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Zbl 1157.65040
Hwang, I.; Li, J.; Du, D.
A numerical algorithm for optimal control of a class of hybrid systems: Differential transformation based approach. (English)
[J] Int. J. Control 81, No. 2, 277-293 (2008). ISSN 0020-7179; ISSN 1366-5820/e

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.
[Jan Lov\'\išek (Bratislava)]

MSC 2000:: *65K10 Optimization techniques (numerical methods)
49J15 Optimal control problems with ODE (existence)
49N10 Linear-quadratic optimal control problems
49M25 Finite difference methods

Keywords: algorithm; optimal control; hybrid systems; differential transformation; two-point boundary value problem; mode sequence; Hamiltonian, Lagrangian multipliers; error analysis; truncated Taylor series; linear quadratic optimal control

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