A differential transformation based computational method for switched linear quadratic optimal control

A computational method based on differential transformation is proposed for solving switched linear quadratic (SLQ) optimal control problems with a predefined switching sequence. From the necessary conditions for optimality, the SLQ optimal control problem is first converted into a two-point boundary value problem (TPBVP) with additional transverse conditions at the switching times. Then we propose a differential transformation algorithm for solving the TPBVP in which the optimal solution is computed in the form of a finite- term Taylor series. We discuss the computational complexity of the differential transformation algorithm and analyze the error of the numerical solution. The method has been shown to be simple to implement. The performance of the differential transformation algorithm is demonstrated through numerical examples.