LMIs in Control Systems

Duan, Guang‐Ren; Yu, Haihua

doi:10.1201/b15060

Cited by 237 publications

(60 citation statements)

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“…This problem is described in [ 20 , 21 , 25 , 41 ]. The ‘Blue Lady’ multidimensional model is described in detail also in e.g., [ 42 ].…”

Section: Lmi Controllermentioning

confidence: 99%

“…In [ 22 , 23 , 24 ] the authors describe LMI use in multidimensional systems with Fuzzy Logic controllers. In [ 25 ] the chapter about applications of a closed loop system shows results of computer simulations for a state space controller controlling the flight path of a missile. In [ 26 ] the authors use a Robust LMI controller with

that includes uncertainties, while [ 27 , 28 , 29 ] describe

norm minimization in controller synthesis.…”

Section: Introductionmentioning

confidence: 99%

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Effectiveness of Multidimensional Controllers Designated to Steering of the Motions of Ship at Low Speed

Gierusz

Rybczak

2020

Sensors

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The article described two full multidimensional controllers applied to steer a real vessel named ‘Blue Lady’ that is used by the Foundation for Safety of Navigation and Environment Protection at its training and research facility loacted at Silm lake in Poland. Both controllers were based on different approaches, but finally gave similar results. The first part describes the object to be controlled which is a training ship used for training of navigators in various conditions, areas and manoeuvres. This is followed by a short description of the theory for both controllers, Robust and Linear Matrix Inequalities (LMI). Next real time trials are described, which are 3 different manouvers for low velocities, executed by both LMI and Robust contrllers. In these trials ‘Blue Lady’ velocities, silhouete trajectory ans wind data are recorded. Finally the quality of work for both controllers is collected in two tables.

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“…This problem is described in [ 20 , 21 , 25 , 41 ]. The ‘Blue Lady’ multidimensional model is described in detail also in e.g., [ 42 ].…”

Section: Lmi Controllermentioning

confidence: 99%

that includes uncertainties, while [ 27 , 28 , 29 ] describe

norm minimization in controller synthesis.…”

Section: Introductionmentioning

confidence: 99%

Effectiveness of Multidimensional Controllers Designated to Steering of the Motions of Ship at Low Speed

Gierusz

Rybczak

2020

Sensors

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“…since M(ξ in )Ψ(ξ in ) = 0 by construction. Now, pre-and post multiplying the above by η a and η a , respectively, leads to (12) taking the definitions of η in and η out in (24) into account and the fact that:…”

Section: Theorem 2 (Regional Stabilization)mentioning

confidence: 99%

“…In the particular case of linear dynamical systems, a large number of stability and stabilization results are cast in terms of linear matrix inequality (LMI) constraints [6], which are numerically solved using dedicated software [30]. The LMI framework is a powerful tool for linear and nonlinear finitedimensional systems, since it can deal with a large diversity of control and systems theory problems such as robust stability, domain of attraction estimation, input-to-output performance, state or dynamic output-feedback control, and state estimation (see [6,7,32,18,13,24] among other references). As a result, LMIs have been successfully applied in a wide diversity of control oriented applications as, for instance, wind turbine operation, satellite attitude regulation, turbo-charged combustion engine control and bioprocess control and estimation [31,19].…”

Section: Introductionmentioning

confidence: 99%

Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions

Caldeira

Prieur

Coutinho

et al. 2018

European Journal of Control

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This paper addresses the boundary control problem of fluid transport in a Poiseuille flow taking the actuator dynamics into account. More precisely, sufficient stability conditions are derived to guarantee the exponential stability of a linear hyperbolic differential equation system subject to nonlinear quadratic dynamic boundary conditions by means of Lyapunov based techniques. Then, convex optimization problems in terms of linear matrix inequality constraints are derived to either estimate the closed-loop stability region or synthesize a robust control law ensuring the local closed-loop stability while estimating an admissible set of initial states. The proposed results are then applied to application-oriented examples to illustrate local stability and stabilization tools.

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“…Obviously, also optimality criteria such as robust H 2 and H∞ tasks can be taken into account by the same LMI-based design framework also considering output and state limitations, see[4,6].…”

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confidence: 99%

Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers

2020

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In real-life applications, dynamic systems are often subject to uncertainty due to model simplifications, measurement inaccuracy or approximation errors which can be mapped to specific parameters. Uncertainty in dynamic systems can come either in stochastic forms or as interval representations. The latter is applied if the uncertainty is bounded as it will be done in this paper. The main idea is to find a joint approach for an interval-based gain scheduling controller while simultaneously reducing overestimation by enclosing state intervals with the least amount of conservativity. The robust and/ or optimal control design is realized using linear matrix inequalities (LMIs) to find an efficient solution and aims at a guaranteed stabilization of the system dynamics over a predefined time horizon. A temporal reduction of the widths of intervals representing worst-case bounds of the system states at a specific point of time should occur due to asymptotic stability proven by the employed LMI-based design. However, for commonly used approaches in the computation of interval enclosures, those interval widths seemingly blow up due to the wrapping effect in many cases. To avoid this, we provide two interval enclosure techniques -an exploitation of cooperativity and an exponential approach -and discuss their applicability taking into account two real-life applications, a high-bay rack feeder and an inverse pendulum.

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LMIs in Control Systems

Cited by 237 publications

References 0 publications

Effectiveness of Multidimensional Controllers Designated to Steering of the Motions of Ship at Low Speed

Effectiveness of Multidimensional Controllers Designated to Steering of the Motions of Ship at Low Speed

Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions

Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers

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