Optimal Control Approach to Robust Control of Linear and Non-linear Systems

This paper presents an optimal control approach to robust control of linear and non-linear systems. The approach translates the robust control problems into optimal control problems of minimizing cost functionals. Because of the uncertainty bound that is reflected in the cost functionals, the solution of the optimal control problems are solutions of the robust control problems. The optimal control approach allows us to solve some non-linear robust control problems that cannot be easily solved otherwise.   Keywords: Robust Control, Optimal Control, Cost Functional, Dynamic Equation, Riccati equation, Uncertainty

A Mathematical Model for Integrating Product of Two Functions

Integration by parts is a well-known method of integrating product of two functions. If the integrand involves a polynomial  of degree n and another function  that can be integrated at least (n+1) times, then the solution to     is guaranteed after n routine applications of integration by parts method. This paper presents a mathematical model for integrating product of two functions without going through the routine application of integration by parts at each stage of integration, thus saving a lot of computational time. Some examples were considered to illustrate the effectiveness of the model. The model is found to be appropriate as it gives the same result with the well-known integration by parts method. Keywords: Integrand; Mathematical model; Integration by parts; Differentiable function

Budget Implementation and Economic Growth in Nigeria

This study examines the effect of budget implementation on the Nigerian economic growth and provides panacea to the problem of budget allocation and its implementation. To achieve this broad goal, the econometric model of ordinary least square (OLS) regression test was employed for analysis and time series data span from 1993 to 2010 was considered. Budget in the public sector of Nigeria has almost become a ritual or a yearly affairs which though good in content but without appreciable result. The issue of budget implementation has long been a source of concern to the public and also considering the important impetus of budget implementation on economic growth and development in Nigeria. The dependent variable was proxied by gross domestic product (GDP), while the independent variables were public total expenditure (PEX), public recurrent expenditure (PRE), public capital expenditure (PCE) and external debt (EXD). The results revealed that budget implementation has a positive effect impact on Nigeria economic growth. The results further showed a positive relationship between GDP and public total expenditure (PEX), public recurrent expenditure (PRE), public capital expenditure, external debt (EXD), while public capital expenditure (PCE) shows a negative relationship to GDP.  The study recommends that government should enact on enabling law that will ensure the workability of its budgets according to plans and increase the proportion of capital expenditure to recurrent expenditure so that the budget can have growth and development inducement among others Keywords: Budget, Budget implementation, Government policy Public expenditure, Fiscal policy

On the Equilibrium Points of Three Mutually Competing, Symmetric and Continuous Time Reproducing Organisms

This work deals with the problem of three mutually competing species within a stable ecosystem. The model is represented by a system of non-linear ordinary differential equations. As much as six non-extinction equilibrium states have been obtained depending on the value of various interaction or efficiency parameters.  A set of numerical schemes for the discrete solution of the resulting system  have been developed using the technique of non-local approximation and renormalisation of  the denominator function which are the bedrock of non-standard finite difference method. The new scheme confirms that the analytic equilibrium points of the system compares favourably with a Runge kutta scheme of order four. Keywords: Mutually competing, Continuous time reproducing organism, Nonstandard Method, Equilibrium point, Non-local approximation

Minimization of Losses on Electric Power Transmission Lines

Availability of electric power has been the most powerful vehicle for facilitating economic, industrial and social developments of any nation. Electric power is transmitted by means of transmission lines which deliver bulk power from generating stations to load centres and consumers. For electric power to get to the final consumers in proper form and quality, losses along the lines must be reduced to the barest minimum. In this paper, a mathematical model of losses along electric power transmission lines was developed using a combination of ohmic and corona losses. The resulting model, which is a nonlinear multivariable unconstrained optimization problem, was minimized using the classical optimization technique. From the results, we were able to see that power losses on transmission lines will be minimized if we transmit electric power at a very low current and at an operating voltage that is very close to the critical disruptive voltage. Also the spacing between the conductors should be large in comparison to their diameters. These results, gotten by the use of an analytical method, conform to the existing results for power transmission. Keywords: Power Losses, Minimization, Transmission, Classical Optimization, Mathematical Model

Growth Performance Characteristics of Okra (Hibiscus esculentus) using Improvised Drip Irrigation System

Okra is a common and popular vegetable crop used in Nigeria.  Irrigation method has very significant influence on okra (Hibiscus esculentus) production. A careful effect of marginal water quality on IDI and control system which were subjected to the same conditions was investigated. An experimental field area of 13.5 m2 by 6.0 m2 was properly cleared, stumped, ploughed, harrowed and leveled.  High yielding and disease resistant okra variety seeds were carefully selected and planted at a regular interval of 0.6 m. The results of statistical analysis obtained using Completely Randomized Blocked Design (CRBD) (P˂0.05) revealed that there were significant differences on water application which reflected an increase in some agronomic parameters such as growth, weight, yield and vegetative development of the okra. These selected okra agronomic parameters showed that the okra performed in IDI. Maximum fruit yield of 71.71% and water utilization efficiency of 55.49% was obtained by using IDI system

Effect of Pretreatments on the Drying Characteristics and Quality of African Star Apple (Chrysophyllum albidum)

Fruits, due to high moisture content, deteriorate quickly when not adequately preserved. Drying, a common preservation method, will affect quality of final product if not properly controlled. Pretreatments prior to drying have been established as a way of retaining product qualities. This study investigated the effect of pretreatments on the qualities of dried African star apple flesh. African star apple fleshes were sliced (2, 4, 6 and 8 mm) and subjected to pretreatments [blanching (80 ºC for 3 min), lime juice (100%), ascorbic acid and salt solution (1:25 w/v)]. Untreated samples served as control. Samples were dried in cabinet dryer (50, 55 and 60 ºC) at 2 m/s constant air flow-rate, monitored at intervals, until constant weight was obtained. Ascorbic acid and colour measurement of the fresh and dried sample were determined using standard method. The moisture contents of the African star apple flesh were observed to reduce from a mean value of 70.44%, 71.55% and 73.24% to 2.38%, 1.91% and 3.23% at temperatures of 50, 55 and 60 °C, respectively. The total drying time ranged between 7 to 8 h. Colour of the dried African star apple was significantly preserved by the pretreatments used, and low overall color change (ΔE) was obtained at the lowest drying temperature (50oC). The ascorbic acid and lime pretreatments however had better colour overall. Lime pretreatment for 2 mm thick at 50ºC gave the best result in terms of ascorbic acid retention. Hence, lime juice pre-treatment has potentials of retaining quality of dried fruits

Water entrepreneurship and financialisation: Complexities for the attainment of SDG in sub-Saharan Africa

This study explores the potential of water financialisation and entrepreneurship in sub-Saharan Africa (SSA) to supplant the traditional responsibility of national, state, and local governments in providing public water supply, aligning with SDG Goals. Despite its typical association with the global north, a shifting landscape reveals emerging financial actors and multinational companies playing a more prominent role, prompting governance and accountability inquiries. Given the dearth of investment and persisting challenges in SSA's water infrastructure, the burgeoning involvement of financial actors and capital management entities in the water cycle seems inevitable. However, this trend raises concerns about exacerbating global water stress. Through qualitative methods, the study engaged 50 SSA participants via open-ended questionnaires, analysed using thematic analysis. The findings underscore a nuanced perspective. While acknowledging the potential of water financialisation and entrepreneurship to drive essential investment in SSA's water sector, the research emphasizes the irreplaceable role of government in policy execution and safeguarding citizens' well-being. Government intervention remains crucial to ensuring equitable water access and sustainability. Additionally, the analysis suggests that overemphasizing water financialisation could divert attention from critical infrastructural and technological advancements needed in SSA's water sector. This underscores the necessity of a balanced and comprehensive approach to address the multifaceted challenges surrounding water availability, governance, and sustainability in the region

Optimisation of Microwave Drying of Tomatoes (Solanum lycopersicum L.) Slices Using Taguchi Method

The effect of the processing parameters on the microwave drying of tomatoes was investigated and the process was optimized by using Taguchi technique. Pretreatments (water blanching (WAB), ascorbic acid (ASA) and sodium metabisulphite (SMB)), slice thickness (4 mm, 6 mm and 8 mm) and microwave power level (90W, 180W and 360W) were the parameters used in the study. The increase in microwave power accelerated the drying process, thus shortening the drying time. The drying rate curves indicated the absence of a constant-rate drying rate period in the entire drying process combinations under study. It was found that the pretreatment with SMB along with 4 mm thick tomato slice and 360 W for microwave oven drying were the best processing combination within the experimental domain considered in the present study. Thus, this is the best level that can guarantee minimum drying time and time of exposure of the samples to drying microwave power thereby retaining the qualities of the dried tomatoes. The results found in this study can be applied to industrial designs and operational guides for the microwave drying of tomato slices. Keywords: Optimisation, microwave drying, drying kinetics, tomatoes, Taguchi technique