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Soft-minimum and soft-maximum barrier functions for safety with

AUTOMATICA 2025年 171卷

作者： Rabiee, Pedram Hoagg, Jesse B. Univ Kentucky Dept Mech & Aerosp Engn Lexington KY 40506 USA

This paper presents two new control approaches for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The first control method relies on a soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that the control is continuous and satisfies the actuator constraints, and a subset of the safe set is forward invariant under the control. Next, we extend this method to allow from multiple backup controls. This second approach relies on a combined soft-maximum/softminimum barrier function, and it has properties similar to the first. We demonstrate these controls on numerical simulations of an inverted pendulum and a nonholonomic ground robot. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Control of constrained systems optimization-based controller synthesis Nonlinear predictive control Safety

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Trajectory tracking: A novel TMPC strategy for dynamic target management

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AUTOMATICA 2025年 177卷

作者： Adelirad, Masoud Afzalian, Ali A. Shahid Beheshti Univ Abbaspour Sch Eng Dept Elect Engn Tehran Iran

This paper presents a novel Tracking Model Predictive Control (TMPC) strategy, specifically designed for managing systems that track targets with unpredictable (priori unknown) trajectories. Traditional Model Predictive Control (MPC) is adept at set point tracking;however, it struggles with maintaining recursive feasibility when faced with variable references. Our TMPC approach addresses this by introducing a relaxation mechanism to the tracking problem's convergence conditions, which ensures the tracking error reduction within a predefined period of p sample times. To facilitate this, TMPC employs a tracking hyperplane as a constraint over the system's initial p-step trajectory, guaranteeing the convergence of the tracking error. We also introduce the concepts of the minimal p-step reachable set for the system and the maximal p-step reachable set for the target. These sets are pivotal in determining whether the system can feasibly track the target. Our approach assures recursive feasibility and the convergence of the tracking error within each p-sample time period. The efficacy of the TMPC strategy is demonstrated through simulation results and further substantiated by experimental validation on a laboratory-scale quadruple tank system. The outcomes confirm that TMPC is a robust solution for tracking control challenges in systems with dynamic targets. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： optimization-based controller synthesis Tracking Control of constrained systems Tracking hyperplane Reachable set Tracking tube

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Observers for systems with nonlinearities satisfying incremental quadratic constraints

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AUTOMATICA 2011年第7期47卷 1339-1348页

作者： Acikmese, Behcet Corless, Martin CALTECH Jet Prop Lab Pasadena CA 91109 USA Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA

We consider the problem of designing observers to asymptotically estimate the state of a system whose nonlinear time-varying terms satisfy an incremental quadratic inequality that is parameterized by a set of multiplier matrices. Observer design is reduced to solving linear matrix inequalities for the observer gain matrices. The proposed observers guarantee exponential convergence of the state estimation error to zero. In addition to considering a larger class of nonlinearities than previously considered, this paper unifies earlier related results in the literature. The results are illustrated by application to several examples. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Nonlinear observer and filter design Application of nonlinear analysis and design optimization-based controller synthesis Linear matrix inequalities

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Robust self-triggered MPC for constrained linear systems: A tube-based approach

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AUTOMATICA 2016年第0期72卷 73-83页

作者： Brunner, Florian David Heemels, Maurice Allgoewer, Frank Univ Stuttgart Inst Syst Theory & Automat Control Stuttgart Germany Eindhoven Univ Technol Dept Mech Engn Control Syst Technol Grp Eindhoven Netherlands

We propose a robust self-triggered control algorithm for constrained linear discrete-time systems subject to additive disturbances based on MPC. At every sampling instant, the controller provides both the next sampling instant, as well as the inputs that are applied to the system until the next sampling instant. By maximizing the inter-sampling time subject to bounds on the MPC value function, the average sampling frequency in the closed-loop system is decreased while guaranteeing an upper bound on the performance loss when compared with an MPC scheme sampling at every point in time. Robust constraint satisfaction is achieved by tightening input and state constraints based on a Tube MPC approach. Moreover, a compact set in the state space, which is a parameter in the MPC scheme, is shown to be robustly asymptotically stabilized. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： optimization-based controller synthesis Networked control systems

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Selective modal control for vibration reduction in flexible structures

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AUTOMATICA 2017年 75卷 282-287页

作者： Canciello, Giacomo Cavallo, Alberto Seconda Univ Napoli Dipartimento Ingn Ind & Informaz I-81031 Aversa CE Italy

The design of a controller for selective reduction of vibrations in flexible low-damped structures is presented. The objective of the active feedback control law is to increase damping of selected modes only, in frequency regions where a disturbance is likely to produce largest effect. Moreover, the stabilizing controller is required to be band-pass, in order to filter out high-frequency sensor noise and low-frequency accelerometer drift, and stable to increase robustness to uncertain parameters. The control design is based on the Inverse Optimal Design approach, through the solution of a matrix Stein equation, resulting in the solution of an optimal H-infinity control problem. A grey-box identification approach of the authors is employed for obtaining the model from experimental data or from detailed Finite Element Model (FEM) simulators. The problem of optimal actuator/sensor location is also addressed. Detailed simulation results are provided to show the effectiveness of the strategy. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Large scale optimization problems and methods Vibration control for flexible structures optimization-based controller synthesis Infinite-dimensional systems Identification methods

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Distributed predictive control with minimization of mutual disturbances

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AUTOMATICA 2017年 77卷 31-43页

作者： Trodden, Paul A. Maestre, J. M. Univ Sheffield Dept Automat Control & Syst Engn Mappin St Sheffield S1 3JD S Yorkshire England Univ Seville Dept Syst Seville Spain Univ Seville Dept Automat Engn Seville Spain

In this paper, a distributed model predictive control scheme is proposed for linear, time-invariant dynamically coupled systems. Uniquely, controllers optimize state and input constraint sets, and exchange information about these - rather than planned state and control trajectories - in order to coordinate actions and reduce the effects of the mutual disturbances induced via dynamic coupling. Mutual disturbance rejection is by means of the tube-based model predictive control approach, with tubes optimized and terminal sets reconfigured on-line in response to the changing disturbance sets. Feasibility and exponential stability are guaranteed under provided sufficient conditions on non-increase of the constraint set parameters. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Decentralization Time-invariant Control of constrained systems optimization-based controller synthesis Parametric optimization

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Design of Marx generators as a structured eigenvalue assignment

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AUTOMATICA 2014年第10期50卷 2709-2717页

作者： Galeani, Sergio Henrion, Didier Jacquemard, Alain Zaccarian, Luca Univ Roma Tor Vergata DICII I-00173 Rome Italy CNRS LAAS F-31400 Toulouse France Univ Toulouse LAAS F-31400 Toulouse France Czech Tech Univ CR-16635 Prague Czech Republic Univ Bourgogne IMB CNRS F-21078 Dijon France Wolfgang Pauli Inst Vienna Austria Univ Trento Dipartimento Ingn Ind Trento Italy

We consider the design problem for a Marx generator electrical network, a pulsed power generator. We show that the components design can be conveniently cast as a structured real eigenvalue assignment with significantly lower dimension than the state size of the Marx circuit. Then we present two possible approaches to determine its solutions. A first symbolic approach consists in the use of Grobner basis representations, which allows us to compute all the (finitely many) solutions. A second approach is based on convexification of a nonconvex optimization problem with polynomial constraints. We also comment on the conjecture that for any number of stages the problem has finitely many solutions, which is a necessary assumption for the proposed methods to converge. We regard the proof of this conjecture as an interesting challenge of general interest in the real algebraic geometry field. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Experiment design Structured eigenvalue assignment Design methodologies Modeling operation and control of power systems optimization-based controller synthesis

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Networked stabilization for multi-input systems over quantized fading channels

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AUTOMATICA 2015年 61卷 1-8页

作者： Gu, Guoxiang Wan, Shuang Qiu, Li Louisiana State Univ Sch Elect Engn & Comp Sci Baton Rouge LA 70803 USA Zhejiang Univ Sci & Techonol Sch Automat & Elect Engn Hangzhou 310023 Zhejiang Peoples R China Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Kowloon Hong Kong Peoples R China

This paper studies feedback stabilization for networked control systems (NCSs) over quantized fading channels placed at the plant input, which cover both logarithmic quantization and packet drop in the actuator channel. The notion of mean-square (MS) stability is developed in the input output setting, and the MS stabilizability is studied for both single-input (SI) and multi-input (MI) systems under state feedback. A necessary and sufficient condition is derived for the MS stabilizability of the NCS over the quantized fading channel by using channel resource allocation. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Networked control systems Optimal controller synthesis for systems with uncertainties optimization-based controller synthesis Stochastic control synthesis of stochastic systems

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Scheduled control for robust attenuation of non-stationary sinusoidal disturbances with measurable frequencies

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AUTOMATICA 2011年第3期47卷 504-514页

作者： Koroglu, Hakan Scherer, Carsten W. King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran 31261 Saudi Arabia Univ Stuttgart Dept Math D-70569 Stuttgart Germany

Attenuation of sinusoidal disturbances with uncertain yet online measurable frequencies is considered. The disturbances are modeled as the outputs of an undisturbed parameter-dependent exogenous system with a skew-symmetric system matrix, obtained in response to nonzero initial conditions. The problem is formulated for a parameter-dependent plant as the synthesis of a parameter-dependent controller in a way to ensure internal stability as well as a desired level of steady-state disturbance attenuation in the face of all admissible parameter variations. The solvability of this problem is first related to the existence of bounded solutions to a matrix differential regulator equation subject to an asymptotic norm constraint. Reformulating this as a parameter-dependent state-feedback like synthesis, based on which suitable solutions to the differential regulator equation can be obtained online, tractable solvability conditions are then provided in the form of parameter-dependent matrix inequalities. controllers that solve the generalized asymptotic regulation problem are also parameterized in terms of the suitable solutions of the differential regulator equation and some free parameter-dependent matrices that are to be designed off-line to ensure stability. A procedure is then developed to design the free parameters in a way to achieve desirable transient behavior. The use of the developed synthesis procedure is illustrated on a simplified version of the course control problem in ship steering. (c) 2011 Elsevier Ltd. All rights reserved.

关键词： Asymptotic (output) regulation Disturbance rejection/attenuation optimization-based controller synthesis Linear matrix inequalities (LMI) Linear parameterically varying (LPV) methodologies H-2 synthesis

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A polynomial eigenvalue test for checking DLMI constraints

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AUTOMATICA 2023年 148卷

作者： Omar Baldissera, Joao Victor Harrop Galvao, Roberto Kawakami Gabriel, Gabriela Werner Inst Tecnol Aeronaut Elect Engn Div BR-12228900 Sao Jose Dos Campos SP Brazil

In order to obtain an optimization problem with a finite number of variables and constraints, Differential Linear Matrix Inequalities (DLMIs) are usually recast into the form of a system of LMIs. To this end, a typical approach consists in parameterizing the solution as a linear combination of known functions, with weights to be optimized. The constraints are then imposed on a finite set of discrete time points. This technical communique is concerned with the problem of checking whether a matrix polynomial solution obtained in this manner satisfies the original DLMI constraints. To this end, a novel test based on the concept of polynomial eigenvalues is presented. The proposed test is illustrated through a numerical example based on the H-infinity synthesis of a sampled-data controller. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Differential Linear Matrix Inequalities Polynomial eigenvalues Sampled-data control optimization-based controller synthesis

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