A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
SUMMARYOptimal guidance for a dynamical system from a given point to a set of targets is discussed. Detecting for the best target is done in such a way that the capture time is minimized and desirability of targets is maximized. By extending measure theoretical approach for the classical optimal control problem to this case, the nearly optimal control is constructed from the solution of a mixed integer linear programming problem. To find the lower bound of the optimal time a search algorithm is proposed. Numerical examples are also given.
Development of a numerical algorithm for solving optimal control problems is reported in this article. The method is a combination of multi-staging of the original problem to a finite dimensional optimization problem and the recently proposed Whale Optimization Algorithm (WOA). The method is proposed to reduce the required number of iterations. The parallel implementation is also proposed and discussed. Numerical examples are given to check the validity and accuracy of the proposed method. Results show that method converges to the exact solution with accuracy comparable to other numerical methods.
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