Optimal guidance laws using generalized weighting functions

Abstract

In this dissertation, a generalized optimal guidance law with an arbitrary weighting function for an interception or an impact angle control is proposed. The generalized formulation of weighted optimal guidance laws that satisfy the required terminal constraints is obtained by solving an optimal control problem with a control energy cost weighted by an arbitrary positive function. From the generalized formulation, a feasible set of weighting functions that can be used for the guidance law design is explicitly determined. Then, the proposed formulation is compared with previous works from a generalization standpoint. Consequently, it is shown that the proposed formulation can be regarded as a more general form of the optimal guidance laws that were reported previously. This result has potential significance because it can provide an additional degree of freedom in designing a new guidance law that accomplishes various guidance objectives through appropriate choices in feasible weighting functions. In order to implement the guidance law, an alternative form of proposed guidance law is derived and a practical time-to-go estimation method is proposed by using an explicit closed-form solution of a curved trajectory that is dependent upon the weighting function. In order to illustrate the proposed result, several weighted optimal guidance laws that provide specific guidance objectives are devised, based on analytical weighting functions, such as a power function, a rational function, an exponential function, Gaussian function, and a sinusoidal function. Furthermore, their characteristics are investigated. Nonlinear simulations are performed to determine the performance of several proposed guidance laws. The results indicate that the proposed guidance laws can achieve the following useful guidance objectives: improving the terminal performance by introducing zero terminal command, alleviating the sensitivities to an initial heading error and a time-to-go estimation e...