Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints and matched input disturbances. A gain-scheduled dynamic output feedback controller, coupled with a disturbance observer to cancel out input disturbance effects, was augmented with an anti-windup compensator to locally stabilize the input-delay LPV system under saturation, model uncertainty, and exogenous disturbances. Sufficient delay-dependent conditions to asymptotically stabilize the closed-loop system were derived using Lyapunov-Krasovskii functionals and a modified generalized sector condition to address the input saturation nonlinearity. The level of disturbance rejection was characterized via the closed-loop induced L2-norm of the closed-loop system in the form of linear matrix inequality (LMI) constraints. The results are examined in the context of the mean arterial pressure (MAP) control in the clinical resuscitation of critical hypotensive patients. The MAP variation response to the injection of vasopressor drugs was modeled as an LPV system with a varying input delay and was susceptible to model uncertainty and input/output disturbances. A Bayesian filtering method known as the cubature Kalman filter (CKF) was used to estimate the instantaneous values of the parameters. The varying delay was estimated via a multiple-model approach. The proposed input-delay LPV control was validated in closed-loop simulations to demonstrate its merits and capabilities in the presence of drug administration constraints.

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“…Proof. The following Lyapunov-Krasovskii functional (LKF) candidate is considered (Salavati et al, 2019)…”

Section: Resultsmentioning

confidence: 99%

“…It leads to poor performance and in severe cases can induce oscillations and cause instability of the closed-loop system (Fridman, 2014). The stability and performance of time-delay LPV systems have been studied extensively in the literature (Briat, 2015;Salavati et al, 2019;Wang et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Observer-Based Control of LPV Systems with Input Delay and Saturation and Matched Disturbances via a Generalized Sector Condition

Salavati

Grigoriadis

Franchek

2021

Front. Control Eng.

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“…Remark 1: From the form of system's perspective, it is worth pointing out that NPV systems can be reduced to NPV systems (Saeed et al, 2019) and nonlinear systems (Bai et al, 2019). For NPV systems in equation ( 7), if we remove the state variable in systems' matrices, the NPV systems can be turned into linear parameter-varying (LPV) systems.…”

Section: Problem Descriptionmentioning

confidence: 99%

Robust observer-based controller design for nonlinear parameter-varying systems with uncertainty and external disturbances

Zhu

Yang

Bai

et al. 2023

Transactions of the Institute of Measurement and Control

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This article investigates the robust observer-based controller design problem for nonlinear parameter-varying systems subject to uncertainty and external disturbances. First, a novel augment vector is constructed, and an corresponding model of the resulting closed-loop system is obtained. Second, by applying the Lyapunov stability theory, a class of state-and-parameter-dependent robust asymptotic stability criteria is established, and the state-and-parameter-dependent sufficient conditions for the design of the robust observer-based controller are then acquired to guarantee the stability of the resulting closed-loop system, which can be effectively solved by sum-of-squares techniques. Different from the previous researches, the proposed control algorithm enables the state-and-parameter-dependent observer and the state-and-parameter-dependent controller design of the nonlinear parameter-varying systems to enjoy the advantage of separate design. The advantage can effectively reduce the computational complexity. Finally, simulation results demonstrate that the proposed robust observer-based controller shows improved performance in presence of uncertainty and external disturbances.

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“…Linear parameter-varying (LPV) systems are linear dynamical systems whose dynamic characteristics depend on a time-varying measurable scheduling parameter vector. In this context of the LPV systems framework, the scheduling parameter vector captures the dynamics of nonlinear or time-varying systems in a systematic fashion (Briat, 2014) and has found applications in flight control (Lu et al, 2006), automotive systems (Tasoujian et al, 2016;Salavati et al, 2019), energy (Bianchi et al, 2005), and biomedical systems (Colmegna et al, 2015;Tasoujian et al, 2019b). Traditional gain-scheduling controllers are designed by interpolation of separately designed controllers for the system's operation points.…”

Section: Introductionmentioning

confidence: 99%

An Improved Integral Inequality for Delay-Dependent Gain-Scheduled LPV Control

Tasoujian

Grigoriadis

Franchek

2021

Front. Control Eng.

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The present work examines the delay-dependent gain-scheduling feedback control with guaranteed closed-loop stability and induced L2 norm performance for continuous-time linear parameter-varying (LPV) systems with arbitrary time-varying delay. An extension of Lyapunov stability utilizing Krasovskii functionals is considered to derive stability analysis and synthesis conditions for delay-dependent dynamic output feedback LPV control design. The main challenges associated with this approach are selecting appropriate Lyapunov-Krasovskii functionals (LKFs) and finding efficient integral inequalities to bound the derivative of the LKF. Accordingly, a novel modified parameter-dependent LKF candidate along with an affine version of Jensen’s inequality bounding technique are employed leading to the derivation of less conservative sufficient conditions expressed in terms of convex linear matrix inequalities (LMIs). The proposed methodology is compared with past work in the literature in terms of conservatism reduction and performance improvement through a numerical example. Finally, the application of the proposed output-feedback LPV control design is evaluated on the automated mean arterial blood pressure (MAP) regulation in critical patient resuscitation via vasoactive drug infusion. Closed-loop simulation results are presented to illustrate the potential of the introduced LPV gain-scheduling design to provide MAP set-point tracking in the presence of disturbances and varying input delays.

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Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

Cited by 11 publications

References 37 publications

Observer-Based Control of LPV Systems with Input Delay and Saturation and Matched Disturbances via a Generalized Sector Condition

Observer-Based Control of LPV Systems with Input Delay and Saturation and Matched Disturbances via a Generalized Sector Condition

Robust observer-based controller design for nonlinear parameter-varying systems with uncertainty and external disturbances

An Improved Integral Inequality for Delay-Dependent Gain-Scheduled LPV Control

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