Abstract
Abstract In the paper, the optimal bang-bang control problem has been treated. The linear time-invariant systems are treated according to the equation : X ˙ _ = A X _ t + B u _ ( t ) , where the primary objective is to transfer a system from an arbitrary initial state x _ o to the determined target set in minimum time tK. The control variable u _ ( t ) is imposed to the constraints of the shape: a i ≤ u _ i ≤ c i , i = 1 , 2 , , m ; t e [ t o , t * ] . The performance index to be minimized is in the form : J ( u _ ) = t f − t o . So, the problem is to find the optimal control law u _ * which satisfies the above conditions. The powerfull procedure for solving the nonlinear programming problems is applied to the optimal control problem described. It is based on set of sequence of linear programs, each solved using LP/PROTRAN software of IMSL. By suitable modifications, we modify our control problem to classical NLP problem, linearize the objective and constraint function, and get the solution iteratively,. The advantages of described approach are well discussed and trends for future research in the area are given.
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