*(English)*Zbl 1157.65040

The authors propose a novel numerical algorithm based on a differential transformation for solving optimal control problems for a class of hybrid systems with a predefined mode sequence. Using the differential transformation, the hybrid optimal control problem is converted to a problem for solving a system of algebraic equations. The advantage of the differential transformation algorithm is that it permits us to solve a system of algebraic equations instead of a discontinuous differential two-point boundary value problem with unknown switching times. Through the inverse differential transformation, the solution in the form of a finite-terms series of a chosen basis system is obtained.

For switched linear quadratic optimal control a computationally efficient differential transformation algorithm (utilizes the special structure of the problem) is proposed. Main result: The proposed differential transformation algorithm can be applied to various hybrid optimal control problems efficiently which is demonstrated by solving illustrative examples; the error of the numerical solution is also analysed. It is also simple to be implemented and easy to be expanded as the numbers of modes and switching times increase.

##### MSC:

65K10 | Optimization techniques (numerical methods) |

49J15 | Optimal control problems with ODE (existence) |

49N10 | Linear-quadratic optimal control problems |

49M25 | Discrete approximations in calculus of variations |