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Linear repetitive process control theory applied to a physical example

Krzysztof Gałkowski, Eric Rogers, Wojciech Paszke, David Owens (2003)

International Journal of Applied Mathematics and Computer Science

In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward...

Linearization by completely generalized input-output injection

Virgilio López Morales, Franck Plestan, Alain Glumineau (1999)

Kybernetika

The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed...

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

Dan Goreac, Oana-Silvia Serea (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of the paper is to provide a linearization approach to the 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 See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating See PDF problems in continuous and lower semicontinuous setting.

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

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 lower semicontinuous...

Linear-wavelet networks

Roberto Galvão, Victor Becerra, João Calado, Pedro Silva (2004)

International Journal of Applied Mathematics and Computer Science

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated...

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Pagavathigounder Balasubramaniam, Shanmugam Lakshmanan, Rajan Rakkiyappan (2012)

International Journal of Applied Mathematics and Computer Science

This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some...

LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

Chaouki Mnasri, Moncef Gasmi (2011)

International Journal of Applied Mathematics and Computer Science

Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering...

Local analysis of hybrid systems on polyhedral sets with state-dependent switching

John Leth, Rafael Wisniewski (2014)

International Journal of Applied Mathematics and Computer Science

This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed...

Local and global null controllability of time varying linear control systems

F. Colonius, R. Johnson (2010)

ESAIM: Control, Optimisation and Calculus of Variations

For linear control systems with coefficients determined by a dynamical system null controllability is discussed. If uniform local null controllability holds, and if the Lyapounov exponents of the homogeneous equation are all non-positive, then the system is globally null controllable for almost all paths of the dynamical system. Even if some Lyapounov exponents are positive, an irreducibility assumption implies that, for a dense set of paths, the system is globally null controllable.

Local asymptotic stability for nonlinear state feedback delay systems

Alfredo Germani, Costanzo Manes, Pierdomenico Pepe (2000)

Kybernetika

This paper considers the problem of output control of nonlinear delay systems by means of state delayed feedback. In previous papers, through the use of a suitable formalism, standard output control problems, such as output regulation, trajectory tracking, disturbance decoupling and model matching, have been solved for a class of nonlinear delay systems. However, in general an output control scheme does not guarantee internal stability of the system. Some results on this issue are presented in this...

Local Controllability around Closed Orbits

Marek Grochowski (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.

Currently displaying 41 – 60 of 97