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63rd IEEE Conference on Decision and control, CDC 2024

作者： Gramlich, Dennis Gao, Sheng Zhang, Hao Scherer, Carsten W. Ebenbauer, Christian Rwth Aachen University Chair of Intelligent Control Systems Aachen52074 Germany Tongji University College of Electronic and Information Engineering Department of Control Science and Engineering Shanghai200092 China University of Stuttgart Chair of Mathematical Systems Theory Stuttgart70569 Germany

ISBN: (纸本)9798350316339

We present a simple and effective way to account for non-convex costs and constraints in state feedback synthesis, and an interpretation for the variables in which state feedback synthesis is typically convex. We achieve this by deriving the controller design using moment matrices of state and input. It turns out that this approach allows the consideration of non-convex constraints by relaxing them as constraints on the expected value of quadratic functions, and that the variables in which state feedback synthesis is typically convexified can be identified with blocks of these moment matrices. The employed relaxation can lead to constraint violation along sample paths. © 2024 IEEE.

关键词： State feedback

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On moment relaxations for linear state feedback controller synthesis with non-convex quadratic costs and constraints

On moment relaxations for linear state feedback controller s...

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IEEE Conference on Decision and control

作者： Dennis Gramlich Sheng Gao Hao Zhang Carsten W. Scherer Christian Ebenbauer Chair of Intelligent Control Systems RWTH Aachen University Aachen Germany Department of Control Science and Engineering College of Electronic and Information Engineering Tongji University Shanghai P. R. China Chair of Mathematical Systems Theory University of Stuttgart Stuttgart Germany

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

关键词： State feedback Costs Additives Noise Quadratic programming Time-varying systems

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On moment relaxations for linear state feedback controller synthesis with non-convex quadratic costs and constraints

arXiv

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arXiv 2024年

作者： Gramlich, Dennis Gao, Sheng Zhang, Hao Scherer, Carsten W. Ebenbauer, Christian Intelligent Control Systems RWTH Aachen University Aachen52074 Germany College of Electronic and Information Engineering the Department of Control Science and Engineering Tongji University Shanghai200092 China Chair of Mathematical Systems Theory University of Stuttgart Stuttgart70569 Germany

We present a simple and effective way to account for non-convex costs and constraints in state feedback synthesis, and an interpretation for the variables in which state feedback synthesis is typically convex. We achieve this by deriving the controller design using moment matrices of state and input. It turns out that this approach allows the consideration of non-convex constraints by relaxing them as expectation constraints, and that the variables in which state feedback synthesis is typically convexified can be identified with blocks of these moment matrices. © 2024, CC BY.

关键词： State feedback

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Flatness-based analysis and control design for 2 × 2 hyperbolic PDEs with nonlinear boundary dynamics

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IFAC-PapersOnLine 2022年第26期55卷 13-19页

作者： F. Woittennek A. Irscheid N. Gehring Institute of Automation and Control Engineering UMIT Tirol Hall in Tirol Austria Chair of Systems Theory and Control Engineering Saarland University Saarbrücken Germany Institute of Automatic Control and Control Systems Technology Johannes Kepler University Linz Linz Austria

Distributed-parameter systems represented by linear one-dimensional 2 × 2 hyperbolic PDEs with nonlinear finite-dimensional differentially flat dynamics at one boundary and control acting linearly via the opposite boundary are considered. Flatness of the overall system, deduced from the flatness of the boundary system, allows for the parametrization of the systems solutions by the trajectory of a flat output. The state associated with this parametrization corresponds to the restriction of the flat-output trajectory to a compact interval. This state is intrinsically linked to a nonlinear hyperbolic controller form and associated with the original system variables by an invertible transformation. Moreover, it allows for immediate and constructive reachability analysis. State feedback for tracking a desired reference trajectory is achieved by choosing arbitrary stable closed-loop dynamics. A numerical example illustrates the control performance for different choices of the closed-loop dynamics.

关键词： hyperbolic system flatness reachability nonlinear controller form state feedback

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Gauss’s principle and tracking control of underactuated mechanical systems

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IFAC-PapersOnLine 2021年第19期54卷 365-370页

作者： Matthias Konz Joachim Rudolph Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany

Gauss’s principle of least constraint is used to derive equations of motion. The principle is then used to motivate a template for the closed loop of the (tracking) controlled system. The control law arises from minimization of the distance between the controlled model and the template in the sense of least constraint. The control template is derived and analysed for the example of a free rigid body. This leads to quite natural formulations of its controlled inertia, damping and stiffness. This template is then used to compute a controller for a quadcopter, an underactuated system. A simulation result for an aerobatic maneuver demonstrates quite good performance of the proposed controller even though there is no formal proof of stability.

关键词： mechanics first-principles energy methods tracking control rigid body quadcopter

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Trajectory Tracking control for a Class of 2×2 Hyperbolic PDE-ODE systems

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IFAC-PapersOnLine 2021年第9期54卷 416-421页

作者： A. Irscheid N. Gehring J. Rudolph Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany Institute of Automatic Control and Control Systems Technology Johannes Kepler University 4040 Linz Austria

This paper introduces an approach to trajectory tracking control of linear 2×2 hyperbolic partial differential equations (PDEs) actuated at one boundary and coupled with ordinary differential equations (ODEs) at the other one. Well-known state feedback methods that benefit from so-called backstepping coordinates are limited to the case of boundary conditions consisting of linear time-invariant ODEs. In a first step, the new approach is introduced for this restricted class of linear dynamic boundary conditions. It is shown that tracking control is immediately achieved by a surprisingly simple, yet elegant, modification of a stabilizing state feedback. Then, a direct extension for solving trajectory tracking problems for a class of nonlinear ODEs at the unactuated boundary is discussed. Numerical studies underline the performance of the proposed method.

关键词： tracking control PDE-ODE systems boundary control predictor feedback distributed parameter systems hyperbolic systems

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Prescribed-time control for a class of semilinear hyperbolic PDE-ODE systems

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IFAC-PapersOnLine 2022年第26期55卷 47-52页

作者： Abdurrahman Irscheid Nicolas Espitia Wilfrid Perruquetti Joachim Rudolph Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany CNRS Centrale Lille Univ. Lille F-59000 Lille France Centrale Lille F-59000 Lille France

A prediction-based controller is shown to achieve prescribed-time stabilization of a nonlinear infinite-dimensional system, which consists of a general boundary controlled first-order semilinear hyperbolic PDE that is bidirectionally interconnected with nonlinear ODEs at its unactuated boundary. The approach uses a coordinate transformation to map the nonlinear system into a form suitable for control. In particular, this transformation is based on predictions of system trajectories, which can be obtained by solving a general nonlinear Volterra integro-differential equation. Then, a prediction-based controller is designed to stabilize the system in prescribed-time. Numerical simulations illustrate the performance of both the prescribed-time controller and an asymptotically stabilizing one, which follows as a special case.

关键词： distributed parameter systems nonlinear PDE-ODE systems semilinear hyperbolic systems boundary control prescribed-time control prediction

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Observer design for 2×2 linear hyperbolic PDEs that are bidirectionally coupled with nonlinear ODEs

Observer design for 2×2 linear hyperbolic PDEs that are bid...

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European control Conference (ECC)

作者： Abdurrahman Irscheid Nicole Gehring Joachim Deutscher Joachim Rudolph Chair of Systems Theory and Control Engineering Saarland University Saarbrücken Germany Institute of Automatic Control and Control Systems Technology Johannes Kepler University Linz Austria Institute for Measurement Control and Microtechnology Ulm University Ulm Germany

A prediction-based observer is designed for systems consisting of 2×2 linear heterodirectional hyperbolic partial differential equations (PDEs) with collocated actuation and measurement at one boundary and bidirectional coupling with nonlinear ordinary differential equations (ODEs) at the other one. Following a preliminary backstepping transformation, a solution-based analysis of the plant allows to draw upon well-known results on the observer design for nonlinear ODEs. For that, the design is split into several steps, with a retarded observer for the ODE state and a prediction thereupon, thus significantly extending existing results for PDE-ODE systems. It is shown that the resulting error system admits a cascaded structure, from which (local) asymptotic convergence follows. Numerical studies underline the performance of the observer.

关键词： Couplings Backstepping Partial differential equations Europe Observers Ordinary differential equations Error correction codes

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Parametrization of algebraic differentiators for disturbance annihilation with an application to the differentiation of quantized signals ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 335-340页

作者： A. Othmane H. Mounier J. Rudolph Université Paris-Saclay CNRS CentraleSupélec Laboratoire des signaux et systèmes 91190 Gif-sur-Yvette France Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany

A method for the systematic parametrization of algebraic differentiators is introduced. It allows the annihilation of disturbances having transfer functions exhibiting repetitive peaks. Using McMahon's expansion for large zeros of Bessel functions, an approach reducing the number of free parameters of the differentiators from five to one is derived. The choice of the parameters is discussed in detail, and the existence of the parametrization for any such disturbance is proven. Error bounds for the annihilation of the repetitive peaks are also derived. The practical applicability of the approach is demonstrated in an experimental case study where the derivative of a quantized signal is numerically estimated using only an algebraic differentiator. A deterministic model for the quantization error which shows repetitive peaks in its transfer function is also proposed.

关键词： numerical differentiation quantized signals algebraic differentiators annihilation of repetitive peaks

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Observers for the Seidel–Herzel model of human autonomic-cardiorespiratory system ⁎

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IFAC-PapersOnLine 2021年第15期54卷 514-519页

作者： A. Othmane H. Mounier Université Paris-Saclay CNRS CentraleSupélec Laboratoire des signaux et systèmes 91190 Gif-sur-Yvette France Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany

The Seidel-Herzel model of the autonomic-cardiorespiratory system is used in this work to derive three observers for the estimation of the concentrations of the neurotransmitters and external excitations of the sympathetic and parasympathetic systems. The observers require noninvasive measurements of respiration and blood pressure which simplifies the development of patient-specific applications. The errors stemming from model approximations and uncertain parameters are analyzed. The applicability of the approach is discussed in a simulation study.

关键词： Nonlinear observers physiology autonomic-cardiorespiratory system

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