Displaying similar documents to “Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra”

An Invariance Problem for Control Systems with Deterministic Uncertainty

Lech Górniewicz, Paolo Nistri (1996)

Banach Center Publications

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This paper deals with a class of nonlinear control systems in R n in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set K ⊂ R n from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics...

Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics

Arturo Enrique Gil García, Vadim Azhmyakov, Michael V. Basin (2014)

Kybernetika

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This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees...

High-Order Control Variations and Small-Time Local Controllability

Krastanov, Mikhail (2010)

Serdica Journal of Computing

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The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is...

Asymptotic null controllability of bilinear systems

Fritz Colonius, Wolfgang Kliemann (1995)

Banach Center Publications

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The region of asymptotic null controllability of bilinear systems with control constraints is characterized using Lyapunov exponents. It is given by the cone over the region of attraction of the maximal control set in projective space containing zero in its spectral interval.

Global linearization of nonlinear systems - A survey

Sergej Čelikovský (1995)

Banach Center Publications

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A survey of the global linearization problem is presented. Known results are divided into two groups: results for general affine nonlinear systems and for bilinear systems. In the latter case stronger results are available. A comparision of various linearizing transformations is performed. Numerous illustrative examples are included.

Control of the underactuated mechanical systems using natural motion

Zdeněk Neusser, Michael Valášek (2012)

Kybernetika

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The paper deals with the control of underactuated mechanical systems between equilibrium positions across the singular positions. The considered mechanical systems are in the gravity field. The goal is to find feasible trajectory connecting the equilibrium positions that can be the basis of the system control. Such trajectory can be stabilized around both equilibrium positions and due to the gravity forces the mechanical system overcomes the singular positions. This altogether constitutes...

State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra

Juri Belikov, Ülle Kotta, Maris Tõnso (2012)

Kybernetika

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In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials....