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Control of a team of mobile robots based on non-cooperative equilibria with partial coordination

Krzysztof Skrzypczyk (2005)

International Journal of Applied Mathematics and Computer Science

In this work we present an application of the concept of non-cooperative game equilibria to the design of a collision free movement of a team of mobile robots in a dynamic environment. We propose the solution to the problem of feasible control synthesis, based on a partially centralized sensory system. The control strategy based on the concept of non-cooperative game equilibria is well known in the literature. It is highly efficient through phases where the solution is unique. However, even in simple...

Control of an induction motor using sliding mode linearization

Erik Etien, Sébastien Cauet, Laurent Rambault, Gérard Champenois (2002)

International Journal of Applied Mathematics and Computer Science

Nonlinear control of the squirrel induction motor is designed using sliding mode theory. The developed approach leads to the design of a sliding mode controller in order to linearize the behaviour of an induction motor. The second problem described in the paper is decoupling between two physical outputs: the rotor speed and the rotor flux modulus. The sliding mode tools allow us to separate the control from these two outputs. To take account of parametric variations, a model-based approach is used...

Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach

Jian Wan, Josep Vehí, Ningsu Luo, Pau Herrero (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional...

Control of distributed delay systems with uncertainties: a generalized Popov theory approach

Dan Ivanescu, Silviu-Iulian Niculescu, Jean-Michel Dion, Luc Dugard (2001)

Kybernetika

The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for γ -attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of H ∞ memoryless control problems in terms of Popov triplets...

Control of linear systems with rational expectations. The case of incomplete information.

Emilio Cerdá Tena (1992)

Trabajos de Investigación Operativa

The problem of optimal control of linear economic systems with rational expectations and quadratic objective function is solved for the case of incomplete information. The case of complete information has been previously studied. In both problems the hypothesis of causality is not satisfied and, therefore, the standard techniques of control theory cannot be directly applied, though the method used is based on these techniques.

Control of networks of Euler-Bernoulli beams

Bertrand Dekoninck, Serge Nicaise (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.

Control of the continuity equation with a non local flow

Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...

Control of the continuity equation with a non local flow

Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...

Control of the surface of a fluid by a wavemaker

Lionel Rosier (2004)

ESAIM: Control, Optimisation and Calculus of Variations

The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.

Control of the surface of a fluid by a wavemaker

Lionel Rosier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in Lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.

Control of the underactuated mechanical systems using natural motion

Zdeněk Neusser, Michael Valášek (2012)

Kybernetika

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 the control...

Control of the wave equation by time-dependent coefficient

Antonin Chambolle, Fadil Santosa (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior...

Control of the Wave Equation by Time-Dependent Coefficient

Antonin Chambolle, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior of...

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