One of my works is in the computation of the minimal polynomial of the Laplacian matrix associated with a weighted undirected graph. The intention is to look for the lowest-order minimal polynomial among all the Laplacian matrices that are consistent with an undirected graph. The order of the minimal polynomial determines the number of steps needed to achieve consensus for states of a network system. The matlab code for finding the minimal polynomial can be downloaded here (10K Zipped). Details of the approach can be found in the paper.

Z. Wang and CJ Ong, Speeding up finite-time consensus via minimal polynomial of a weighted graph - a numerical approach, submitted for publication consideration.

In the study of switching dynamical system, a common condition is that a minimal dwell time in each mode is needed before switching is allowed. When such a system is subject to constraints, the design and analysis becomes even more complicated. One useful set for such a purpose is a Constraint-Admissible Dwell Time Returnable (CADTR) set. A point x in a CADTR set will return to the same set after the minimal dwell time. Here (6K) is a Matlab M file for the computation of a Constraint-Admissible Dwell Time Returnable CADTR) set. The details of the code can be found in our paper.

CJ Ong, Z. Wang and M.Dehghan, Model Predictive Control for Switching System with Dwell-time Restriction, IEEE Transactions on Automatic Control, Volume 61, Issue 12, Dec. 2016.

One of my works is in the development of an improved algorithm for the numerical solution of the entire regularization path of the Support Vector Machine (SVM)-ISVMP. The ISVMP algorithm is able to handle datasets having duplicate points, nearly duplicate points and linearly dependent points, a common feature among many real world datasets. The Matlab source code for the SVMP algorithm can be downloaded here (25K Zipped). The details of the improvement can be found in our paper.

CJ Ong, S.Y. Shao and J.B.Yang, An improved algorithm for the solution of the entire regularization path of Support Vector Machine, IEEE Transactions on Neural Networks, Vol. 21, No. 3, pp451-462, 2010.

One of my other works is in the characterization of the growth distance between two convex objects. Growth distance is a measure of both separation and penetration between two convex objects. A C version of the source code for computing the growth distance can be downloaded here (36K Zipped). The implementation of the code is described in the paper.

CJ Ong, E Huang and SM Hong, A Fast Growth Distance Algorithm for Incremental Motions, IEEE Transactions on Robotics and Automation, Vol. 16, No.6, 2000.

while the properties of the Growth Distance can be found in

C.J. Ong and EG Gilbert, Growth Distances: New Measures for Object Separation and Penetration, IEEE Transactions on Robotics and Automation, Vol. 12, No. 6, Dec 1996