In this research, time-optimal open-loop and closed-loop guidance laws for MAVs, such as Samarai, were investigated. Open-loop optimal solutions were achieved with a new technique,based on using mathematical methods, such as calculus of variation and the GA-PSO optimization algorithm. This novel method could overcome difficulties of the usual optimal control methods. The TS approach developed closed-loop guidance that dealt with the novel neural-fuzzy training algorithm based on open-loop optimal trajectories to achieve closed-loop guidance. By feed forwarding the optimal control as a nominal optimum trajectory plus deviation, closed-loop optimal control can be generated. On the other hand, (TS) fuzzy logic needs storing nominal optimal trajectories to train the system. As discussed, the responses of the optimal closed-loop guidance were achieved, and the robustness of closed-loop policies against noises and/or disturbances was studied. However, it was difficult to obtain closed-loop solutions when the other methods, such as dynamic programming or analytical methods, were considered. The case mentioned is an important innovative idea for autonomous MAVs, whose results are important for further developments of Samarai monocopter. The results of this work demonstrated that the closed-loop optimal responses based on TS fuzzy logic methods can damp disturbances for minimum time criterion. However, the result of fuzzy logic is perfectly suitable, where higher noises were applied. Therefore, it can be concluded that fuzzy logic was robust and efficient in eliminating perturbations. It is proposed that aerospace engineers, such as primary trajectory designers, use TS fuzzy training guidance because its robustness was guaranteed by this work, especially for MAVs, such as Samarai.

In this work, a new algorithm is presented with regard to the free initial condition for solving optimal control problems. The reason for presentation of such an algorithm is to develop a suitable method that simplifies difficulties of the optimal control problems that researchers face in common methods of optimal control theory. Also, initial condition as true anomaly is considered to be free in this optimal control problem. To do so, issues such as optimal control theory, orthogonal functions in the Hilbert space, and evolutionary optimizations such as genetic algorithm-particle swarm optimization and imperial competition algorithm are utilized. The algorithm was solved for low-thrust orbital transfer problems which included nonlinear dynamic equations. To validate the algorithm, simplified Edelbaum low-thrust equations are compared with the proposed analytical solutions. Next, the algorithm is investigated for the low-thrust orbital transfers with respect to the equinoctial orbital equations of the minimum-time problem. Results are achieved for two evolutionary optimization methods genetic algorithm-particle swarm optimization and imperial competition algorithm and three orthogonal functions such as Fourier, Chebyshev, and Legendre. Two optimization methods and three orthogonal functions are covered and compared precisely. With respect to the results, this algorithm has the capability to overcome difficulties of the optimal control problems and can be considered as a novelty in this field for the free initial condition problems.

A new guidance scheme for the problem of low-thrust transfer between inclined orbits is developed within the framework of optimal control theory. The objective of the guidance scheme is to provide the appropriate thrust steering program that will transfer the vehicle from inclined low earth orbits to high earth orbits. The presented guidance scheme is determined using Pontryagin's principle such that three desired performance measures are minimized and boundary conditions for this unspecified final time problem are satisfied. One of the novelties of this work is changing the independent variable from time to thrust angle and considering properties of autonomous system equations to reduce to one where an exact analytical solution is obtained. Finally, three performance measure results are compared and the best policy is proposed.