A Robust Computational Technique for Model Order Reduction of Two-Time-Scale Discrete Systems via Genetic Algorithms

A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach

Solution of Inverse Kinematics Problem using Genetic Algorithms

In this paper, the solution of inverse kinematics problem of robot manipulators using genetic algorithms (GA) is presented. Two versions of genetic algorithms are used which include the conventional GA and the continuous GA. The inverse kinematics problem is formulated as an optimization problem based on the concept of minimizing the accumulative path deviation in the absence of any obstacles in the workspace. Simulation results show that the continuous GA outperforms the conventional GA from all aspects. The superiority of the continuous GA is seen in that it will always provide smooth and faster solutions as compared with the conventional GA

A Residual Power Series Technique for Solving Systems of Initial Value Problems

In this article, a residual power series technique for the power series solution of systems of initial value problems is introduced. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed technique obtains Taylor expansion of the solution of a system and reproduces the exact solution when the solution is polynomial. Numerical examples are included to demonstrate the efficiency, accuracy, and applicability of the presented technique. The results reveal that the technique is very effective, straightforward, and simple