In this chapter, we intend to use Vasileva's method (Vasileva, 1963; Wasow, 1965) where the approximate solution is made up of an outer series, inner series and intermediate series. It should be noted that, as shown in Chapter 2, the boundary-layer correction is equivalent to the difference between the inner and intermediate series. However, in working out a large number of control problems by Vasileva's method and the boundary-layer method (Naidu, 1977), it has been found that the former has computational advantages, especially in the case of nonlinear equations as will be apparent at the end of this Chapter. Thus, the contents of this Chapter depend mainly on results from Naidu (1977), Naidu and Rajagopalan (1980) and Rajagopalan and Naidu (19806).

Chapter Contents:

• 6.1 Linear regulator problem
• 6.2 Singular perturbation method
• 6.2.1 Outer-series solution
• 6.2.2 Inner- and intermediate-series solutions
• 6.2.3 Main results
• 6.3 Steady-state regulator problem
• 6.4 Fixed-end-point problem
• 6.4.1 Problem formulation
• 6.4.2 Outer series
• 6.4.3 Inner and intermediate series
• 6.4.4 Main results
• 6.5 Time-scale analysis
• 6.5.1 Slow and fast subsystems
• 6.5.2 Subsystem regulator designs
• 6.6 Conclusions and discussion

Inspec keywords: optimal control; continuous systems; closed loop systems

Other keywords: closed-loop optimal control; nonlinear equation; boundary-layer method; continuous system; approximate solution; Vasileva method; boundary-layer correction

Subjects: Optimal control