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In this paper, an explicit optimal line-of-sight guidance law for second-order binomial control systems is derived in closed-loop without acceleration limit. The problem geometry is assumed in one dimension and the final time and final position are fixed. The formulation is normalized in three forms to give more insight into the design and performance analysis of the guidance law. The computational burdun of the guidance law is reasonable for now-a-day microprocessors; however curve fitting or look-up table may be used for the implementation of the second-order optimal guidance law. The performance of the second-order optimal guidance law is compared in normalized forms with zero-lag and first-order optimal guidance laws using third-, fourth-, and sixth-order binomial control systems with/without acceleration limit. Moreover, the effect of the final time, the equivalent time constant of the vehicle control system, the vehicle-to-target line-of-sight weighting factor in cost function, and acceleration limit are investigated. Normalized miss distance analysis shows that the miss distance of the second-order guidance law is smaller than the two mentioned schemes for small total flight times, especially with large maneuvering capability.

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In this paper, an explicit formulation of optimal line-of-sight strategy is derived in closed-loop for integrated guidance and control (IGC) system without consideration of fin deflection limit. The airframe dynamics is modeled by a second-order nonminimum phase transfer function, describing short period approximation. In the derivation of our optimal control problem, the actuator is assumed to be perfect and without limitation on fin deflection, whereas fin deflection limit is applied for the performance analysis of the presented optimal IGC solution. The problem geometry is assumed in one dimension and the final position and final time are fixed. The formulation is obtained in four different normalized forms to give more insight into the design and performance analysis of the optimal IGC strategy. In addition, guidance gains are obtained analytically in explicit form for steady-state solution. In overall, the performance of IGC is better than that of IGC with steady-state gains, but have more computational burden; however, it is reasonable for now-a-day microprocessors. Curve fitting or look-up table may be used instead for an implementation of optimal IGC strategy. Moreover, parametric study of nondimensional IGC parameters is carried out, such as weighing factor, dc gain, and short period frequency. Finally, the performance of the both IGC strategies is evaluated with airframe model uncertainties.