The linear quadratic optimization theory is applied to the missile guidance problem including a running cost on the state vector. This inclusion enables to develop a new and effective way for trajectory shaping. For this case, optimal control signal decomposition is presented and the control signal components are established. Then a new optimal guidance control decomposition strategy is developed whereby the terminal guidance phase is separated from the trajectory-shaping phase, thus producing a sub-optimal control. A new formulation of linear quadratic differential game with a penalty on the target estimation error is then proposed for the noise-corrupted environment. This approach, together with the inclusion of a running cost on the state vector, enables to develop a new effective guidance law against smart targets. Numerical comparisons of the new guidance law with some widely used representative guidance laws are performed.
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