SPM for One- and Multi- Parameter DCS and their Applications

Study of a generalized problem is very important in the sense it provides complete picture of the problem. Accordingly a generalized singularly perturbed multiparemter discrete control system with n parameters is the focus of this study. Individual problems can be studied easily from the generalized study. For example in a n parameter study for n=2 results in the study of a two-parameter problem. Singularly perturbed systems are nothing but time-scale systems that exhibit computational stiffness and obtaining the exact solution of two-point boundary value of these systems is considerably difficult requiring special numerical techniques. An n parameter system exhibits n+1 time-scales leading to chaos. Singular perturbation methods that reduce the order of the system, remove the stiffness of the system and satisfy the specified boundary conditions with a suboptimal solution close to exact solution are very much welcome for stiff boundary value problems and optimal control problems.