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Design of the Impulsive Goodwin's Oscillator in 1-cycle

IFAC-PapersOnLine 2023年第2期56卷 6660-6665页

作者： Alexander Medvedev Anton V. Proskurnikov Zhanybai T. Zhusubaliyev Information Technology Uppsala University SE-752 37 Uppsala Sweden the Department of Electronics and Telecommunications Politecnico di Torino Turin Italy 10129 Zhanybai T. Zhusubaliyev is with the Department of Computer Science International scientific Laboratory for Dynamics of Non-Smooth Systems Southwest State University Kursk Russia

This paper presents a systematic approach to design a hybrid oscillator that admits an orbitally stable periodic solution of a certain type with pre-defined parameters. The parsimonious structure of the Impulsive Goodwin's oscillator (IGO) is selected for the implementation due to its well-researched rich nonlinear dynamics. The IGO is a feedback interconnection of a positive third-order continuous-time LTI system and a nonlinear frequency and amplitude impulsive modulator. A design algorithm based on solving a bilinear matrix inequality is proposed yielding the slope values of the modulation functions that guarantee stability of the fixed point defining the designed periodic solution. Further, assuming Hill function parameterizaton of the pulse-modulated feedback, the parameters of those rendering the desired stationary properties are calculated. The character of perturbed solutions in vicinity of the fixed point is controlled through localization of the multipliers. The proposed design approach is illustrated by a numerical example. Bifurcation analysis of the resulting oscillator is performed to explore the nonlinear phenomena in vicinity of the designed dynamics.

关键词： Hybrid and switched systems modeling Event-based control Control in systems biology controller constraints and structure Application of nonlinear analysis and design

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A non-iterative approach to Linear Quadratic Static Output Feedback

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IFAC-PapersOnLine 2023年第2期56卷 9540-9545页

作者： Hadriano Morales Escamilla Paul Trodden Visakan Kadirkamanathan Department of Automatic Control and Systems Engineering ACSE The University of Sheffield Sheffield UK

This paper considers the problem of static output feedback (SOF) synthesis for linear time-invariant (LTI) systems. Static output feedback, and more generally structured controller synthesis, is of special interest to any industrial application where a reduced-order controller is desired, e.g., high-order systems, or a specific structure is to be imposed, i.e., distributed/decentralised control. A simple two-step process is proposed, solving one Riccati equation and one optimisation problem with linear matrix inequality (LMI) constraints, enabled via a dilation using the distance to the full-state feedback optimum gain. Numerical analysis shows considerable computational savings, with negligible differences in the performance, when compared to current iterative methods.

关键词： Output feedback control controller constraints and structure Linear multivariable systems Linear matrix inequalities Optimal Control Static controller synthesis S-procedure

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A convex set of robust D — stabilizing controllers using Cauchy's argument principle

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IFAC-PapersOnLine 2022年第25期55卷 49-54页

作者： Philippe Schuchert Alireza Karimi Laboratoire d'Automatique Ecole Polytechinique Fédérale de Lausanne (EPFL) Switzerland

A new approach is presented to obtain a convex set of robust D — stabilizing fixed structure controllers, relying on Cauchy's argument principle. A convex set of D — stabilizing controllers around an initial D — stabilizing controller for a multi-model set is represented by an infinite set of Linear Matrix Inequalities (LMIs). By appropriate sampling of the D — stability boundary, a Semi-Definite Programming (SDP) is proposed that can be integrated in other synthesis approaches to ensure D — stability along other design specifications. To showcase utility of the proposed approach, two different examples are given: a boost converter with multi-model uncertainty and a laser-beam system modeled by an identified finite impulse response.

关键词： controller constraints and structure Convex optimization Robust controller synthesis Data-based control

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Model predictive control for regular linear systems

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AUTOMATICA 2020年 119卷 109066-109066页

作者： Dubljevic, Stevan Humaloja, Jukka-Pekka Univ Alberta Chem & Mat Engn Dept Edmonton AB T6G 2V4 Canada Tampere Univ Comp Sci Math POB 692 Tampere 33014 Finland

The present work extends known finite-dimensional constrained optimal control realizations to the realm of well-posed regular linear infinite-dimensional systems modeled by partial differential equations. The structure-preserving Cayley-Tustin transformation is utilized to approximate the continuous-time system by a discrete-time model representation without using any spatial discretization or model reduction. The discrete-time model is utilized in the design of model predictive controller accounting for optimality, stabilization, and input and output/state constraints in an explicit way. The proposed model predictive controller is dual-mode in the sense that predictive controller steers the state to a set where exponentially stabilizing unconstrained feedback can be utilized without violating the constraints. The construction of the model predictive controller leads to a finite-dimensional constrained quadratic optimization problem easily solvable by standard numerical methods. Two representative examples of partial differential equations are considered. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Infinite-dimensional systems Modeling and control optimization controller constraints and structure Model predictive control Regular linear systems Cayley-Tustin transform

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Design of PI controllers for Irrigation Canals Based on Linear Matrix Inequalities

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WATER 2020年第3期12卷 855页

作者： Arauz, Teresa Maestre, Jose M. Tian, Xin Guan, Guanghua Univ Seville Dept Syst & Automat Engn Seville 41092 Spain Delft Univ Technol Dept Water Management Delft 2611 CD Netherlands KWR Water Res Inst Groningenhaven 7 Nieuwegein 3433 PE Netherlands Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China

A new Proportional-Integral (PI) tuning method based on Linear Matrix Inequalities (LMIs) is presented. In particular, an LMI-based optimal control problem is solved to obtain a sparse feedback that provides the PI tuning. The ASCE Test Canal 1 is used as a case study. Using a linearised model of the canal, different tunings for the design of the PI controller are developed and tested using the software Sobek. Furthermore, the proposed method is also compared with other tunings proposed for the same canal available in the literature. Our results show that the proposed method reduces by half the maximum errors with respect to other assessed alternatives and minimizes undesired mutual interactions between canal pools. Also, our method improves the optimality degree of the PI tuning by 30%. Therefore, it is concluded that the LMI based PI controllers lead to satisfactory performance in regulating water levels and canal flows/structure outflows, outperforming other tested alternatives, thus becoming a useful tool for irrigation canal control.

关键词： decentralized control controller constraints and structure multivariable systems irrigation canals PI design

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Divergent stutter bisimulation abstraction for controller synthesis with linear temporal logic specifications

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AUTOMATICA 2021年 130卷 109723-109723页

作者： Mohajerani, Sahar Malik, Robi Wintenberg, Andrew Lafortune, Stephane Ozay, Necmiye Chalmers Univ Technol Dept Elect Engn Gothenburg Sweden Univ Waikato Dept Software Engn Hamilton New Zealand Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

This paper proposes a method to synthesise controllers for systems with possibly infinite number of states that satisfy a specification given as an LTL\degrees. formula. A common approach to handle this problem is to first compute a finite-state abstraction of the original state space and then synthesise a controller for the abstraction. This paper proposes to use an abstraction method called divergent stutter bisimulation to abstract the state space of the system. As divergent stutter bisimulation factors out stuttering steps, it typically results in a coarser and therefore smaller abstraction, at the expense of not preserving the temporal "next'' operator. The paper leverages results about divergent stutter bisimulation from model checking and shows that divergent stutter bisimulation is a sound and complete abstraction method when synthesising controllers subject to specifications in LTL\degrees. (C) 2021 The Author(s). Published by Elsevier Ltd.

关键词： Control synthesis Computational issues controller constraints and structure Abstraction LTL specification

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Lifting to Passivity for H2-Gain-Scheduling Synthesis with Full Block Scalings 21st

Lifting to Passivity for H2-Gain-Scheduling Synthesis with F...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Roesinger, Christian A. Scherer, Carsten W. Univ Stuttgart Dept Math Stuttgart Germany

We focus on the H-2-gain-scheduling synthesis problem for time-varying parametric scheduling blocks with scalings. Recently, we have presented a solution of this problem for D- and positive real scalings by guaranteeing finiteness of the H-2-norm for the closed-loop system with suitable linear fractional plant and controller representations. In order to reduce conservatism, we extend these methods to full block scalings by designing a triangular scheduling function and by introducing a new lifting technique for gain-scheduled synthesis that enables convexification. Copyright (C) 2020 The Authors.

关键词： Linear parameter-varying systems controller constraints and structure Convex optimization

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Compositional synthesis of supervisors in the form of state machines and state maps

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AUTOMATICA 2017年 76卷 277-281页

作者： Mohajerani, Sahar Malik, Robi Fabian, Martin Volvo Cars Corp Vehicle Dynam & Act Safety Ctr Gothenburg Sweden Univ Waikato Dept Comp Sci Hamilton New Zealand Chalmers Dept Signals & Syst Gothenburg Sweden

This paper investigates the compositional abstraction-based synthesis of least restrictive, controllable, and nonblocking supervisors for discrete event systems that are given as a large number of finite-state machines. It compares a previous algorithm that synthesises modular supervisors in the form of state machines, with an alternative that records state maps after each abstraction step and uses these to control the system. The state map-based algorithm supports all abstraction methods used previously, and in addition allows for nondeterminism, hiding, and transition removal. It has been implemented in the software tool Supremica and applied to several large industrial models. The experimental results and the complexity analysis show that state maps can be computed efficiently and in many cases require less memory than state machine-based supervisors. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Discrete event systems Compositional synthesis controller constraints and structure Algorithms and software Computational issues

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Generalization of Tensor Product Model Transformation for Control Design

Generalization of Tensor Product Model Transformation for Co...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Kuti, Jozsef Galambos, Peter Baranyi, Peter Obuda Univ Antal Bejczy Ctr Intelligent Robot Becsi Ut 96-B H-1034 Budapest Hungary Budapest Univ Technol & Econ Dept Telecommun & Media Informat Magyar Tudosok Krt 2 H-1117 Budapest Hungary Szechenyi Istvan Univ Dept Informat Egyet Ter 1 H-9026 Gyor Hungary

The paper shows that the separated structure of parameter dependencies within the Polytopic Tensor-Product (TP) model can be exploited during the controller design by applying controller candidates that depend only on certain parameter sets. This approach combines the polytopic uncertainty and Parallel Distributed Compensation (PDC) concepts in such a way, that they become special cases of the proposed formulation. Motivated by this recognition and the fact that the separation of parameter dependencies increases the complexity and computational cost, the definition of Polytopic TP representation for LPV/qLPV models is relaxed. The new definition allows for the use of arbitrarily chosen parameter sets in the model according to the control goals and the separation can be performed only for these sets. Through the derivation, an appropriate transformation algorithm and the unique Affine TP model is introduced discussing the related concepts of tensor algebra and affine geometry as well. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Gain sheduling LPV methodologies controller constraints and structure TP model tranformation Polytopic model based control Polytopic TP model based control

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Sparse Memoryless LQR Design for Uncertain Linear Time-Delay Systems

Sparse Memoryless LQR Design for Uncertain Linear Time-Delay...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Bahavarnia, M. Motee, N. Lehigh Univ Dept Mech Engn & Mech Packard Lab Bethlehem PA 18015 USA

The sparse memoryless LQR design problem is formulated for uncertain linear time delay systems. In such a problem, the goal is to minimize a quadratic cost supplemented by sparsity-promoting term (weighted-l(1) in our case) subject to stability of closed-loop system under norm-bounded uncertainty. It is shown that such an optimization problem can be reformulated as a rank-constrained optimization problem which consists of convex constraints except one rank constraint. Utilizing the bi-linear rank penalty technique, the sparse memoryless LQR is designed. Numerous numerical results depict that there exists a trade-off between time delay and sparsification quality. In addition, the larger time-delay, the poorer performance sparsity trade-off is observed. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Linear systems Systems with time-delays controller constraints and structure Convex optimization

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