This chapter is dedicated to the development of the optimum control theory, which forms the basis of control systems analysis and design for a large number of problems and those that occur in differential game theory. Theoretical developments are aimed at optimization of a general, non‐linear costfunction (performance index) where the evolution of the states is defined by a set of non‐linear differential equations. The chapter introduces the use of the Euler‐Lagrange multiplier for incorporating equality constraints, and the construction of the Hamiltonian for deriving optimum control strategies for parties involved in a game. It then considers the dynamic optimization problem utilizing the Bolza formulation and uses variational calculus to derive necessary and sufficient conditions for optimality. Finally, the chapter considers the application of the linear system with quadratic performance index (LQPI) problem to two‐party and three‐party differential game guidance problems. These are recognized as the pursuer‐evader games.


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    Title :

    Optimum Control and Differential Game Theory


    Contributors:


    Publication date :

    2017-04-25


    Size :

    47 pages




    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English




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