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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, a nonlinear suboptimal three-dimensional guidance strategy based on a finite-time state-dependent Riccati equation technique is proposed to achieve interception of a non-maneuvering target at a desired impact time. To design the proposed guidance, range error for a spatial engagement between an interceptor and non-maneuvering target is introduced as the difference between the desired range-to-go and range-to-go of the predicted interception point. It is shown that forcing the range error and its rate to the origin are sufficient to achieve impact time constrained interception. Several existing impact time guidance strategies require a time-to-go estimate, to implement their guidance command, which may become erroneous in the presence of measurement noise and affect their performance. However, the proposed guidance does not require any such time-to-go estimate in its design process. Furthermore, guidance for the case of planar engagements is shown to be a special case of the proposed guidance scheme. Finally, numerical simulation studies for multiple engagement geometries, along with a comparison study with an existing strategy, are provided to demonstrate the efficacy of the proposed technique. [ABSTRACT FROM AUTHOR]