A study on solution of matrix riccati differential equations using ant colony programming and simulink / Mohd Zahurin Mohamed Kamali

Mohamed Kamali, Mohd Zahurin (2015) A study on solution of matrix riccati differential equations using ant colony programming and simulink / Mohd Zahurin Mohamed Kamali. PhD thesis, University of Malaya.

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Abstract

Swarm intelligence is a modern artificial intelligence discipline that is concerned with the design and optimization of multiagent systems with applications in robotics. This non-traditional approach is fundamentally different from the traditional approaches. In- stead of a sophisticated controller that governs the global behavior of the system, the swarm intelligence principle is based on many unsophisticated entities (for example such as ants, termites, bees etc.) that cooperate and interact in order to exhibit a desired behav- ior. In this thesis, we implement the modified ant colony programming (ACP) algorithm for solving the matrix Riccati differential equation (MRDE). Solving MRDE, especially nonlinear MRDE is the central issue in optimal control theory. It has been found that by implementing the ACP algorithm, the solution predicted is approximately close or similar to the exact solution. Besides that, we compared our present work with numerical solution obtained by Runge-Kutta fourth order (RK4) and a non-traditional method such as the ge- netic programming (GP). Furthermore, in this work, we also showed the implementation of the Simulink, for solving the MRDE in order to get the optimal solutions. This add-on Simulink package in the Matlab software can be used to create a block of diagrams which can be translated into a system of ordinary differential equations. Illustrative examples are shown to prove the effectiveness of the proposed algorithm. Moreover, the proposed method have been well applied to biological and engineering problems such as linear and nonlinear singular systems, human immunodeficiency virus (HIV) models, microbial growth model and ethanol fermentation process. iii

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