Pseudospectral technique for continuation methods with application to nonlinear control problems

Abstract

Continuation methods have been successfully applied to complicated nonlinear control systems design. Using a continuation algorithm, a nonlinear control problem can be transferred into a sequence of linear time-varying controls that can be solved using linear control theory. However, since the sequence of linear controls requires that the values of the previous state variables and control signal at each time interval be memorised and integrated as the initial values for the next linear control, the computation is quite intensive. Pseudospectral methods are proposed to solve the problem so that the heavy computational burden can be eased. Since a nonlinearly constrained programming problem becomes a sequence of linearly constrained programming problems due to the application of the continuation method, the presented algorithm prevents a main difficulty encountered in normally using pseudospectral algorithms for nonlinear optimal systems: a local minimum. This advantage makes the proposed scheme attractive to solve problems involving large and highly nonlinear control systems.