Singular perturbation analysis of discrete control systems / D. S. Naidu, A. K. Rao

This monograph presents a tutorial description of singular perturbation analysis of difference equations and its potential use in the synthesis of optimal control laws. Almost every topic is illustrated with numerical results for simple examples.

The first chapter is devoted to scalar nth order difference equations with a small parameter raised to the appropriate power multiplying either the highest order coefficients or the lowest order coefficients. The second chapter is devoted to state space representations of difference equations (vector first order difference equations). Methods are presented for assessing the applicability of singular perturbation analysis, and appropriate formulations if applicable. The use of singular perturbations to simplify the computation of optimal open-loop trajectories for linear systems with quadratic cost functions is described in Chapter 3. Here it is shown how solutions may be obtained as the sum of three components, the degenerate solution, an initial boundary layer solution and a final boundary layer solution. The final chapter shows how the singular perturbation method may be applied to nonlinear equations with degenerate linear equations. The use of the singular perturbation method in solving the Riccati equation for optimal control of systems described by linear difference equations is also described in this chapter.

The book contains a significant number of typographical errors, but it is easy to read and has an extensive list of references. (Zentralblatt)