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Finite-time multi-agent deployment: A nonlinear PDE motion planning approach

AUTOMATICA 2011年第11期47卷 2534-2542页

作者： Meurer, Thomas Krstic, Miroslav Vienna Univ Technol Automat & Control Inst A-1040 Vienna Austria Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

The systematic flatness-based motion planning using formal power series and suitable summability methods is considered for the finite-time deployment of multi-agent systems into planar formation profiles along predefined spatial-temporal paths. Thereby, a distributed-parameter setting is proposed, where the collective leader-follower agent dynamics is modeled by two boundary controlled nonlinear time-varying PDEs governing the motion of an agent continuum in the plane. The discretization of the PDE model directly induces a decentralized communication and interconnection structure for the multi-agent system, which is required to achieve the desired spatial-temporal paths and deployment formations. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Motion planning Multi-agent deployment Flatness distributed-parameter systems Formation control

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Design of Uncertain Nonlinear Feedback systems with Inputs and Outputs Satisfying Bounding Conditions

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IFAC Proceedings Volumes 2011年第1期44卷 10970-10975页

作者： Mai Van Sy Suchin Arunsawatwong Eyad H. Abed Department of Electrical Engineering Chulalongkorn University Bangkok 10330 Thailand Department of Electrical and Computer Engineering University of Maryland College Park MD 20742 USA

Abstract This paper develops a computational method for designing a feedback control system where the plant is an uncertain linear time-invariant convolution subsystem with a static memoryless input nonlinearity. The main design objective is to determine a controller ensuring that the error and the controller output are always within respective bounds for all uncertainties and for all inputs having bounded magnitude and slope. First, using Schauder fixed point theorem, we show that (if exists) a design solution for an uncertain linear system obtained by replacing the nonlinearity with a gain and a bounded disturbance is also a solution for the original problem. Then, by extending a known theory and applying it to the so-obtained linear problem, we derive design inequalities that can readily be solved in practice. The usefulness of the developed method is illustrated by a design example of an uncertain heat-conduction process.

关键词： Nonlinear control systems computer-aided control system design robust control uncertain dynamical systems distributed-parameter systems Popov criterion

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Polytopic Control of the Magnetic Flux Profile in a Tokamak Plasma

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IFAC Proceedings Volumes 2011年第1期44卷 6686-6691页

作者： Federico Bribiesca Argomedo Christophe Prieur Emmanuel Witrant Sylvain Brémond Control Systems Department GIPSA-lab Université de Grenoble/CNRS/Université Joseph Fourier Grenoble France Association EURATOM-CEA CEA/IRFM Saint Paul Lez Durance France

Abstract In this paper, the problem of steady-state regulation of the magnetic flux profile in a tokamak plasma using the lower hybrid current drive as actuator is considered. Based on a simplified control-oriented model of the magnetic flux dynamics in a tokamak plasma a polytopic control law was developed. Shape constraints on the actuator are considered and conditions to derive a polytopic linear parameter-varying controller that guarantees stability of the closed-loop system are given. Validation and implementation issues are discussed and numerical simulations are presented.

关键词： Linear parameter-varying model time-varying systems distributed-parameter systems nuclear power

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Internal Nonlinear Predictive Control of Semilinear Parabolic Equations

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IFAC Proceedings Volumes 2011年第1期44卷 5525-5530页

作者： Lianjun Bai Daniel Coca Department of Automatic Control & Systems Engineering The University of Sheffield Sheffield S1 3JD UK

Abstract This paper introduces a method for synthesizing reduced-order nonlinear model-based predictive controllers that have support in an arbitrary open subset, for semilinear parabolic equations. The predictive control law is computed based on reduced-order, nonlinear multi-step-ahead finite-element predictors, identified directly from experimental input-output data. An advantage of this approach is that it does not require knowledge of the partial differential equation (PDE) model of the process. The proposed approach is computationally efficient and suitable for real-time implementation as it does not involve solving a complex nonlinear programming problem. The design method can deal effectively with load disturbances and noise in a similar manner to that adopted in the classical Generalized Predictive Control framework. The method is used to design and evaluate numerically a nonlinear predictive controller for a one-dimensional nonlinear parabolic equation.

关键词： Generalized Predictive Control distributed-parameter systems Finite Element Method Nonlinear System Identification

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Local ISS of Reaction-Diffusion systems

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IFAC Proceedings Volumes 2011年第1期44卷 11018-11023页

作者： Sergey Dashkovskiy Andrii Mironchenko Faculty of Mathematics and Computer Science University of Bremen Bibliothekstraße 1 28334 Bremen Germany

Abstract In the present paper we study local input-to-state stability of reaction-diffusion control systems by viewing them as control systems, based on differential equations in abstract spaces. We develop Lyapunov methods for verification of local input-to-state stability property and prove linearisation principle, that allows studying of local input-to-state stability of nonlinear systems from the stability properties of linearised systems. We illustrate theory on two examples of linear and nonlinear reaction-diffusion equations.

关键词： Nonlinear control systems distributed-parameter systems stability analysis linearization Lyapunov methods

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Boundary model predictive control of Kuramoto-Sivashinsky equation with input and state constraints

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COMPUTERS & CHEMICAL ENGINEERING 2010年第10期34卷 1655-1661页

作者： Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2G6 Canada

In this work an asymptotic stabilization of highly dissipative Kuramoto-Sivashinsky equation (KSE) by means of boundary model modal predictive control (MMPC) in the presence of input and state constraints is demonstrated. The KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE). An appropriate discrete infinite-dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller (MMPC) incorporating both the pointwise enforced KSE state constraints and input constraints. The proposed control problem formulation and the performance of the closed-loop system in the full state feedback controller realization have been evaluated through simulations. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Kuramoto-Sivashinsky equation Boundary control Model predictive control (MPC) Input/state constraints

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Model predictive control of Kuramoto-Sivashinsky equation with state and input constraints

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CHEMICAL ENGINEERING SCIENCE 2010年第15期65卷 4388-4396页

作者： Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada

This work focuses on the model predictive control design methodology that successfully accounts for the state and input constraints applied in the context of highly dissipative Kuramoto-Sivashinsky (KS) partial differential equation (PDE) describing stability of a thin film thickness in the two-phase annular flow in vertical pipes. The evolution of a linear dissipative KSEPDE state is given by an abstract evolution equation in an appropriate functional space. The proposed constrained predictive control law utilizes a low order modal representation in the optimization functional, while higher modes are included only in the PDE state constraints. Simulation results demonstrate a successful application of the proposed predictive control technique that achieves optimal stabilization of a spatially-uniform unstable steady state of Kuramoto-Sivashinsky equation in the presence of input and state constraints. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Kuramoto-Sivashinsky equation Model predictive control Input/state constraints

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Identification of Time-non local Models under Diffusive Representation

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IFAC Proceedings Volumes 2010年第21期43卷 378-385页

作者： C. Casenave CNRS LAAS 7 avenue du colonel Roche F-31077 Toulouse France Université de Toulouse UPS INSA INP ISAE F-31077 Toulouse France.

In this paper, we show how the so-called diffusive representation can be used in order to identify nonlinear Volterra models of the form H (∂ t ) X = f ( u, X ) + v . Several methods are described, all being based on a suitable parameterization of H (∂ t ) by means of its γ-symbol. Following this idea, the complex dynamic nature of H (∂ t ) can be summarized by a few parameters on which the identification of the dynamic part of the model will focus. For illustration, we implement the methods on a concrete numerical example.

关键词： Least squares identification Sampled data Operators Convolution integral Continuous time systems Dynamic systems distributed-parameter systems

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Discrete mechanics optimal control (DMOC) and model predictive control (MPC) synthesis for reaction-diffusion process system with moving actuator

Discrete mechanics optimal control (DMOC) and model predicti...

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American Control Conference

作者： Stevan Dubljevic Marin Kobilarov James Ng Chemical & Materials Engineering Department University of Alberta AB T6G 2V4 Canada Control and Dynamics Systems California Institute of Technology Pasadena CA 91125 USA

ISBN: (纸本)9781424474264

This paper is concerned with the computation of optimal motion control as well as the optimal input injection policy of an actuator arm regulating the temperature in a reaction-diffusion system. The system has two dynamical components consisting of the arm mechanics with inertial, elastic and damping properties, which is driven by bounded mechanical actuation controls and an underlying reaction-diffusion system described by the parabolic PDE. The state of the actuator arm parametrizes the input injection operator of the parabolic PDE systems model and causes coupling between the two dynamical systems generally operating at different time scales. The method proposed in this paper is aimed at solving this coupled problem. The actuator mechanics and its control are achieved in the discrete mechanics and optimal control (DMOC) framework, while the input injection for the reaction diffusion system is calculated by the modal model predictive control (MMPC) algorithm suitable for the dissipative systems. The actuation arm policy and input to the parabolic PDE system include in its realization low-order discrete representation of the parabolic PDE evolution and incorporate optimality with respect to both the state of the PDE and the actuator displacement cost from current to some more optimal control position as well as naturally present input and PDE state constraints. The proposed actuation arm policy and optimal stabilization of the unstable reaction-diffusion system in the presence of constraints in the full state-feedback controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Moving Actuator Discrete Mechanics Optimal Control (DMOC) Model Predictive Control (MPC) Input/State Constraints

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Optimal scanning control of flexible structures in two-dimensional space

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第2期233卷 389-404页

作者： Sadek, Ibrahim Abdul-Hamid, Husein Scott, Julie Amer Univ Sharjah Dept Math & Stat Sharjah U Arab Emirates Univ Maryland UC Off Evaluat Res & Grants E Adelphi MD 20783 USA Qual Improvement Res & Biostat Support Blue Cross Blue Shield N Carolina Durham NC 27702 USA

A class of optimal control problems for hyperbolic systems in two-dimensional space is considered. An approach is proposed to damp the undesirable vibrations in the structures by pointwise moving force actuators extending over the spatial region occupied by the structure. A class of performance indices is introduced that includes functions of the state variable, its first and second-order space derivatives and first-order time derivative evaluated at a preassigned terminal time, and a suitable penalty term involving the control forces. A maximum principle is given for such general scanning control problem that facilitates the determination of the unique optimal control. A solution method is developed for the active vibration control of plates of general shape. The implementation of the method is presented and the effectiveness of a single moving force actuator is investigated and compared to a single fixed force actuator by a specific numerical example. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Moving actuators distributed-parameter systems Optimal control Maximum principle

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