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not available Bangladesh Med Res Counc Bull 2020; 46(3): 240-244

In this paper, we consider a class of nonlinear systems driven by measures generalizing the class of impulsive systems. We use measures as control and prove existence of optimal controls (measures) and present necessary conditions of optimality. We apply the general results to derive necessary conditions of optimality for purely impulse-driven systems. These results are then applied to optimal control problems related to geosynchronous satellites with some numerical results.

In this paper, we use a recently developed dynamic model for urban traffic flow subject to practical constraint characteristics of intersections equipped with traffic light. We define an objective functional based on the analytical expressions for traffic throughput, congestion, and drivers’ waiting time at an intersection. Following this, an optimization problem is formulated and an algorithm is presented based on the principle of optimality due to Bellman. The solution, if implemented, is expected to improve throughput, reduce congestion, avoid traffic jams, and promote driver satisfaction. The system is simulated with a series of numerical experiments and the corresponding optimization problems are solved using the proposed algorithm. The optimal feedback control laws independent of initial state are acquired, and the optimal cost is found according to any given initial condition. It is believed that this dynamic model would be potentially applicable for the real-time adaptive traffic control system.

GIS and multivariate statistics along with the geochemical approaches were applied in this study to investigate the hydrogeochemical behavior, source apportionment of groundwater pollutants and their spatial distribution in the aquifer system of Dhaka City, Bangladesh. A total of 33 groundwater samples were collected and analyzed, in order to evaluate the geochemical constituents of groundwater. Results found that, the trends of cations and anions are Na+ > Mg2+ > Ca2+ > K+ and HCO3− > Cl− > SO42− > NO3− respectively, and Ca2+–Mg2+–HCO3− is the dominant groundwater type. Except Na+, K+, Cl−, F− and NO3− all others measured parameters fall within the permissible limits. However, silicate weathering was identified as the major processes of controlling the groundwater solute content. Besides, cation exchange plays a significant role, influencing the water chemistry of the aquifers. Aqueous speciation model revealed that, aquifer materials were more saturated with aragonite, calcite and dolomite, and under-saturated with halite. From regression and correlation analysis it was found that, EC, Cl− and SO42− were correlated with each other's; which might helpful for site specific monitoring of groundwater quality. Principal component analysis (PCA) and cluster analysis (CA) were also employed to appraise the sources of contaminants, and it was explored that both natural and anthropogenic factors were influencing the groundwater quality. Groundwater was contaminated due to induced river recharge and rapid infiltration of contaminated water through the recharge areas. In this situation it is expected that, outcomes of this study will provide useful insights to planners for sustainable management of groundwater resources of this megacity.

In this paper we consider optimal feedback control problems for a general class of nonlinear partially observed stochastic evolution equations on Banach spaces. The system is governed by a pair of ...

Noninvasive ventilation (NIV) has now become an integral tool within the treatment of both acute and chronic respiratory failure, and at an equivalent time reducing the necessity for invasive ventilation. A cross sectional, retrospective study based on a retrospective review of hospital medical records of patients who underwent NIV in the period between January 2017 and December 2019, to determinate the efficacy of NIV in pediatrics whom admitted to Pediatric intensive care unit (PICU) with respiratory failure (short term evaluation), demographic and clinical data were collected before and after applying the NIV. The data included heart rate (HR), respiratory rate (RR), oxygen concentration (P02) and CO2 concentration (PCO2). NIV was used for a total of 61 pediatric patients admitted to PICU during the period of the study. Pneumonia was the commonest indication for the NIV (n=25, 41.0%), and continuous positive airway pressure (CPAP) was used in 52(85.2%) patients. The mean duration of NIV was 817.2 days, there was a significant clinical improvement after one hour from application of NIV The mean improvement in RR was from 48.412.2 to 35.01I.5 (P=0.000), SPO2 was improved from 88.111.8 to 96.510.7 (P= 0.000), and the PCO2 was improved from 61.4±6.1 to 48.713 7 (P=0.002). Five patients were failing to respond to the NIV and shifted to mechanical ventilation. The NIV is a useful tool for treatment of respiratory failure in pediatrics, especially under the age of one year. Pneumonia was the commonest indication for the use of the NB!. More investigation is needed to fully evaluate the ramifications of increased use of this technology in the PICU.

In this paper, we develop a stochastic dynamic model for the network of city bus routes subject to resource and other practical constraints. We define an objective function on the basis of four terms: fuel cost, operating cost, customers waiting time, and revenue of the bus company. Hereafter, an optimization problem is formulated and solved by use of nonlinear integer programming. If the technique presented here is implemented, it is expected to boost the bus company's revenue, reduce waiting time and therefore promote customer satisfaction. A series of numerical experiments is carried out and the corresponding optimization problems are addressed giving the optimal number of buses allocated to each of the bus routes in the network. Since the dynamic model proposed here can be applied to any network of bus routes, it is believed that the procedure developed in this paper is of great potential for both the city bus company and the customers.

This chapter presents numerous results on existence of optimal controls and necessary conditions of optimality for systems governed by stochastic differential equations controlled by vector measures. Important convergence theorems are also presented guaranteeing convergence of any algorithm based on the necessary conditions of optimality.

This chapter deals with the question of existence of optimal controls from the class of regular controls (vector valued measurable functions), relaxed controls (measure-valued functions), and controls determined by vector measures, where both fully and partially observed control problems are considered.

This chapter presents computational algorithms applied to several practical examples. Detailed numerical results are presented which demonstrate the applicability of theoretical results developed in this book.

Pulmonary rehabilitation (PR) program of a sufficient duration has impact on consequence of COPD. To evaluate the effects of combination of pursed lip breathing (PLB), diaphragmatic breathing (DB) and lower extremity endurance training (LEET) as part of PR program in stable patients with COPD on oxygenation status, dyspnea and fatigue. This prospective interventional study was performed in the Department of Physiology, Bangabandhu Sheikh Mujib Medical University, Dhaka, Bangladesh from July 2010 to June 2011 and was performed on 116 male stable moderate COPD patients aged 50 to 65 years. Among them, 56 patients were without PR (control group) and 60 patients were intervened with PR (experimental group). The experimental patients were advised to perform the home based PR program (PLB, DB and LEET) for 30 minutes duration per session at home twice per day, along with standard drug treatment of COPD for uninterrupted 60 days. The control patients continued their treatment of COPD with standard drug for successive 60 days were advised. To evaluate the effects of PR, Peripheral capillary oxygen saturation (SpO₂, by pulse Oximeter), level of dyspnea and level of fatigue by Modified Borg Scale from baseline to end of six minute walk test (6MWT) of all subjects were recorded on day 0 and day 60 for both the groups. Independent sample 't' test and paired Student's 't' test were done with SPSS software. In the interpretation of results, p value of0.05 was considered as statistically significant. In the present study, we found less decrement of SpO₂ and less increment of level of dyspnea as well as level of fatigue after 6MWT in the COPD patients with PR on 60th day of follow up. The study reveals that oxygenation status, dyspnea and fatigue improve after execution of regular home based PR program in patients with moderate stable COPD.

In this paper we consider a class of stochastic reaction diffusion equations with polynomial nonlinearities. We prove existence and uniqueness of weak solutions and their regularity properties. We introduce a suitable topology on the space of stochastic relaxed controls and prove continuous dependence of solutions on controls with respect to this topology and the norm topology on the natural space of solutions. Also we prove that the attainable set of measures induced by the weak solutions is weakly compact. Then we consider some optimal control problems, including the Bolza problem, and some target seeking problems in terms of the attainable sets in the space of measures and prove existence of optimal controls. In the concluding section we present briefly some extensions of the results presented here.

Casualty, in relation to personnel, any person who is lost to his organization; by reason of being declared dead, wounded, diseased, detained, captured or missing. Casualty service or department is not well organized in the hospitals of our country. We have recently started functioning casualty department to manage casualties properly in spite of the increasing workload and emerging needs of this department. This study was conducted in the Casualty department, Mymensingh Medical College Hospital (MMCH), Mymensingh, Bangladesh to analyze the number of patients and pattern of casualties. A total number of 17435 patients were enrolled in this retrospective observational study. Data was collected from hospital records of all patients attending in the Casualty Department, MMCH between November 19, 2017 and May 18, 2018 and patients were categorized on the basis of their mode of injury. The demographic characteristics of patients with mode of Casualty were analyzed. Male were 75% and female 25%. Avergae per day patient attended in the Casualty department was 96, maximum was 176 and minimum 33. According to age sub-division, 11-20 years age group attended maxiumum was 48. One day attended Road traffic accident (RTA) maximum was 65 and minimum was 3, Non-RTA maximum was 83 and minimum 25, physical assaults maximum was 48 and minimum 1. Injury due to fall and RTA were the common mode of casualty especially in the young population in the study area. Study showed that injury caused by fall was 44% among the all patients. Patients due to fall from tree was highest (35%) in April-May. Incidents of fall were followed by RTA which was 25%. Physical assaults (17%), machinery injury (9%) and others were 5%.

Background: The COVID-19 pandemic has become a formidable threat to global health and economy. The coronavirus SARS-CoV-2 that causes COVID-19 is known to spread by human-to-human transmission, and in about 40% cases, the exposed individuals are asymptomatic which makes it difficult to contain the virus. Methods: This paper presents a modified SEIR epidemiological model and uses concepts of optimal control theory for analysis of the effects of intervention methods of the COVID19. Fundamentally the pandemic intervention problem can be viewed as a mathematical optimization problem as there are contradictory outcomes in terms of reduced infection and fatalities but with serious economic downturns. Results: Concepts of optimal control theory have been used to determine the optimal control (intervention) levels of i) social contact mitigation and suppression, and ii) pharmaceutical intervention modalities, with minimum impacts on the economy. Numerical results show that with optimal intervention policies, there is a significant reduction in the number of infections and fatalities. The computed optimum intervention policy also provides a timeline of systematic enforcement and relaxation of stay-at-home regulations, and an estimate of the peak time and number of hospitalized critical care patients. Conclusion: The proposed method could be used by local and state governments in planning effective strategies in combating the pandemic. The optimum intervention policy provides the necessary lead time to establish necessary field hospitals before getting overwhelmed by new patient arrivals. Our results also allow the local and state governments to relax social contact suppression guidelines in an orderly manner without triggering a second wave.

In this paper we present a mathematical model describing the physical dynamics of a building maintenance unit (BMU) equipped with reaction jets. The momentum provided by reaction jets is considered as the control variable. We introduce an objective functional based on the deviation of the BMU from its equilibrium state due to external high-wind forces. Pontryagin minimum principle is then used to determine the optimal control policy so as to minimize possible deviation from the rest state thereby increasing the stability of the BMU and reducing the risk to the workers as well as the public. We present a series of numerical results corresponding to three different scenarios for the formulated optimal control problem. These results show that, under high-wind conditions the BMU can be stabilized and brought to its equilibrium state with appropriate controls in a short period of time. Therefore, it is believed that the dynamic model presented here would be potentially useful for stabilizing building maintenance units thereby reducing the risk to the workers and the general public.

In this paper, we develop a stochastic dynamic model for the city bus route subject to practical constraints. We define an objective functional based on the expressions for fuel cost, operating cost, customers waiting time, and revenue of the bus company. Following this, an optimization problem is formulated and solved using calculus of variations. It is expected to improve the bus company's revenue, reduce customers waiting time and promote their satisfaction if the solution presented here is implemented. The system is simulated with a series of numerical experiments and the corresponding optimization problems are solved giving the optimal number of buses allocated to a bus route. Since the dynamic model can be generally applied to any bus route, it is strongly believed that the procedure developed in this paper has a great potential of benefits for both the city bus company and the customers served.

In this paper, we develop a stochastic dynamic model for the queuing system in a commercial bank. We define an objective functional based on the expressions of servers wage and customers waiting time. By following this, an optimization problem is formulated and solved. Furthermore, we introduce a tentative method of choosing the optimum number of open service windows by classifying the servers into two categories: primary servers and experienced servers. It is anticipated to reduce the bank's expense as well as customers waiting time and promote their satisfaction if the technique presented here is implemented. The dynamic system is simulated with numerical experiments and the corresponding optimization problems are solved giving the optimal number of service windows required to open. Since the proposed dynamic model can be generally applied to any commercial banks, it is strongly believed that the procedure developed in this paper is of great benefit for both the bank and the customers served.

This article is concerned with a semilinear McKean–Vlasov type stochastic evolution equation in a real Hilbert space. The main goal of the article is to study the existence and uniqueness of mild solutions, Yosida approximations of mild solutions of such equations, and to deduce the weak convergence of the corresponding induced probability measures. As an application, we also study the exponential stability of mild solutions of such equations.

In this paper we consider a class of stochastic evolution equations arising from initial boundary value problems with both boundary and distributed noise. We prove existence and regularity of mild solutions. Then we consider a controlled version of the model and prove the existence of optimal controls and develop the necessary conditions of optimality for partially observed problems using relaxed controls.

The cross sectional, retrospective descriptive study was done to document the number of GBS patient needed critical care, pattern of their presentation, management, complications and outcome in Pediatric intensive care unit (PICU) of Dhaka Shishu Hospital from January 2011 to December 2013. Data was collected from the admission record file in PICU. A total of 30 patients aged 1 to 15 years diagnosed as Cruillain-Barre syndrome were included in the study. Detailed history, clinical examination, investigations, treatment modality and outcome for GBS was recorded including age, gender, cause of transfer to ICU, antecedent illness, respiratory muscles and bulbar paralysis, cranial nerve involvement, sensory and autonomic dysfunction, CSF study. During the study period, a total of 214 patients were diagnosed as GBS in the hospital and 30 patients were transferred to PICU. Among those, 29 (96.7%) patient were classical GBS and 1 (3.3%) relapse GBS. Common cause of transfer to ICU was respiratory muscle and bulbar paralysis (27, 90%). Most patients were in the age range of 1-5 years (20, 66.7%). Autonomic dysfunction was present in 16 (53.3%) cases and cranial nerve involvement in 1 (3.3%) cases. In 22 (73.3%) patients the antecedent event was respiratory infections and diarrhea in 2 (20%) cases. CSF study was done in 25 (83.3%) patients and albuminocytological dissociation was found in 19 (76%) cases. Total 26 (86.7%) patients were treated with IVIG and rest were with steroid (4, 13.3%). 12 (40%) patients needed mechanical ventilation, respiratory muscle paralysis (9, 75%) was the commonest indication. Most common complication during treatment was aspiration pneumonia (14, 46.7%). Twenty-three patients (76.7%) were improved and transfer-red to ward, 7 (23.3%) expired. Bulbar involvement with respiratory failure is the most common indication of admission in ICU. WIG is the effective treatment modality and need of mechanical ventilation indicates poor outcome.

In this paper we develop the necessary conditions of optimality for partially observed control problems governed by stochastic neutral evolution equations on Hilbert spaces driven by relaxed controls.

In this note we present sufficient conditions for the existenceof Radon-Nikodym derivatives (RND) of operator valued measures withrespect to scalar measures. The RND is characterized by the Bochnerintegral in the strong operator topology of a strongly measurable operatorvalued function with respect to a nonnegative finite measure. Using thisresult we also obtain a characterization of compact sets in the space ofoperator valued measures. An extension of this result is also given usingthe theory of Pettis integral. These results have interesting applicationsin the study of evolution equations on Banach spaces driven by operatorvalued measures as structural controls. 1. IntroductionOne of the most important topics in the theory of vector measures is thequestion of existence of Radon-Nikodym derivatives (RND) of one vector mea-sure with respect to another. In particular, the question of existence of RNDof a vector measure with respect to a nonnegative scalar measure is historicallythe most important one. It is well known that this classifies Banach spaceswhich have Radon-Nikodym Property (RNP) and those which lack this prop-erty. This property has major implications in the study of weak compactnessin function spaces like L

In this paper we propose a dynamic model representing the temporal evolution of the levels of power generation (installed capacity) from two competing sources. These are renewable and conventional (fossil) sources. The percentage penetration rates of renewable and nonrenewable sources are considered as control or decision variables. We introduce an objective functional based on energy demand, production of pollution associated with usage of fossil fuels, and the cost of their systematic substitution by renewable sources. Pontryagin minimum principle is used to determine optimal control policy through minimizing energy generation from fossil fuels while meeting the energy demand as closely as possible through gradual replacement of nonrenewable sources by renewable ones. For different choices of plan periods, optimal generation path along with the corresponding control policies are presented. These results demonstrate that modern control theory can be used effectively to formulate optimal socio-economic policies.

In this paper we consider a class of partially observed semilinear stochastic evolution equations on infinite dimensional Hilbert spaces subject to measurement uncertainty. We prove the existence of optimal feedback control law from a class of operator valued functions furnished with the Tychonoff product topology. This is an extension of our previous results for uncertain systems governed by deterministic differential equations on Banach spaces. Also we present a result on existence of optimal feedback control law for a class of uncertain stochastic systems modeled by differential inclusions.

a b s t r a c t In this paper we present a technique for the design of decentralized controllers for mean square stability of a large scale system with cascaded clusters of subsystems. Each subsystem is linear and time-invariant and both system and measurement are subject to Gaussian noise. For stability analysis of this system we consider the effects of Additive White Gaussian Noise (AWGN) channels used for exchanging information between subsystems.