Optimal control methods for drug delivery in cancerous tumour by anti‐angiogenic therapy and chemotherapy

There are numerous mathematical models simulating the behaviour of cancer by considering variety of states in different treatment strategies, such as chemotherapy. Among the models, one is developed which is able to consider the blood vessel‐production (angiogenesis) in the vicinity of the tumour and the effect of anti‐angiogenic therapy. In the mentioned‐model, normal cells, cancer cells, endothelial cells, chemotherapy and anti‐angiogenic agents are taking into account as state variables, and the rate of injection of the last two are considered as control inputs. Since controlling the cancerous tumour growth is a challenging matter for patient''s life, the time schedule design of drug injection is very significant. Two optimal control strategies, an open‐loop (calculus of variations) and a closed‐loop (state‐dependent Riccati equation), are applied on the system in order to find an optimal time scheduling for each drug injection. By defining a proper cost function, an optimal control signal is designed for each one. Both obtained control inputs have reasonable answers, and the system is controlled eventually, but by comparing them, it is concluded that both methods have their own benefits which will be discussed in details in the conclusion section.     

Novel algebraic meal disturbance estimation based adaptive robust control design for blood glucose regulation in type 1 diabetes patients

This study designs a robust closed‐loop control algorithm for elevated blood glucose level stabilisation in type 1 diabetic patients. The control algorithm is based on a novel control action resulting from integrating algebraic meal disturbance estimator with back‐stepping integral sliding mode control (BISMC) technique. The estimator shows finite time convergence leading to accurate and fast estimation of meal disturbance. Moreover, compensation of the estimated disturbance in controller provides significant reduction in chattering phenomenon, which is inherent drawback of sliding mode control (SMC). The controller is applied to one of the most reliable models of type 1 diabetic patients, named Bergman''s minimal model. The effectiveness and superiority of the designed controller is shown by comparing it to classical SMC and super‐twisting sliding mode control. The designed controller is subject to three different cases for detailed analysis of the controller''s robustness against meal disturbance. The three cases considered are hyperglycaemia, hyperglycaemia combined with meal disturbance and three meal disturbance. The simulation results confirm superior performance of algebraic disturbance estimator based BISMC controller for all the cases mentioned above.Inspec keywords: closed loop systems, robust control, sugar, medical control systems, variable structure systems, control system synthesis, blood, nonlinear control systems, adaptive control, diseasesOther keywords: adaptive robust control design, blood glucose regulation, type 1 diabetes patients, closed‐loop control algorithm, elevated blood glucose level stabilisation, type 1 diabetic patients, novel control action, algebraic meal disturbance estimator, mode control technique, accurate estimation, estimated disturbance, super‐twisting sliding mode control, algebraic disturbance estimator, BISMC controller, algebraic meal disturbance estimation, back‐stepping integral sliding mode control technique     

Controllability and observability analysis of basal ganglia model and feedback linearisation control

Deep brain stimulation (DBS) is a clinical remedy to control tremor in Parkinson''s disease. In DBS, one of the two main areas of basal ganglia (BG) is stimulated. This stimulation is produced with no feedback of the tremor and often causes a wide range of unpleasant side effects. Using a feedback signal from tremor, the stimulatory signal can be reduced or terminated to avoid extra stimulation and as a result decrease the side effects. To design a closed‐loop controller for the non‐linear BG model, a complete study of controllability and observability of this system is presented in this study. This study shows that the BG model is controllable and observable. The authors also propose the idea of stimulating the two BG areas simultaneously. A two‐part controller is then designed: a feedback linearisation controller for subthalamic nucleus stimulation and a partial state feedback controller for globus pallidus internal stimulation. The controllers are designed to decrease three indicators: the hand tremor, the level of delivered stimulation signal in disease condition, and the ratio of the level of delivered stimulation signal in health condition to disease condition. Considering these three indicators, the simulation results show satisfactory performance.Inspec keywords: feedback, brain, neurophysiology, diseases, medical control systems, closed loop systems, controllers, linearisation techniques, bioelectric phenomenaOther keywords: controllability analysis, observability analysis, basal ganglia model, feedback linearisation control, deep brain stimulation, clinical remedy, tremor control, Parkinson''s disease, feedback signal, closed‐loop controller, nonlinear BG model, feedback linearisation controller, two‐part controller, subthalamic nucleus stimulation, partial state feedback controller, globus pallidus internal stimulation, disease condition, delivered stimulation signal     

Sliding mode control for a fractional‐order non‐linear glucose‐insulin system

By providing the generalisation of integration and differentiation, and incorporating the memory and hereditary effects, fractional‐order modelling has gotten significant attention in the past few years. One of the extensively studied and utilised models to describe the glucose–insulin system of a human body is Bergman''s minimal model. This non‐linear model comprises of integer‐order differential equations. However, comparison with the experimental data shows that the fractional‐order version of Bergman''s minimal model is a better representative of the glucose–insulin system than its original integer‐order model. To design a control law for an artificial pancreas for a diabetic patient using a fractional‐order model, different techniques, including feedback linearisation, have been applied in the literature. The authors’ previous work shows that the fractional‐order version of Bergman''s model describes the glucose–insulin system in a better way than the integer‐order model. This study applies the sliding mode control technique and then compares the obtained simulation results with the ones obtained using feedback linearisation.Inspec keywords: nonlinear control systems, feedback, variable structure systems, differential equations, medical control systems, diseases, control system synthesis, sugar, nonlinear dynamical systemsOther keywords: fractional‐order nonlinear glucose‐insulin, hereditary effects, fractional‐order modelling, extensively, utilised models, glucose–insulin system, Bergman''s minimal model, nonlinear model, integer‐order differential equations, fractional‐order version, original integer‐order model, fractional‐order model, Bergman''s model, sliding mode control technique     

Sliding‐mode‐based controllers for automation of blood glucose concentration for type 1 diabetes

Destruction of β‐cells in pancreas causes deficiency in insulin production that leads to diabetes in the human body. To cope with this problem, insulin is either taken orally during the day or injected into the patient''s body using artificial pancreas (AP) during sleeping hours. Some mathematical models indicate that AP uses control algorithms to regulate blood glucose concentration (BGC). The extended Bergman minimal model (EBMM) incorporates, as a state variable, the disturbance in insulin level during medication due to either meal intake or burning sugar by engaging in physical exercise. In this research work, EBMM and proposed finite time robust controllers are used, including the sliding mode controller (SMC), backstepping SMC (BSMC) and supertwisting SMC (second‐order SMC or SOSMC) for automatic stabilisation of BGC in type 1 diabetic patients. The proposed SOSMC diminishes the chattering phenomenon which appears in the conventional SMC. The proposed BSMC is a recursive technique which becomes robust by the addition of the SMC. Lyapunov theory has been used to prove the asymptotic stability of the proposed controllers. Simulations have been carried out in MATLAB/Simulink for the comparative study of the proposed controllers under varying data of six different type 1 diabetic patients available in the literature.     

Chattering‐ free hybrid adaptive neuro‐fuzzy inference system‐particle swarm optimisation data fusion‐based BG‐level control

In this study, a closed‐loop control scheme is proposed for the glucose–insulin regulatory system in type‐1 diabetic mellitus (T1DM) patients. Some innovative hybrid glucose–insulin regulators have combined artificial intelligence such as fuzzy logic and genetic algorithm with well known Palumbo model to regulate the blood glucose (BG) level in T1DM patients. However, most of these approaches have focused on the glucose reference tracking, and the qualitative of this tracking such as chattering reduction of insulin injection has not been well‐studied. Higher‐order sliding mode (HoSM) controllers have been employed to attenuate the effect of chattering. Owing to the delayed nature and non‐linear property of glucose–insulin mechanism as well as various unmeasurable disturbances, even the HoSM methods are partly successful. In this study, data fusion of adaptive neuro‐fuzzy inference systems optimised by particle swarm optimisation has been presented. The excellent performance of the proposed hybrid controller, i.e. desired BG‐level tracking and chattering reduction in the presence of daily glucose‐level disturbances is verified.Inspec keywords: fuzzy control, variable structure systems, particle swarm optimisation, neurocontrollers, fuzzy neural nets, blood, genetic algorithms, closed loop systems, medical control systems, fuzzy reasoning, diseases, nonlinear control systems, sugarOther keywords: data fusion, adaptive neuro‐fuzzy inference systems, particle swarm optimisation, hybrid controller, desired BG‐level tracking, chattering reduction, daily glucose‐level disturbances, closed‐loop control scheme, glucose–insulin regulatory system, type‐1 diabetic mellitus patients, innovative hybrid glucose–insulin regulators, artificial intelligence, fuzzy logic, genetic algorithm, Palumbo model, blood glucose level, T1DM patients, glucose reference tracking, insulin injection, mode controllers, glucose–insulin mechanism, chattering‐free hybrid adaptive neuro‐fuzzy inference system, particle swarm optimisation data fusion‐based BG‐level control     

Non‐fragile reliable control synthesis of the sugarcane borer

This study considers the problem of non‐fragile reliable control synthesis for mathematical model of interaction between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid Trichogramma galloi. In particular, the control could be substituted by periodic releases of a small population of natural enemies and hence it is important to propose the time‐varying controller in sugarcane borer. The main aim of this study is to design a state feedback non‐fragile (time‐varying) reliable controller such that the states of the sugarcane borer system reach the equilibrium point within the desired period. A novel approach is proposed to deal with the uncertain matrices which appear in non‐fragile reliable control. Finally, simulations based on sugarcane borer systems are conducted to illustrate the advantages and effectiveness of the proposed design technique. The result reveals that the proposed non‐fragile control provides good performance in spite of periodic releases of a small population of natural enemies occurs.Inspec keywords: microorganisms, plant diseases, biology computing, state feedback, biocontrol, control system synthesisOther keywords: nonfragile reliable control synthesis, sugarcane borer, mathematical model, Diatraea saccharalis, egg parasitoid, Trichogramma galloi, periodic releases, natural enemies, state feedback nonfragile time‐varying reliable controller, equilibrium point, design technique     

Observer‐based resilient finite‐time control of blood gases model during extra‐corporeal circulation

This study aims at designing an observer‐based resilient controller to regulate the amount of oxygen and carbon dioxide in the blood of patients during the extra‐corporeal blood circulation process. More precisely, in this study, a suitable observer‐based resilient controller is constructed to regulate the levels of patient blood gases in a finite interval of time. The finite‐time boundedness with the prescribed H∞ performance index of the considered blood gases control system against modelling uncertainty and external disturbances is ensured by using Lyapunov stability analysis. Moreover, a set of sufficient conditions for obtaining the controller gain is developed in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust finite‐time control scheme is verified through simulation results. The result reveals that the blood gases are maintained in their physiological ranges during a stable extra‐corporeal circulation process via the proposed observer‐based resilient controller.Inspec keywords: blood, haemodynamics, oxygen, carbon compounds, controllers, medical control systems, biomedical equipment, Lyapunov methods, linear matrix inequalitiesOther keywords: observer‐based resilient finite‐time control, observer‐based resilient controller, oxygen amount, carbon dioxide amount, extracorporeal blood circulation process, patient blood gas levels, finite time interval, finite‐time boundedness, H_∞ performance index, blood gases control system, Lyapunov stability analysis, controller gain, linear matrix inequalities, physiological ranges, LMIs, CO₂ , O₂      

Blood glucose concentration control for type 1 diabetic patients: a non‐linear suboptimal approach

In this study, a closed‐loop treatment strategy is proposed for the control of blood glucose levels in type 1 diabetic patients. Toward this end, a non‐linear technique for designing suboptimal tracking controllers, called the state‐dependent Riccati equation tracker, is used based on a mathematical model of the glucose–insulin regulatory system. Since two state variables of the utilised model are not available to the controller, a non‐linear filter is also designed to estimate these variables using the measured blood glucose concentration. Effects of unannounced meals and regular exercise are investigated for a nominal patient and nine diabetic patients with unknown parameters. Numerical simulations are given to show the effectiveness of the proposed treatment strategy even in the presence of parametric uncertainties and the observation noise.Inspec keywords: blood, biochemistry, diseases, patient treatment, Riccati equations, nonlinear filters, medical signal processingOther keywords: blood glucose concentration control, type 1 diabetic patients, nonlinear suboptimal approach, closed‐loop treatment strategy, suboptimal tracking controllers, state‐dependent Riccati equation tracker, glucose‐insulin regulatory system, nonlinear filter, unannounced meals, regular exercise, treatment strategy, parametric uncertainties, observation noise     

Positive input observer‐based controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

In practice, there are many physical systems that can have only positive inputs, such as physiological systems. Most conventional control methods cannot ensure that the main system input is positive. A positive input observer‐based controller is designed for an intravenous glucose tolerance test model of type 1 diabetes mellitus (T1DM). The backstepping (BS) approach is employed to design the feedback controller for artificial pancreas (AP) systems, based on the Extended Bergman''s Minimal Model (EBMM). The EBMM represents the T1DM in terms of the blood glucose concentration (BGC), insulin concentration, and plasma level and the disturbance of insulin during medication due to either meal intake or burning sugar by doing some physical exercise. The insulin concentration and plasma level are estimated using observers, and these estimations are applied as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Moreover, it is proved that the system is bounded input‐bounded output (BIBO) stable in the presence of uncertainties generated by uncertain parameters and external disturbance. For realistic situations, we consider only the BGC to be available for measurement and additionally inter‐and intra‐patient variability of system parameters is considered.     

Design of dual hormone blood glucose therapy and comparison with single hormone using MPC algorithm

The complete automated control and delivery of insulin and glucagon in type 1 diabetes is the developing technology for artificial pancreas. This improves the quality of life of a diabetic patient with the precise infusion. The amount of infusion of these hormones is controlled using a control algorithm, which has the prediction property. The control algorithm model predictive control (MPC) predicts one step ahead and infuses the hormones continuously according to the necessity for the regulation of blood glucose. In this research, the authors propose a MPC control algorithm, which is novel for a dual hormone infusion, for a mathematical model such as Sorenson model, and compare it with the insulin alone or single hormone infusion developed with MPC. Since they aim for complete automatic control and regulation, unmeasured disturbances at a random time are integrated and the performance evaluation is projected through statistical analysis. The blood glucose risk index (BGRI) and control variability grid analysis (CVGA) plot gives the additional evaluation for the comparative results of the two controllers claiming 88% performance by dual hormone evaluated through CVGA plot and 2.05 mg/dl average tracking error, 2.20 BGRI. The MPC developed for dual hormone significantly performs better and the time spent in normal glycaemia is longer while eliminating the risk of hyperglycaemia and hypoglycaemia.Inspec keywords: sugar, diseases, statistical analysis, biochemistry, blood, predictive control, patient treatment, artificial organsOther keywords: dual hormone blood glucose therapy, insulin, glucagon, type 1 diabetes, artificial pancreas, diabetic patient, glucose level, model predictive control, MPC control algorithm, dual hormone infusion, single hormone infusion, complete automatic control, blood glucose risk index, control variability grid analysis plot, Sorenson model, statistical analysis, normal glycaemia, hyperglycaemia, hypoglycaemia     

Ice-cream storage energy efficiency with model predictive control of a refrigeration system coupled to a PCM tank

A model predictive controller (MPC) was developed in order to optimise energy management of an ice-cream warehouse refrigeration system coupled to a phase-change material (PCM) tank. The controller's internal model was based on a steady-state refrigeration cycle model and energy balances on the PCM tank and warehouse. Considering crystal growth in ice-cream, the quality evolution was based on Ostwald ripening equation. The product temperature field was determined by a 1-D finite difference equation. An original PCM model was developed for better performance of Levenberg–Marquardt's optimisation algorithm which was modified in order to take into account control variables' bounds. Simulation of the ice-cream storage for a period of 90 days lead to good results on the optimised control sequence with efficient energy management thanks to the PCM tank. Ice crystals size remained below the defined target: 26 μm. This study showed the great potential of MPC to reduce energy consumption and guarantee food quality.     

Estimation of parameters for plasma glucose regulation in type‐2 diabetics in presence of meal

In this study, the authors propose a methodology for the estimation of glucose masses in stomach (both in solid and liquid forms), intestine, plasma and tissue; insulin masses in portal vein, liver, plasma and interstitial fluid using only plasma glucose measurement. The proposed methodology fuses glucose–insulin homoeostasis model (in the presence of meal intake) and plasma glucose measurement with a Bayesian non‐linear filter. Uncertainty of the model over individual variations has been incorporated by adding process noise to the homoeostasis model. The estimation is carried out over 24 h for the healthy people as well as a type II diabetes mellitus patients. In simulation, the estimator follows the truth accurately for both the cases. Moreover, the performances of two non‐linear filters, namely the unscented Kalman filter (KF) and cubature quadrature KF are compared in terms of root mean square error. The proposed methodology will be helpful in future to: (i) observe a patient''s insulin–glucose profile, (ii) calculate drug dose for any hyperglycaemic patients and (iii) develop a closed‐loop controller for automated insulin delivery system.Inspec keywords: blood, diseases, biochemistry, parameter estimation, biological tissues, liver, Bayes methods, nonlinear filters, Kalman filters, drugs, drug delivery systems, medical signal processingOther keywords: automated insulin delivery system, closed‐loop controller, hyperglycaemic patients, drug dose, root mean square error, cubature quadrature KF, Kalman filter, type II diabetes mellitus, process noise, Bayesian nonlinear filter, glucose‐insulin homoeostasis model, interstitial fluid, liver, portal vein, insulin mass, biological tissues, intestine, stomach, glucose mass, meal intake, type‐2 diabetics, plasma glucose regulation, parameter estimation     

Blood glucose regulation and control of insulin and glucagon infusion using single model predictive control for type 1 diabetes mellitus

This study elaborates on the design of artificial pancreas using model predictive control algorithm for a comprehensive physiological model such as the Sorensen model, which regulates the blood glucose and can have a longer control time in normal glycaemic region. The main objective of the proposed algorithm is to eliminate the risk of hyper and hypoglycaemia and have a precise infusion of hormones: insulin and glucagon. A single model predictive controller is developed to control the bihormones, insulin, and glucagon for such a development unmeasured disturbance is considered for a random time. The simulation result for the proposed algorithm performed good regulation lowering the hypoglycaemia risk and maintaining the glucose level within the normal glycaemic range. To validate the performance of the tracking of output and setpoint, average tracking error is used and 4.4 mg/dl results are obtained while compared with standard value (14.3 mg/dl).Inspec keywords: predictive control, blood, medical control systems, sugar, diseases, artificial organs, patient treatment, physiological models, biochemistryOther keywords: blood glucose, longer control time, insulin, single model predictive controller, glucagon infusion, single model predictive control, type 1 diabetes mellitus, model predictive control algorithm, comprehensive physiological model, Sorensen model     

Full-scale field test of a model predictive control system for a 3 MW wind turbine

Model predictive control (MPC) is a strong candidate for modern wind turbine control. While the design of model predictive wind turbine controllers in simulations has been extensively investigated in academic studies, the application of these controllers to real wind turbines reveals open research challenges. In this work, we focus on the validation of a linear time-variant MPC system for a 3 MW wind turbine in a full-scale field test. First, the study proves the MPC’s capability to control the real wind turbine in the partial load region. Compared to the turbine’s baseline PID controller, the MPC system offers similar results for the electrical power output and for the occurring mechanical loads. Second, the study validates a previously proposed, simulation-based rapid control prototyping process for a systematic MPC development. The systematic development process allows to completely design and parameterize the MPC system in a simulative environment independent of the real wind turbine. Through the rapid control prototyping process, the MPC commissioning in the wind turbine’s programmable logic controller can be realized within a few hours without any modifications required in the field. Thus, this study establishes the proof of concept for a linear time-variant MPC system for a 3 MW wind turbine in a full-scale field test and bridges the gap between the control design and field testing of MPC systems for wind turbines in the multi-megawatt range.

     

System‐based strategies for p53 recovery

The authors have proposed a systems theory‐based novel drug design approach for the p53 pathway. The pathway is taken as a dynamic system represented by ordinary differential equations‐based mathematical model. Using control engineering practices, the system analysis and subsequent controller design is performed for the re‐activation of wild‐type p53. p53 revival is discussed for both modes of operation, i.e. the sustained and oscillatory. To define the problem in control system paradigm, modification in the existing mathematical model is performed to incorporate the effect of Nutlin. Attractor point analysis is carried out to select the suitable domain of attraction. A two‐loop negative feedback control strategy is devised to drag the system trajectories to the attractor point and to regulate cellular concentration of Nutlin, respectively. An integrated framework is constituted to incorporate the pharmacokinetic effects of Nutlin in the cancerous cells. Bifurcation analysis is also performed on the p53 model to see the conditions for p53 oscillation.Inspec keywords: proteins, tumours, cancer, cellular biophysics, molecular biophysics, molecular configurations, biochemistry, differential equations, closed loop systems, bifurcation, biology computingOther keywords: system‐based strategies, p53 recovery, systems theory‐based novel drug design approach, dynamic system, ordinary differential equations‐based mathematical model, control engineering practices, subsequent controller design, wild‐type p53, p53 revival, oscillatory, control system paradigm, mathematical model, Nutlin effect, attractor point analysis, domain‐of‐attraction, two‐loop negative feedback control strategy, cellular concentration, pharmacokinetic effects, cancerous cells, bifurcation analysis, p53 oscillation, anomalous cell     

Optimal neuro‐fuzzy control of hepatitis C virus integrated by genetic algorithm

Hepatitis C blood born virus is a major cause of liver disease that more than three per cent of people in the world is dealing with, and the spread of hepatitis C virus (HCV) infection in different populations is one of the most important issues in epidemiology. In the present study, a new intelligent controller is developed and tested to control the hepatitis C infection in the population which the authors refer to as an optimal adaptive neuro‐fuzzy controller. To design the controller, some data is required for training the employed adaptive neuro‐fuzzy inference system (ANFIS) which is selected by the genetic algorithm. Using this algorithm, the best control signal for each state condition is chosen in order to minimise an objective function. Then, the prepared data is utilised to build and train the Takagi–Sugeno fuzzy structure of the ANFIS and this structure is used as the controller. Simulation results show that there is a significant decrease in the number of acute‐infected individuals by employing the proposed control method in comparison with the case of no intervention. Moreover, the authors proposed method improves the value of the objective function by 19% compared with the ordinary optimal control methods used previously for HCV epidemic.Inspec keywords: epidemics, diseases, blood, medical computing, microorganisms, genetic algorithms, fuzzy control, neurocontrollers, adaptive control, medical control systemsOther keywords: genetic algorithm, hepatitis C blood born virus, liver disease, hepatitis C virus infection, epidemiology, intelligent controller, optimal adaptive neuro‐fuzzy controller, adaptive neuro‐fuzzy inference system, ANFIS, genetic algorithm, control signal, state condition, objective function minimisation, Takagi‐Sugeno fuzzy structure, acute‐infected individuals, ordinary optimal control methods, HCV epidemic