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Optimal Control of the Viscous Burgers Equation by the Hopf-Cole Transformation and Its Properties

IFAC-PapersOnLine 2016年第18期49卷 134-139页

作者： Iwamoto T. Fujimoto K. Department of Aeronautics and Astronautics Graduate School of Engineering Kyoto University Kyoto 615-840 Japan

This paper discusses an optimal control problem for the viscous Burgers equation using the Hopf-Cole transformation. Using this transformation, an optimal control problem for the Burgers equation is transformed into that for a linear heat equation. Although this transformation makes the boundary condition complicated, we use a state feedback to overcome the difficulty. Using the state feedback, an exact solution of the heat equation is obtained by Laplace transformation which enables us to obtain the optimal control input for the heat equation exactly. In fact, it is obtained by a solution of a well-known Fredholm integral equation. Furthermore, we discuss how to choose an achievable desired terminal state from the controllability point of view. In addition, we exhibit the effectiveness of the proposed approach through a numerical simulation. It verifies that when the solution of the heat equation at terminal time converges to its desired value, that of the corresponding viscous Burgers equation also converges to the desired one. © 2016

关键词： distributed parameter systems optimal control state feedback

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Design of decentralized local controllers of spatially distributed systems by approximation of feedback kernels

Design of decentralized local controllers of spatially distr...

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American Control Conference (ACC)

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781467386821

This paper considers the problem of decentralized controllers for spatially distributed systems. The spatially distributed systems are assumed to have a network of control units and the decentralized design is solved by approximation of the feedback kernels. By first obtaining the full state feedback controllers corresponding to the centralized design, the individual feedback operators are numerically approximated by the product of static feedback gains with spatial delta functions representing the spatial distribution of the sensing devices. The resulting kernel approximation produces both the interconnection topology between the control units and their interconnection strengths. Since the feedback kernels are themselves based on quadratic control costs, then the kernel approximation method results in a suboptimal controller design with a significantly improved communication costs that reduces the information exchange between the control units. As a special case of a SISO system, the kernel approximation can also provide an optimal sensor location with respect to the energy of the resulting closed loop system. Extensive numerical studies for a diffusion partial differential equation (PDE) in one spatial dimension having four collocated actuator/sensor pairs along with the joint sensor and static gain optimization of a SISO diffusion PDE are included.

关键词： distributed parameter systems distributed local controllers networked systems kernel approximation

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Observability and Controllability Analysis of Pipeline systems

Observability and Controllability Analysis of Pipeline Syste...

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2nd International Conference on Industrial Informatics - Computing Technology, Intelligent Technology, Industrial Information Integration (ICIICII)

作者： Lei, Cheng Li, Xiangshun Wei, Di Wuhan Univ Technol Sch Automat Wuhan 430070 Peoples R China

ISBN: (纸本)9781509035755

Pipeline systems are widely applied in the areas of power, chemistry and petroleum. Model-based leak detection methods for the pipeline systems get more and more attentions. Among these model-based methods, the state observer and state feedback based methods are usually used. While the observability and controllability are prerequisites in using these methods. In this paper, the observability and controllability of the pipeline systems are analyzed. The pipeline systems are modeled as distributed parameter systems and the hyperbolic PDEs are established. The theorem is proposed to determine the observability and controllability of the systems without calculating the rank of observability and controllability matrices. An illustrative example is provided to show the validity and effectiveness of the results.

关键词： observability controllability pipeline systems distributed parameter systems hyperbolic PDEs

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Cascade Balance-Based Adaptive Control of Heating System - Simulation Validation 21

Cascade Balance-Based Adaptive Control of Heating System - S...

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21st International Conference on Methods and Models in Automation and Robotics (MMAR)

作者： Fratczak, Michal Czubasiewicz, Rafal Silesian Tech Univ Fac Automat Control Elect & Comp Sci Inst Automat Control Gliwice Poland

ISBN: (纸本)9781509018666

This paper is dedicated to simulation validation of cascade control structure for heating system consisting of single heat source and single heat receiver. In this structure, two Balance-Based Adaptive Controllers are applied. One of them has the conventional form while the second one (so-called distributed parameter Balance-Based Adaptive Controller operating in primary loop) is derived based on simplified distributed parameter modeling of plate heat exchanger. Modeling of heating system is based on measurement data collected from real laboratory plant and the simulation validation shows significant superiority of the suggested control approach in terms of control performance.

关键词： balance-based adaptive control heating systems control cascade control distributed parameter systems

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Gradient-based schemes of mobile sensor guidance for estimating spatially distributed systems in hazardous environments using value of information 55

Gradient-based schemes of mobile sensor guidance for estimat...

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55th IEEE Conference on Decision and Control (CDC)

作者： Demetriou, Michael A. WPI Aerosp Engn Worcester MA 01609 USA

ISBN: (纸本)9781509018376

In many situations, a mobile sensor must traverse in hazardous environments to collect information about spatially distributed processes. Without any constraints, the sensor will be guided in spatial locations that tend to improve the performance of the state estimator. This translates to larger values of the state estimation error. Such a guidance is information-sensitive as the sensor seeks "more" useful information within the spatial region. However, when exposure to hazardous environments affect the reliability and life-expectancy of the sensor, then a modification to the guidance must be considered in order to increase the life-expectancy of the sensor. Assuming that the cumulative exposure to the spatial field has a limit, beyond of which the sensor is rendered inoperable, then a modification to the information-sensitive guidance is warranted in order to prolong the life of the sensor. This of course compromises the value of information as an information-averse guidance will certainly prolong the life of a sensor, but the sensor will provide measurements with reduced value for the estimator. These concerns are considered here and a sensor guidance scheme is proposed that provides information-sensitive guidance when the accumulated exposure is below a user-defined limit and then switches to an information-averse guidance in order to prolong the life-expectancy of the sensor. Numerical studies for a diffusion partial differential equation with a single mobile sensor are provided to provide some insights on the modified sensor guidance policy and its increased life expectancy.

关键词： distributed parameter systems mobile sensors gradient schemes sensor guidance

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Design of damping for optimal energy dissipation of vibrations 55

Design of damping for optimal energy dissipation of vibratio...

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55th IEEE Conference on Decision and Control (CDC)

作者： Morris, Kirsten A. Vest, Ambroise Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Lycee Henri Poincare Nancy France

ISBN: (纸本)9781509018376

In control of vibrations, the location, size, distribution and number of actuating and sensing devices are part of the controller design problem. For instance, in control of flexible structures and acoustic noise reduction, both the type of actuators and sensors, as well as their locations, can be chosen. Furthermore, due to advances in materials, the shape of the hardware is sometimes also a design variable. Previous work on optimal actuator location is generalized to include the situation where the actuator affects the internal dynamics of the system, and also for the design of optimal passive damping. Two examples are provided to illustrate the applicability of the result.

关键词： distributed parameter systems optimal actuator location optimal damping linear-quadratic H-2-control spatial disturbances

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BOUNDARY CONTROL OF THE BLACK-SCHOLES PDE FOR OPTION DYNAMICS STABILIZATION

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ANNALS OF FINANCIAL ECONOMICS 2016年第2期11卷

作者： Rigatos, Gerasimos G. Ind Syst Inst Unit Ind Automat Rion 26504 Greece

The objective of the paper is to develop a boundary control method for the Black-Scholes PDE which describes option dynamics. It is shown that the procedure for numerical solution of Black-Scholes PDE results into a set of nonlinear ordinary differential equations (ODEs) and an associated state equations model. For the local subsystems, into which a Black-Scholes PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the Black-Scholes PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the Black-Scholes PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the Black-Scholes PDE system so as to assure that all its state variables will converge to the desirable setpoints.

关键词： Black-Scholes PDE options pricing differential flatness theory distributed parameter systems nonlinear feedback control

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ADAPTIVE TRACKING CONTROL FOR LINEAR INFINITE DIMENSIONAL systems

ADAPTIVE TRACKING CONTROL FOR LINEAR INFINITE DIMENSIONAL SY...

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ASME Conference on Smart Materials, Adaptive Structures and Intelligent systems

作者： Balas, Mark J. Frost, Susan A. Embry Riddle Aeronaut Univ Daytona Beach FL 32114 USA NASA Ames Res Ctr Moffett Field CA 94035 USA

ISBN: (纸本)9780791850497

Tracking an ensemble of basic signals is often required of control systems in general. Here we are given a linear continuous-time infinite-dimensional plant on a Hilbert space and a space of tracking signals generated by a finite basis, and we show that there exists a stabilizing direct adaptive control law that will stabilize the plant and cause it to asymptotically track any member of this collection of signals. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. There is no state or parameter estimation used in this adaptive approach. Our results are illustrated by adaptive control of general linear diffusion systems.

关键词： Tracking control Diffusion (Physics) Control systems parameter estimation Adaptive control distributed parameter systems Signals

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Computational and Analog Modeling of Parabolic Transport Equations using Cellular Neural Networks 20

Computational and Analog Modeling of Parabolic Transport Equ...

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20th International Conference on System Theory, Control and Computing (ICSTCC)

作者： Danciu, Daniela Univ Craiova Dept Automat & Elect 13 AI Cuza Str RO-200585 Craiova Romania

ISBN: (纸本)9781509027200

This paper is concerned with the numerical and analog modeling issues for a class of parabolic transport equations of the type reaction-advection-diffusion. The computational procedure relies on the Method of Lines concept and the canonical cell-based neural networks paradigm. It is derived from a recently proposed procedure for solving hyperbolic propagation equations with non-standard boundary conditions. The resulted highly structured and repetitive computational device allows both computational and analog modeling of the considered distributed parameter system. The procedure is applied to a nonlinear bioreactor distributed parameter model of the type reaction-advection-diffusion with Hadane kinetic function.

关键词： Parabolic partial differential equations distributed parameter systems Method of Lines Cellular Neural Networks Numerical modeling

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NASA Technical Reports Server (Ntrs) 20110015951: Flight Test of Orthogonal Square Wave Inputs for Hybrid-Wing-Body parameter Estimation

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2016年

NASA Technical Reports Server (Ntrs) 20110015951: Flight Test of Orthogonal Square Wave Inputs for Hybrid-Wing-Body parameter Estimation by NASA Technical Reports Server (Ntrs); published by

关键词： (ntrs) 20110015951: control equipment control surfaces distributed parameter systems estimation flight flight control flight tests hybrid-wing-body nasa technical reports server (ntrs) noise generators proving ratnayake, nalin a. square waves taylor, brian r. wings

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