Model Predictive Guidance Law Design in a Two-Dimensional Guidance Problem in Presence of Input Constraint

In this paper, an LMI based guidance algorithm is mainly addressed to design a model predictive guidance law in presence of the input acceleration constraint. For achieving this purpose, firstly, the model predictive guidance problem is mathematically formulated in a two-dimensional problem. In the proposed algorithm, the future behavior of the guidance problem can be predicted by using a dynamical model. At each certain time, the commanded acclamation would be determined while a typical cost function is minimized. In this study, an acceleration command proportional to the line of sight (LOS) rate is considered as the predictive guidance policy with unknown variable gain. Then the model predictive guidance problem would be translated into another minimization problem subject to some linear matrix inequalities (LMI). Hence such an optimization problem can be numerically solved at each known time in the real-time applications. Then the gain of the proposed guidance algorithm can be automatically updated. The proposed method will be used in a typical two-dimensional guidance problem. The simulation results will show the effectiveness of the suggested method in comparing with the existing guidance algorithms.