Offset-free MPC strategy for nonzero regulation of linear impulsive systems

Villa-Tamayo, María F.; Caicedo, Michelle A.; Rivadeneira, Pablo S.

doi:10.1016/j.isatra.2020.01.005

Cited by 22 publications

(23 citation statements)

References 36 publications

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“…An impulsive control approach has also been used in the context of type-1 diabetes to regulate the injection of insulin [ 26 , 27 ]. The results highlight that the impulsive control scheme delivers reasonable treatment regimes in both contexts to achieve therapeutic goals despite parameter and modelling uncertainties [ 24 , 25 , 27 , 28 ]. Thus, it is sensible to apply control theory for oncolytic virus therapy to investigate effective and robust protocols to sustain tumour regression.…”

Section: Introductionmentioning

confidence: 99%

Oncolytic virus therapy benefits from control theory

2020

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Oncolytic virus therapy aims to eradicate tumours using viruses which only infect and destroy targeted tumour cells. It is urgent to improve understanding and outcomes of this promising cancer treatment because oncolytic virus therapy could provide sensible solutions for many patients with cancer. Recently, mathematical modelling of oncolytic virus therapy was used to study different treatment protocols for treating breast cancer cells with genetically engineered adenoviruses. Indeed, it is currently challenging to elucidate the number, the schedule, and the dosage of viral injections to achieve tumour regression at a desired level and within a desired time frame. Here, we apply control theory to this model to advance the analysis of oncolytic virus therapy. The control analysis of the model suggests that at least three viral injections are required to control and reduce the tumour from any initial size to a therapeutic target. In addition, we present an impulsive control strategy with an integral action and a state feedback control which achieves tumour regression for different schedule of injections. When oncolytic virus therapy is evaluated in silico using this feedback control of the tumour, the controller automatically tunes the dose of viral injections to improve tumour regression and to provide some robustness to uncertainty in biological rates. Feedback control shows the potential to deliver efficient and personalized dose of viral injections to achieve tumour regression better than the ones obtained by former protocols. The control strategy has been evaluated in silico with parameters that represent five nude mice from a previous experimental work. Together, our findings suggest theoretical and practical benefits by applying control theory to oncolytic virus therapy.

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Section: Introductionmentioning

confidence: 99%

Oncolytic virus therapy benefits from control theory

2020

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“…It is also to remark that x • (k) = x(τ k ) describes the ICS before the input is applied, while x • = x(τ + k ) is the state when the control input has already been applied. For this reason, despite both subsystems are necessary to characterize the ICS, the first subsystem x • is the one used in the control strategy to generate the control action [29]. In addition, as defined for the nonlinear case, the state x • s represents a control equilibrium of system (6) when satisfying…”

Section: B Nonlinear Impulsive Control Systemsmentioning

confidence: 99%

“…Regarding impulsive systems, the linear offset-free MPC was developed in [29], where observability conditions for the augmented system with a disturbance are established, and a straightforward way to select the disturbance model matrices is introduced based on the properties of ICS. To the best of the authors' knowledge, offset-free MPC formulations for nonlinear ICS have not yet been presented.…”

Section: Introductionmentioning

confidence: 99%

Offset-Free Nonzero Tracking for Nonlinear Impulsive Systems With Application to Biomedical Processes

et al. 2022

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Impulsive control systems have shown strong potential to represent and address challenging problems, especially in the biomedical field. In recent research, these problems have been tackled with advances in linear impulsive control systems. However, many biomedical applications are better described by nonlinear impulsive models, and therefore, it is necessary to develop analysis tools and control strategies in this context. In the literature, the main properties of nonlinear impulsive control systems have been fully understood, but there is no major development of control strategies. Particularly, there is no substantiation of model predictive control (MPC) strategies maintaining convexity of the optimization problem and closedloop stability, and there is no control strategy to reduce the offset problem when there are parameter variations, which is a common situation in biological processes. Therefore, the main novelties of this paper are: (i) an MPC formulation extended to nonlinear impulsive systems that addresses non-zero tracking, (ii) the sufficient and necessary conditions to guarantee the stability of the closed-loop system at an equilibrium target, (iii) a comprehensive description of an offset-free MPC to handle low to moderate plant-model mismatches, (iv) the conditions to guarantee offset-free control. Finally, the MPC and offset-free MPC are tested to address the drug administration problem in two biomedical applications: oncolytic virus therapy, to regulate tumor dynamics using doses of oncolytic, and type 1 diabetes treatment, to regulate glycemia using insulin injections. Satisfactory results were obtained in simulation scenarios including parameter variations in nonlinear models that represent the corresponding dynamics.

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“…x a = Ax a + B u u a + E Offset-free zone model predictive control with artificial variables (ZMPC-AV-OF) (12) This strategy compensates for the effect of a plant-model mismatch. To that end, the state is augmented with a disturbance d(k+1)=d(k), it is estimated with the state estimator, and then, this information is provided to the MPC problem in the prediction model and equilibrium constraints.…”

Section: Zone Model Predictive Control With Artificial Variables (Zmpc-av) (37)mentioning

confidence: 99%

“…From these, MPC has received increasing attention due to its good performance in simulation and clinical tests (5,6). Some MPC works in literature are the zone MPC (7) which incorporated the glycemia target as a set instead of a single point, some MPC designs with asymmetric cost function (8,9), an MPC which drives glycemia to equilibrium sets and considers impulsive inputs (10), and an offset-free MPC with impulsive inputs that uses a disturbance model to compensate for a plant-model mismatch (11,12). In addition, adaptive control strategies have been formulated as the MPC with adaptive penalization functions for matrices Q, R (13) and the impulsive offset-free strategy with adaptive features introduced in ( 14) and (15).…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Different Embedded Systems and Open-Source Optimization Packages Towards an Impulsive MPC Artificial Pancreas

et al. 2021

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Current technological advances have brought closer to reality the project of a safe, portable, and efficient artificial pancreas for people with type 1 diabetes (T1D). Among the developed control strategies for T1D, model predictive control (MPC) has been emphasized in literature as a promising control for glucose regulation. However, these control strategies are commonly designed in a computer environment, regardless of the limitations of a portable device. In this paper, the performances of six embedded platforms and three open-source optimization solver algorithms are assessed for T1D treatment. Their advantages and limitations are clarified using four MPC formulations of increasing complexity and a hardware-in-the-loop methodology to evaluate glucose control in virtual adult subjects. The performance comparison includes the execution time, the difference concerning the evolution obtained in MATLAB, the processor temperature, energy consumption, time percentage in normoglycemia, and the number of hypo- and hyperglycemic events. Results show that Quadprog is the package that faithfully follows the results obtained with control strategies designed and tuned on a computer with the MATLAB software. In addition, the Raspberry Pi 3 and the Tinker Board S embedded systems present the appropriate characteristics to be implemented as portable devices in the artificial pancreas application according to the criteria set out in this work.

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Offset-free MPC strategy for nonzero regulation of linear impulsive systems

Cited by 22 publications

References 36 publications

Oncolytic virus therapy benefits from control theory

Oncolytic virus therapy benefits from control theory

Offset-Free Nonzero Tracking for Nonlinear Impulsive Systems With Application to Biomedical Processes

Performance Analysis of Different Embedded Systems and Open-Source Optimization Packages Towards an Impulsive MPC Artificial Pancreas

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