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In this paper, we derive the necessary conditions for time-energy optimal control of input-affine nonlinear systems using Hamilton–Jacobi–Bellman equation. The objective function is chosen as a weighted combination of control effort and time-horizon minimisation. The necessary conditions of optimality are transformed such that the resultant conditions are structurally similar to a differential matrix Riccati equation. A closed-form approximate solution to these necessary conditions is derived such that the resulting closed-loop dynamics is locally exponentially stable around the origin. Furthermore, it is also shown that the states converge within a ball of an arbitrarily small radius around the origin within a finite time. Finally, the performance of the proposed controller is tested using numerical simulations for Vander Pol's oscillator as well as spacecraft detumbling problem. Furthermore, the performance of the proposed controller is also tested in comparison to the infinite-horizon state-dependent Riccati equation controller. [ABSTRACT FROM AUTHOR]

In this paper, cooperative guidance strategies for the survival of cooperating team of two unmanned aerial vehicles (UAVs) against two attackers are proposed. The guidance schemes are designed under the assumptions that each UAV is being pursued by one attacker without cooperation with other attacker. The guidance schemes are designed to combat attackers guided either by proportional navigation (PN) or augmented PN guidance methodologies. The attackers are lured onto a collision course with each other such that intra-attacker interception is achieved before the target UAVs are captured. Sliding mode control techniques are employed to satisfy the sufficiency conditions for the survival within a finite time. Due to the nonlinear framework used for guidance design, the proposed strategies remain effective even for the engagements with large heading angle errors. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance strategies under various engagement geometries. [ABSTRACT FROM AUTHOR]