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A numerical algorithm for optimal control of a class of hybrid systems: Differential transformation based approach. (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:
65K10Optimization techniques (numerical methods)
49J15Optimal control problems with ODE (existence)
49N10Linear-quadratic optimal control problems
49M25Discrete approximations in calculus of variations