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Variable measurement step in 2-sliding control

Arie Levant (2000)

Kybernetika

Sliding mode is used in order to retain a dynamic system accurately at a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes are known to feature finite time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main properties, improve its precision with discrete measurements and remove the chattering...

Variable structure observer design for a class of uncertain systems with a time-varying delay

Wen-Jeng Liu (2012)

International Journal of Applied Mathematics and Computer Science

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for...

Variational approach to some optimization control problems

R. Bianchini (1995)

Banach Center Publications

This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.

Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

Andreas Rauh, Johanna Minisini, Eberhard P. Hofer (2009)

International Journal of Applied Mathematics and Computer Science

Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical...

Viability Kernels and Control Sets

Dietmar Szolnoki (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset Q of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of Q can be represented by the union of domains of attraction of chain control sets, defined relative to the given set Q. In particular,...

Weak and exact domination in distributed systems

Larbi Afifi, El Mostafa Magri, Abdelhaq El Jai (2010)

International Journal of Applied Mathematics and Computer Science

In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems....

Weak regularizability and pole assignment for non-square linear systems

Tetiana Korotka, Jean-Jacques Loiseau, Petr Zagalak (2012)

Kybernetika

The problem of pole assignment by state feedback in the class of non-square linear systems is considered in the paper. It is shown that the problem is solvable under the assumption of weak regularizability, a newly introduced concept that can be viewed as a generalization of the regularizability of square systems. Necessary conditions of solvability for the problem of pole assignment are established. It is also shown that sufficient conditions can be derived in some special cases. Some conclusions...

Weak structure at infinity and row-by-row decoupling for linear delay systems

Rabah Rabah, Michel Malabre (2004)

Kybernetika

We consider the row-by-row decoupling problem for linear delay systems and show some close connections between the design of a decoupling controller and some particular structures of delay systems, namely the so-called weak structure at infinity. The realization by static state feedback of decoupling precompensators is studied, in particular, generalized state feedback laws which may incorporate derivatives of the delayed new reference.

Weighted ℋ ∞ mixed-sensitivity minimization for stable distributed parameter plants under sampled data control

Delano R. Carter, Armando A. Rodriguez (1999)

Kybernetika

This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted ℋ ∞ -style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite-...

Well-formed dynamics under quasi-static state feedback

J. Rudolph (1995)

Banach Center Publications

Well-formed dynamics are a generalization of classical dynamics, to which they are equivalent by a quasi-static state feedback. In case such a dynamics is flat, i.e., equivalent by an endogenous feedback to a linear controllable dynamics, there exists a Brunovský type canonical form with respect to a quasi-static state feedback.

Well-posed linear systems - a survey with emphasis on conservative systems

George Weiss, Olof Staffans, Marius Tucsnak (2001)

International Journal of Applied Mathematics and Computer Science

We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space....

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

Well-posedness and sliding mode control

Tullio Zolezzi (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.

Well-posedness and sliding mode control

Tullio Zolezzi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.

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