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Papers by MASIALA MAVUNGU

Research paper thumbnail of Control and Path Planning for a Three-Wheeled Autonomous Vehicle Robot

Three-Wheeled Mobile Robot, 2024

The purpose of this paper is to design and calculate feasible control functions and the correspon... more The purpose of this paper is to design and calculate feasible control functions and the corresponding feasible system response to drive a three-wheeled autonomous vehicle robot from a given initial state to a final state such that the total running cost is minimized. To find the solution of the problem, the following way is used: The feasible controls, obtained from the normal equations of optimality, are defined as functions involving the state and the costate variables. After the substitution of such controls into the state and the costate systems of ordinary differential equations, a combined control-free state-costate system of ordinary differential equations is obtained and solved numerically by using a fourth-order Runge-Kutta method coded into Matlab. Computational Simulations are developed and provided to demonstrate the effectiveness and the reliability of the approach..

Research paper thumbnail of Feb2024 Three Wheeled Cover Letter

Research paper thumbnail of Open-loop Control Strategies and Feasible System Response for a Rear-Axle Bicycle Robot

This paper aims at computing feasible control strategies and the corresponding feasible state tra... more This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin's Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

Research paper thumbnail of Optimal Control Strategies and Optimal Trajectory for a Four-Wheeled Autonomous Vehicle Robot

Optimal Control Strategies and Optimal Trajectory for a Four-Wheeled Autonomous Vehicle Robot, 2023

This paper aims at calculating optimal control strategies to drive a four-wheeled autonomous vehi... more This paper aims at calculating optimal control strategies to drive a four-wheeled autonomous vehicle from a given initial state to a final state in a such a way that a running cost is minimized. To solve the problem the following approach is used: The vehicle is mathematically modeled as a non-linear system of seven ODEs with seven state variables and four control variables. A costate system of seven ODEs is generated. The control's optimality conditions generate four constrained optimal control strategies and each of them is defined as a function of state and costate variables. Their expressions are substituted into the state and the costate systems. Such systems are combined to give a nonlinear system of fourteen ODEs. The results are the optimal system response defined by the optimal state functions which involve the robot optimal path in the horizontal plane and the robot velocity, the optimal costate functions, the optimal control functions. Computational Simulations are developed to show the effectiveness and the reliability of the results.

Research paper thumbnail of Modeling and Control of a Front-Axle Bicycle Robot

This paper develops feasible control strategies and associated system responses to bring an auton... more This paper develops feasible control strategies and associated system responses to bring an autonomous front-axle bicycle robot from specified initial conditions to final conditions such that a specific performance index is minimized. To solve the problem, the following approach is used: The feasible controls derived from the normal equations of optimality are substituted into the state and the costate systems and form a combined control-free state-costate system which is vectorized to enable and ease the application of a numerical method. A computer program written in Matlab computer programming language, codes a fourth-order Runge-Kutta numerical method and then solve the combined state-costate system of ordinary differential equations. The obtained results are the feasible bicycle robot trajectory, the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations are designed and provided to persuade on the effectiveness and the reliability of the approach.

Research paper thumbnail of Computation of financial risk using principal component analysis

Algorithmic Finance

This article uses Principal Component Analysis to compute and extract the main factors for the fi... more This article uses Principal Component Analysis to compute and extract the main factors for the financial risk of a portfolio, to determine the most dominating stock for each risk factor and for each portfolio and finally to compute the total risk of the portfolio. Firstly, each dataset is standardized and yields a new datasets. For each obtained dataset a covariance matrix is constructed from which the eigenvalues and eigenvectors are computed. The eigenvectors are linearly independent one to another and span a real vector space where the dimension is equal to the number of the original variables. They are also orthogonal and yield the principal risk components (pcs) also called principal risk axis, principal risk directions or main risk factors for the risk of the portfolios. They capture the maximum variance (risk) of the original dataset. Their number may even be reduced with minimum (negligible) loss of information and they constitute the new system of coordinates. Every princip...

Research paper thumbnail of Open-loop Control Strategies and Feasible System Response for a Rear-Axle Bicycle Robot

This paper aims at computing feasible control strategies and the corresponding feasible state tra... more This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

Research paper thumbnail of Feasible Control Strategies and Feasible System Response for the Navigation of an Autonomous Ship Robot

This paper develops a methodology to control the navigation of an autonomous ship robot from an i... more This paper develops a methodology to control the navigation of an autonomous ship robot from an initial state to a final. To solve the problem the following approach is used: The ship robot system is modelled as a control system of six ordinary differential equations involving six state variables and three control variables. After having computed the system Hamiltonian, the feasible controls for optimality are derived from the normal equations of optimality as functions of the state and costate variables. Such controls are substituted into the state and the costate equations and give a combined control-free state-costate system of ordinary differential equations which is solved numerically by using a developed Matlab computer program. Associated computational simulations are designed and provided to show the reliability of the approach.

Research paper thumbnail of Control and Trajectory Planning of an Autonomous Bicycle Robot

Computation

This paper addresses the modeling and the control of an autonomous bicycle robot where the refere... more This paper addresses the modeling and the control of an autonomous bicycle robot where the reference point is the center of gravity. The controls are based on the wheel heading’s angular velocity and the steering’s angular velocity. They have been developed to drive the autonomous bicycle robot from a given initial state to a final state, so that the total running cost is minimized. To solve the problem, the following approach was used: after having computed the control system Hamiltonian, Pontryagin’s Minimum Principle was applied to derive the feasible controls and the costate system of ordinary differential equations. The feasible controls, derived as functions of the state and costate variables, were substituted into the combined nonlinear state–costate system of ordinary differential equations and yielded a control-free, state–costate system of ordinary differential equations. Such a system was judiciously vectorized to easily enable the application of any computer program writ...

Research paper thumbnail of Point-to-point stochastic control of a self-financing portfolio

Algorithmic Finance

This paper aims at computing optimal control policies to drive a self-financing portfolio of fina... more This paper aims at computing optimal control policies to drive a self-financing portfolio of financial assets from a given initial financial state to a final state in a given time horizon such that for the first case, the functional portfolio financial risk is minimized and, for the second case, the functional portfolio profit is maximized. The optimal control policies are the optimal investment allocation processes, the optimal state process is the optimal investor’s wealth process, also called the system response to the input control and is obtained by solving the combined system of differential equations formed by the state and costate system of differential equations derived and extracted from Pontryagin’s Minimum Principle. Computational simulations are provided to show the effectiveness and the reliability of the approach.

Research paper thumbnail of Computation of optimal investment allocations in a sequential portfolio optimisation

Orientation: This article is related to Financial Risk Management, Investment Management and Port... more Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from p...

Research paper thumbnail of Nonlinear control of an autonomous vehicle

Research paper thumbnail of Modelling and computational simulation of optimal auction design and bidding strategies

Journal of Economic and Financial Sciences

Research paper thumbnail of Computation of optimal investment allocations in a sequential portfolio optimisation

Journal of Economic and Financial Sciences

Orientation: This article is related to Financial Risk Management, Investment Management and Port... more Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from p...

Research paper thumbnail of Cooperative Spectrum Sensing in the DSA: Simulation of Spectrum Sensing Time Consumptions by Cognitive Radio Secondary Users

Lecture Notes in Electrical Engineering, 2017

Research paper thumbnail of Nonlinear control of an autonomous vehicle

Research paper thumbnail of Computation of optimal investment allocations in a sequential portfolio optimisation

Journal of Economic and Financial Sciences

Orientation: This article is related to Financial Risk Management, Investment Management and Port... more Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from p...

Research paper thumbnail of Control and Path Planning for a Three-Wheeled Autonomous Vehicle Robot

Three-Wheeled Mobile Robot, 2024

The purpose of this paper is to design and calculate feasible control functions and the correspon... more The purpose of this paper is to design and calculate feasible control functions and the corresponding feasible system response to drive a three-wheeled autonomous vehicle robot from a given initial state to a final state such that the total running cost is minimized. To find the solution of the problem, the following way is used: The feasible controls, obtained from the normal equations of optimality, are defined as functions involving the state and the costate variables. After the substitution of such controls into the state and the costate systems of ordinary differential equations, a combined control-free state-costate system of ordinary differential equations is obtained and solved numerically by using a fourth-order Runge-Kutta method coded into Matlab. Computational Simulations are developed and provided to demonstrate the effectiveness and the reliability of the approach..

Research paper thumbnail of Feb2024 Three Wheeled Cover Letter

Research paper thumbnail of Open-loop Control Strategies and Feasible System Response for a Rear-Axle Bicycle Robot

This paper aims at computing feasible control strategies and the corresponding feasible state tra... more This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin's Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

Research paper thumbnail of Optimal Control Strategies and Optimal Trajectory for a Four-Wheeled Autonomous Vehicle Robot

Optimal Control Strategies and Optimal Trajectory for a Four-Wheeled Autonomous Vehicle Robot, 2023

This paper aims at calculating optimal control strategies to drive a four-wheeled autonomous vehi... more This paper aims at calculating optimal control strategies to drive a four-wheeled autonomous vehicle from a given initial state to a final state in a such a way that a running cost is minimized. To solve the problem the following approach is used: The vehicle is mathematically modeled as a non-linear system of seven ODEs with seven state variables and four control variables. A costate system of seven ODEs is generated. The control's optimality conditions generate four constrained optimal control strategies and each of them is defined as a function of state and costate variables. Their expressions are substituted into the state and the costate systems. Such systems are combined to give a nonlinear system of fourteen ODEs. The results are the optimal system response defined by the optimal state functions which involve the robot optimal path in the horizontal plane and the robot velocity, the optimal costate functions, the optimal control functions. Computational Simulations are developed to show the effectiveness and the reliability of the results.

Research paper thumbnail of Modeling and Control of a Front-Axle Bicycle Robot

This paper develops feasible control strategies and associated system responses to bring an auton... more This paper develops feasible control strategies and associated system responses to bring an autonomous front-axle bicycle robot from specified initial conditions to final conditions such that a specific performance index is minimized. To solve the problem, the following approach is used: The feasible controls derived from the normal equations of optimality are substituted into the state and the costate systems and form a combined control-free state-costate system which is vectorized to enable and ease the application of a numerical method. A computer program written in Matlab computer programming language, codes a fourth-order Runge-Kutta numerical method and then solve the combined state-costate system of ordinary differential equations. The obtained results are the feasible bicycle robot trajectory, the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations are designed and provided to persuade on the effectiveness and the reliability of the approach.

Research paper thumbnail of Computation of financial risk using principal component analysis

Algorithmic Finance

This article uses Principal Component Analysis to compute and extract the main factors for the fi... more This article uses Principal Component Analysis to compute and extract the main factors for the financial risk of a portfolio, to determine the most dominating stock for each risk factor and for each portfolio and finally to compute the total risk of the portfolio. Firstly, each dataset is standardized and yields a new datasets. For each obtained dataset a covariance matrix is constructed from which the eigenvalues and eigenvectors are computed. The eigenvectors are linearly independent one to another and span a real vector space where the dimension is equal to the number of the original variables. They are also orthogonal and yield the principal risk components (pcs) also called principal risk axis, principal risk directions or main risk factors for the risk of the portfolios. They capture the maximum variance (risk) of the original dataset. Their number may even be reduced with minimum (negligible) loss of information and they constitute the new system of coordinates. Every princip...

Research paper thumbnail of Open-loop Control Strategies and Feasible System Response for a Rear-Axle Bicycle Robot

This paper aims at computing feasible control strategies and the corresponding feasible state tra... more This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

Research paper thumbnail of Feasible Control Strategies and Feasible System Response for the Navigation of an Autonomous Ship Robot

This paper develops a methodology to control the navigation of an autonomous ship robot from an i... more This paper develops a methodology to control the navigation of an autonomous ship robot from an initial state to a final. To solve the problem the following approach is used: The ship robot system is modelled as a control system of six ordinary differential equations involving six state variables and three control variables. After having computed the system Hamiltonian, the feasible controls for optimality are derived from the normal equations of optimality as functions of the state and costate variables. Such controls are substituted into the state and the costate equations and give a combined control-free state-costate system of ordinary differential equations which is solved numerically by using a developed Matlab computer program. Associated computational simulations are designed and provided to show the reliability of the approach.

Research paper thumbnail of Control and Trajectory Planning of an Autonomous Bicycle Robot

Computation

This paper addresses the modeling and the control of an autonomous bicycle robot where the refere... more This paper addresses the modeling and the control of an autonomous bicycle robot where the reference point is the center of gravity. The controls are based on the wheel heading’s angular velocity and the steering’s angular velocity. They have been developed to drive the autonomous bicycle robot from a given initial state to a final state, so that the total running cost is minimized. To solve the problem, the following approach was used: after having computed the control system Hamiltonian, Pontryagin’s Minimum Principle was applied to derive the feasible controls and the costate system of ordinary differential equations. The feasible controls, derived as functions of the state and costate variables, were substituted into the combined nonlinear state–costate system of ordinary differential equations and yielded a control-free, state–costate system of ordinary differential equations. Such a system was judiciously vectorized to easily enable the application of any computer program writ...

Research paper thumbnail of Point-to-point stochastic control of a self-financing portfolio

Algorithmic Finance

This paper aims at computing optimal control policies to drive a self-financing portfolio of fina... more This paper aims at computing optimal control policies to drive a self-financing portfolio of financial assets from a given initial financial state to a final state in a given time horizon such that for the first case, the functional portfolio financial risk is minimized and, for the second case, the functional portfolio profit is maximized. The optimal control policies are the optimal investment allocation processes, the optimal state process is the optimal investor’s wealth process, also called the system response to the input control and is obtained by solving the combined system of differential equations formed by the state and costate system of differential equations derived and extracted from Pontryagin’s Minimum Principle. Computational simulations are provided to show the effectiveness and the reliability of the approach.

Research paper thumbnail of Computation of optimal investment allocations in a sequential portfolio optimisation

Orientation: This article is related to Financial Risk Management, Investment Management and Port... more Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from p...

Research paper thumbnail of Nonlinear control of an autonomous vehicle

Research paper thumbnail of Modelling and computational simulation of optimal auction design and bidding strategies

Journal of Economic and Financial Sciences

Research paper thumbnail of Computation of optimal investment allocations in a sequential portfolio optimisation

Journal of Economic and Financial Sciences

Orientation: This article is related to Financial Risk Management, Investment Management and Port... more Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from p...

Research paper thumbnail of Cooperative Spectrum Sensing in the DSA: Simulation of Spectrum Sensing Time Consumptions by Cognitive Radio Secondary Users

Lecture Notes in Electrical Engineering, 2017

Research paper thumbnail of Nonlinear control of an autonomous vehicle

Research paper thumbnail of Computation of optimal investment allocations in a sequential portfolio optimisation

Journal of Economic and Financial Sciences

Orientation: This article is related to Financial Risk Management, Investment Management and Port... more Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from p...