathematical Modelling of Natural Phenomena

In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties...

On the solution of the constrained multiobjective control problem with the receding horizon approach

Daniele De Vito, Riccardo Scattolini (2008)

Kybernetika

This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem...

On the stability of T-S fuzzy control for non-linear systems.

Zoe Doulgeri, John B. Theocharis (2000)

Mathware and Soft Computing

This work concerns the stability analysis of a non-linear system controlled by a fuzzy T-S control law. It is shown that the closed loop system is in general expressed by a T-S fuzzy system composed of rules with affine linear systems in their consequent parts. The stability of affine T-S systems is then investigated for a special case using as an example the regulation problem of single link robot arm. Stability conditions are derived using the indirect and direct Lyapunov method and simulation...

On the state observation and stability for uncertain nonlinear systems

Mohamed Ali Hammami (2000)

Kybernetika

In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [3,2,1,4]. We consider continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded. We study the problems of state observation and obtaining stabilizing controller for uncertain nonlinear systems, where the uncertainties are characterized by known bounds.

On the structure of linear recurrent error-control codes

Michel Fliess (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.

On the structure of linear recurrent error-control codes

Michel Fliess (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.

On-line wavelet estimation of Hammerstein system nonlinearity

Przemysław Śliwiński (2010)

International Journal of Applied Mathematics and Computer Science

A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.

On-off intermittency in continuum systems driven by the Chen system

Qian Zhou, Zeng-Qiang Chen, Zhu Zhi Yuan (2008)

Kybernetika

Previous studies on on-off intermittency in continuum systems are generally based on the synchronization of identical chaotic oscillators or in nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five- dimensional continuum systems, respectively, where each system has a two- dimensional subsystem driven by the chaotic Chen system. The phenomenon of intermingled basins is observed below the blowout...

Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria

Hassan Saberi Nik, Ping He, Sayyed Taha Talebian (2014)

Kybernetika

In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...

Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation

George Avalos, Irena Lasiecka (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function ℰ min ( T ) , as terminal time T ↓ 0 . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator 𝒜 , as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate...

Optimal control for 2-D nonlinear control systems

Barbara Bily (2002)

Applicationes Mathematicae

Necessary conditions for some optimal control problem for a nonlinear 2-D system are considered. These conditions can be obtained in the form of a quasimaximum principle.

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