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50th Annual Conference on Society of Instrument and control Engineers, SICE 2011

作者： Kashima, Kenji Papachristodoulou, Antonis Allgöwer, Frank Graduate School of Information Science and Engineering Tokyo Institute of Technology Tokyo Japan Department of Engineering Science University of Oxford Parks Road Oxford OX1 3PJ United Kingdom Institute for Systems Theory and Automatic Control University of Stuttgart Stuttgart Germany

ISBN: (纸本)9784907764395

FitzHugh-Nagumo is one of the best known nonlinear neuronal models in mathematical physiology. In particular, spatio-temporal forms of this model have been used for modeling oscillatory behavior in living organisms such as the behavior of cardiac pacemaker cells. In this paper, we investigate the stability of their spatially discretized form, that is, diffusively coupled large-scale networks of piecewisely affine approximated FitzHugh-Nagumo models. Scalable criteria for ultimate boundedness are given taking connection profile (coupling strength, delay length, subsystem heterogeneity) robustness into account. This result is accomplished through a linear multi-agent system perspective for a class of piecewise affine systems. © 2011 SICE.

关键词： Large scale systems

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On state-constrained control of a CSTR

On state-constrained control of a CSTR

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作者： Bayer, Florian Bürger, Mathias Guay, Martin Allgöwer, Frank Institute for Systems Theory and Automatic Control University of Stuttgart Pfaffenwaldring 9 70550 Stuttgart Germany Department of Chemical Engineering Queen's University Kingston ON K7L 3N6 Canada

ISBN: (纸本)9783902661937

In this note, we study the problem of multiple hard output constraints imposed on a continuous stirred tank reactor (CSTR) subject to external disturbances. Constraints on the concentration and on the temperature are considered. We show, analytically and with simulations, that there are critical combinations of constraints, where robust constraint satisfaction cannot be guaranteed. As a consequence violation of at least one constraint has to be allowed. © 2011 IFAC.

关键词： Robust control

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control of an underactuated manipulator using similarities to the double integrator

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IFAC Proceedings Volumes 2011年第1期44卷 11501-11507页

作者： Carsten Knoll Klaus Röbenack Institute of Control Theory Faculty of Electrical and Computer Engineering Technische Universität Dresden 01062 Dresden Germany (Tel: +49351-463-33268)

Abstract A horizontally mounted two-link manipulator is considered. We assume that only the first joint is actuated, while the second joint is passive and frictionless. The system exposes challenging properties, e. g. it is not controllable in the equilibrium points. We transform the equations of motion in Byrnes-Isidori normal form and consider the projection into the subspace spanned by the velocity-like state variables. From this viewpoint the manipulator system reveals qualitative similarities to the well-understood double integrator. In particular the drift vector field is investigated. Exploiting these similarities, an approach for equilibrium point transition based on sliding mode control is proposed.

关键词： underactuated manipulator double integrator Byrnes-Isidori normal form sliding mode point symmetry

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Offline NMPC for continuous-time systems using sum of squares

Offline NMPC for continuous-time systems using sum of square...

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2011 American control Conference (ACC)

作者： Frederik Deroo Christoph Maier Christoph Bohm Frank Allgower Institute of Automatic Control Engineering (LSR) Technische Universität München Germany Allgöwer Institute for Systems Theory and Automatic Control (IST) University of Stuttgart Germany

An offline nonlinear model predictive control (NMPC) approach for continuous time nonlinear systems subject to input and state constraints is presented. The approach deals with nonlinear systems which can be represented by polynomial parameter-varying systems. Since the applicability of NMPC is often limited by the speed at which an optimization problem can be solved online, we propose an NMPC scheme with drastically reduced online computational burden. The basic idea involves the offline computation of nested invariant sets and associated feedback laws by solving a convex optimization problem subject to sum of squares (SOS) constraints via semidefinite programming (SDP). Online, a search algorithm is executed to determine the feedback law suitable for the current state. The resulting offline NMPC controller guarantees stability and constraint satisfaction. Its applicability and effectiveness is shown by means of simulation of an example system.

关键词： Polynomials Optimization Nonlinear systems Trajectory Symmetric matrices Lyapunov methods

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The Minimum Principle for Time-Varying Hybrid Systems with State Switching and Jumps

The Minimum Principle for Time-Varying Hybrid Systems with S...

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IEEE Conference on Decision and control

作者： Benjamin Passenberg Marion Leibold Olaf Stursberg Martin Buss Institute of Automatic Control Department of Electrical Engineering and Information Technology Technische Universitat Munchen Munchen Germany Institute of Control and System Theory Department of Electrical Engineering and Computer Science University of Kassel Kassel Germany

ISBN: (纸本)9781612848006

The hybrid minimum principle (HMP) is extended to hybrid systems with autonomous (internally forced) switching on switching manifolds, controlled (externally forced) switching, jumps of the continuous state when switching, and time-varying functions for specifying the continuous and discrete dynamics. The formulation of the hybrid optimal control problem (HOCP) includes running, switching, and terminal costs. The HMP provides necessary optimality conditions for a solution of the HOCP and can be used as basis for developing numerical optimal control algorithms.

关键词： minimum principle hybrid systems switching time varying Manifolds

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Feedback design for the Acrobot walking-like trajectory tracking and computational test of its exponential stability

Feedback design for the Acrobot walking-like trajectory trac...

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1st Joint Symposium on Computer-Aided control System Design, CACSD 2011 and Systems with Uncertainty, SU 2011

作者： Anderle, Milan Čelikovský, Sergej Czech Technical University in Prague Faculty of Electrical Engineering Department of Control Engineering Technická 2 166 27 Prague Czech Republic Institute of Information Theory and Automation Academy of Sciences of the Czech Republic Pod Vodárenskou věží 4 182 08 Prague Czech Republic

ISBN: (纸本)9781457710667

This paper aims to the further improve of the previously developed design for the Acrobot walking based on the partial exact feedback linearization of order 3. Namely, such an exact system transformation leads to an almost linear system where error dynamics along trajectory to be tracked is a 4 dimensional linear time varying system having 3 time varying entries only. Unlike previous approaches treating time varying entries as uncertainties with various extent of conservatism, the present paper takes into the account an information about these time varying functions including their derivatives up to order 4. Using that, the time varying state and the feedback transformation enable to design a fundamental matrix of the error dynamics in an explicit form and pre-designed stability properties. In particular, product of that fundamental matrix at the end of the single support walking phase by the impact map Jacobian enables directly prove stability of the hybrid cyclic walking like trajectory by computing certain 44 matrix and determining numerically whether its eigenvalues lie within the unit circle. This combination of analytical and numerical computations provides the justification of the exponential stability of the walking-like trajectory tracking. Moreover, it is supported by numerical simulations showing practically unlimited number of steps of the Acrobot "walking". © 2011 IEEE.

关键词： Trajectories

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Stability analysis of the Acrobot walking with observed geometry

Stability analysis of the Acrobot walking with observed geom...

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ISBN: (纸本)9783902661937

This paper aims to extend of the previously developed analytical design for the Acrobot walking. The corresponding state feedback controller is completed in this paper by an observer to estimate some states of the Acrobot. Both the controller and the observer are based on the partial exact feedback linearization of order 3. The feedback controller and the observer are extended for the tracking of the cyclic walking-like trajectory in order to demonstrate the cyclic Acrobot walking. The cyclic walking-like trajectory starts continuous phase from certain initial conditions, that at the end of the step makes an impact and after the impact it reaches the same initial conditions as at the beginning of the step. This cyclic motion of the Acrobot enable us to prove the stability of the feedback tracking with the observer numericaly by the method of Poincaré mappings. This numerical proof of the stability is supported by numerical simulations showing practically unlimited number of steps of the stable Acrobot walking. © 2011 IFAC.

关键词： Stability

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A Lie Bracket Approximation for Extremum Seeking Vehicles

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IFAC Proceedings Volumes 2011年第1期44卷 11393-11398页

作者： Miloš S Stanković Hans-Bernd Dürr Karl Henrik Johansson Institute for Systems Theory and Automatic Control University of Stuttgart Germany ACCESS Linnaeus Center School of Electrical Engineering Royal Institute of Technology (KTH) 100-44 Stockholm Sweden

Abstract In this paper we propose a novel methodology for the analysis of autonomous vehicles seeking the extremum of an arbitrary smooth nonlinear map in the plane. By interpreting the extremum seeking schemes as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we calculate a simplified system which approximates the qualitative behavior of the original one better than existing methods. By examining this approximate Lie bracket system, we are able to directly derive properties of the original one. Thus, by showing that the Lie bracket direction is directly related to the unknown gradient of the objective function we prove global uniform practical asymptotic stability of the extremum point for vehicles modeled as single integrators and non-holonomic unicycles. We illustrate the proposed method through simulations.

关键词： Extremum Seeking Autonomous Mobile Robots Stability Nonlinear control Systems

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Event-based NMPC for Networked control Systems over UDP-like Communication Channels

Event-based NMPC for Networked Control Systems over UDP-like...

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2011 American control Conference (ACC)

作者： Paolo Varutti Rolf Findeisen Laboratory for Systems Theory and Automatic Control Institute for Automation Engineering Otto-von-Guericke University of Magdeburg Magdeburg Germany

Networked controlled systems have recently received attention from the industry since they allow for flexibility and cost reduction. However, due to the fact that communication media can be subject to random delays, packet dropouts, jitters and other uncertainties, destabilization of the closed loop system can occur. Model predictive control has demonstrated to be a valid solution to cope with these issues. On the other hand, it typically relies on TCP-like (or connection oriented) protocols, i.e. either the received or the lost information is acknowledged. In this work, we propose an event-based model predictive control algorithm for nonlinear continuous time systems subject to state and input constraints which is based on UDP-like communication. We show that without the use of any acknowledgment or error message we can derive a compensation algorithm, which used in combination with the controller, under mild conditions, guarantees closed loop stability. The solution is applied to a continuous stirred tank reactor where an exothermic irreversible reaction takes place. The simulations show the effectiveness of the presented algorithm.

关键词： Loss measurement Delay Stability analysis Predictive models Asymptotic stability Prediction algorithms Closed loop systems

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Tube MPC Scheme based on Robust control Invariant Set with Application to Lipschitz Nonlinear Systems

Tube MPC Scheme based on Robust Control Invariant Set with A...

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IEEE Conference on Decision and control

作者： Shuyou Yu Hong Chen Frank Allgower Institute of Systems Theory and Automatic Control University of Stuttgart Germany State Key Laboratory of Automobile Dynamic Simulation and Department of Control Science and Engineering Jilin University PR China

ISBN: (纸本)9781612848006

The paper presents a tube model predictive control (MPC) scheme of continuous-time nonlinear systems based on robust control invariant set. The optimization problem considered has a general cost functional rather than the quadratic one. The scheme has the same online computational burden as the standard MPC with guaranteed nominal stability. Robust stability, as well as recursive feasibility, is guaranteed if the optimization problem is feasible at the initial time instant. Furthermore, an optimization based control scheme is proposed, which inherits the robust properties of the tube MPC scheme. The related optimization problem is solved only at the initial time instant. In particular, we consider a scheme to obtain robust control invariant set for Lipschitz nonlinear systems, and show the effectiveness of the proposed schemes by a simple example.

关键词： Robust control Scheme Invariant COHERENT TUBE MODEL

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