Observability criteria for impulsive control systems with applications to biomedical engineering processes

Rivadeneira, Pablo S.; Moog, Claude H.

doi:10.1016/j.automatica.2015.02.042

Cited by 44 publications

(22 citation statements)

References 16 publications

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“…Recently, impulsive control has provided an effective approach for a class of dynamical systems including biomedical engineering, robotic manipulators, formation control and neural networks [2,8,10,11,19,25,35,36,40]. For example, in [25], nonlinear impulsive control could be applied to dynamical systems from biomedical engineering processes. In [10], impulsive control have been considered to synchronize neural networks with reaction-diffusion terms.…”

Section: Model Description and Some Preliminariesmentioning

confidence: 99%

“…Actually, impulsive control has provided an effective approach for a class of dynamical systems including biomedical engineering and neural networks [2,8,10,11,19,25,35,36,40]. Despite its engineering importance, there still exist some fundamental difficulties in theory that delayed impulsive control is used to synchronize discrete-time complex networks with distributed delays.…”

Section: Introductionmentioning

confidence: 99%

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Delayed impulsive synchronization of discrete-time complex networks with distributed delays

Fang

Zhang

et al. 2015

Nonlinear Dyn

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In this paper, a novel delayed impulsive control strategy is proposed for synchronization of discrete-time complex networks with distributed delays. Different from the existing results, the involving time delays include distributed delays and impulsive input delays. Employing the Razumikhin theorem and the mathematical induction method, several sufficient criteria are derived in terms of algebraic conditions, which depend on impulsive input delays and impulsive control gains. Meanwhile, the derived criteria also reveal the relationship between the bounds of impulsive intervals and impulsive input delays. Finally, two examples are given to illustrate the effectiveness of the proposed approach.

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Section: Model Description and Some Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delayed impulsive synchronization of discrete-time complex networks with distributed delays

Fang

Zhang

et al. 2015

Nonlinear Dyn

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“…Recently, an incursion of impulsive control strategies applied to biomedical systems has been done. Due to the characteristics of T1DM treatment, the input can be approximated as an impulse when the insulin bolus is injected because of its short duration in relation to the sample time [8]. Many biomedical applications, such as HIV, malaria, and diabetes, are better modeled and controlled as impulsive systems [8].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Due to the characteristics of T1DM treatment, the input can be approximated as an impulse when the insulin bolus is injected because of its short duration in relation to the sample time [8]. Many biomedical applications, such as HIV, malaria, and diabetes, are better modeled and controlled as impulsive systems [8]. In [9], an initial application of impulsive ZMPC (iZMPC) to T1DM patient dynamics is introduced.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Handling Parameter Variations during the Treatment of Type 1 Diabetes Mellitus: In Silico Results

Villa-Tamayo

Alvarez

Rivadeneira

2019

Mathematical Problems in Engineering

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Type 1 diabetic patients need a strict treatment to regulate blood glucose concentration in a target range. Despite the development of different control strategies, the model parameter variations, given by physiological changes, can generate an inaccurate treatment and in consequence hyperglycemia and hypoglycemia episodes. Therefore, it is necessary to use control techniques that compensate such effects and maintain the control goals. Here, the effect of parametric variations is examined by the sensitivity analysis from which the most influential parameters in glycemia dynamics are detected. Based on that, an offset-free MPC strategy for impulsive systems is given for the first time in literature and simulated for type 1 diabetes treatment. This scheme along with the impulsive zone MPC with artificial variables reestablishes the normoglycemia behavior since the parameter variations are adequately rejected. However, only parametric variations up to 50% from their nominal values are well compensated, which suggests that more robust formulations are needed to ensure a greater rejection of physiological variations.

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“…The properties have also been used for the design of finite‐time convergent observers (see, eg, References and ) and for the design of homogeneous observers with uniform convergence . In the nonlinear context, algebraic criteria for testing this property are obtained for the nonlinear case in Reference . In the context of piecewise hybrid systems, some observability conditions have been proposed in Reference and an observer design is introduced in Reference .…”

Section: Introductionmentioning

confidence: 99%

State estimation for linear hybrid systems with periodic jumps and unknown inputs

Ríos

Dávila

Teel

2020

Intl J Robust & Nonlinear

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In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger-like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input-to-state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding-mode observer is added to the Luenberger-like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.

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Observability criteria for impulsive control systems with applications to biomedical engineering processes

Cited by 44 publications

References 16 publications

Delayed impulsive synchronization of discrete-time complex networks with distributed delays

Delayed impulsive synchronization of discrete-time complex networks with distributed delays

Handling Parameter Variations during the Treatment of Type 1 Diabetes Mellitus: In Silico Results

State estimation for linear hybrid systems with periodic jumps and unknown inputs

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