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Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation

J. Tsinias (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The concepts of stability, attractivity and asymptotic stability for systems subject to restrictions of the input values are introduced and analyzed in terms of Lyapunov functions. A comparison with the well known input-to-state stability property introduced by Sontag is provided. We use these concepts in order to derive sufficient conditions for global stabilization for triangular and feedforward systems by means of saturated bounded feedback controllers and also recover some recent results...

Input-output decoupling of nonlinear recursive systems

Ülle Kotta (2000)

Kybernetika

The input-output decoupling problem is studied for a class of recursive nonlinear systems (RNSs), i. e. for systems, modelled by higher order nonlinear difference equations, relating the input, the output and a finite number of their time shifts. The solution of the problem via regular static feedback known for discrete-time nonlinear systems in state space form, is extended to RNSs. Necessary and sufficient conditions for local solvability of the problem are proposed. This is the alternative to...

Integrated design of observer based fault detection for a class of uncertain nonlinear systems

Wei Chen, Abdul Q. Khan, Muhammmad Abid, Steven X. Ding (2011)

International Journal of Applied Mathematics and Computer Science

Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the...

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (2012)

ESAIM: Control, Optimisation and Calculus of Variations

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (2012)

ESAIM: Control, Optimisation and Calculus of Variations

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (2012)

ESAIM: Control, Optimisation and Calculus of Variations

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant tracking

Philippe Martin, Pierre Rouchon, Joachim Rudolph (2004)

ESAIM: Control, Optimisation and Calculus of Variations

The problem of invariant output tracking is considered: given a control system admitting a symmetry group G , design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of G . Invariant output errors are defined as a set of scalar invariants of G ; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required...

Invariant tracking

Philippe Martin, Pierre Rouchon, Joachim Rudolph (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The problem of invariant output tracking is considered: given a control system admitting a symmetry group G, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of G. Invariant output errors are defined as a set of scalar invariants of G; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the...

Inversion in indirect optimal control of multivariable systems

François Chaplais, Nicolas Petit (2008)

ESAIM: Control, Optimisation and Calculus of Variations

This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.

Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

Yanjun Shen, Dawei Wang, Zifan Fang (2022)

Kybernetika

In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities...

Linear adaptive structure for control of a nonlinear MIMO dynamic plant

Stanisław Bańka, Paweł Dworak, Krzysztof Jaroszewski (2013)

International Journal of Applied Mathematics and Computer Science

In the paper an adaptive linear control system structure with modal controllers for a MIMO nonlinear dynamic process is presented and various methods for synthesis of those controllers are analyzed. The problems under study are exemplified by the synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system, use is made of a set of (stable)...

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...

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 201 – 220 of 438