This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest-order derivatives of a given system’s dynamics. The underlying method uses orthogonal polynomial integral collocation by which successive integrals are taken to approximate all lower-order states. Hence, one set of polynomial coefficients can represent an entire coordinate’s degree of freedom. Specifically, Chebyshev polynomials of the first and second kinds and Legendre polynomials are used over their associated common interpolating grids derived from the bases’ roots and extrema. Simple example problems compare different polynomial bases’ performance to analytical solutions. The planar circular orbit raising problem is used to verify the method with solutions obtained by other pseudospectral methods in literature. Finally, a rocket landing flip maneuver problem is solved to demonstrate the ability to solve complex problems with multiple states and control variables with constraints. Simulations establish this method’s performance and reveal that the polynomial/node choice for a given problem notably affects the performance.

Separating rigid-body motion from elastic vibrations in launch vehicles is critical yet challenging, especially when the first-order elastic frequency is close to or coincident with the rigid-body control bandwidth. To address this, this paper proposes a novel control technology that leverages existing onboard sensors without requiring additional hardware. The key innovations are as follows: First, a signal differencing strategy using two inertial measurement devices at distinct locations is employed to eliminate rigid-body components physically, isolating pure elastic information. Second, a direct lattice adaptive notch filter (DLANF) with a forward–backward error-normalized stochastic gradient algorithm is applied to accurately track time-varying elastic frequencies. Third, based on these identified frequencies, a predefined-time nonsingular sliding mode observer is constructed to decouple the rigid-body and first-order elastic signals in the time domain. This approach overcomes the phase-lag limitations of traditional filters and the observability issues of conventional observers. Crucially, the method is validated not only through simulations but also using closed-loop data from an actual rocket flight, demonstrating its capability to identify weak low-order frequencies and recover clean rigid-body states for autonomous stability control.

This paper presents a higher-order fully actuated system (HOFAS) approach for integrated guidance and control of launchers during orbit insertion, addressing the limitations of traditional decoupled architectures in handling the coupled translational and rotational dynamics, as well as underactuation constraints. By integrating the attitude dynamics directly into the position tracking framework, a unified HOFAS model is formulated that inherently accommodates cascade dynamics and eliminates the need for sequential attitude reference generation. A HOFAS-based control architecture is developed using a recursive control strategy to construct a set of decoupled linear closed-loop subsystems, enabling parametric eigenstructure assignment across all subsystems. Furthermore, a feedback gain optimization framework is introduced to enhance dynamic performance under physical constraints and actuator limitations, making full use of the design freedom of every closed-loop subsystem. Comparative simulations demonstrate that under equivalent control effort the proposed HOFAS-based framework achieves faster convergence, reduced oscillation, and improved compliance with actuator limitations compared to conventional state-space-based methods. The results validate the effectiveness and robustness of the HOFAS approach in addressing coupled and cascade system dynamics and highlight its potential as a new paradigm for aerospace control under stringent nonlinear constraints.

A bilevel optimal control framework is introduced to solve the low-thrust rephasing problem on quasi-periodic invariant tori in multibody environments where deviations away from the torus during a maneuver are considered unsafe or irresponsible. It is shown for a large class of mechanical systems that conformity to the torus manifold during periods of nonzero control input is infeasible. The most feasible trajectories on the torus surface are generated through the minimization of fictitious control input in the torus space using phase space control variables mapped via the torus function. These reference trajectories are then transitioned to the phase space both through a minimum-tracking-error homotopy and minimum-time patched solutions. Results are compared to torus-agnostic low-thrust transfers using measures of fuel consumption, cumulative torus error, and coast time spent on the torus during a maneuver. Modifications to the framework are made for the inclusion of quasi-periodically forced dynamical systems. Lastly, minimum-time recovery trajectories with free final torus conditions expose the disparity between the proposed framework and torus-agnostic approaches. Examples are drawn from the circular and elliptical restricted three-body problems.

This paper presents a transformation-based robust nonlinear control design framework based on the concepts of incremental nonlinear dynamic inversion (INDI) and quasi-linear parameter-varying (q-LPV) control. The duality between these popular control design paradigms is investigated. Control-oriented q-LPV model representations of INDI and nonlinear dynamic inversion (NDI)-based closed-loop systems are presented for various inversion strategies, which creates a basis for robust synthesis and analysis of INDI and NDI-based designs in the LPV sense. This includes extensions to singular perturbations that limit exact inversion in reality. The presented approach is demonstrated in a design case study for a nonlinear aeroservoelastic system, where INDI-based controllers are synthesized and quantitatively compared with direct q-LPV control based on linear fractional transformations.

This paper presents a reinforcement-learning (RL)-based multiphase robust trajectory design method for low-thrust exploration with gravity assist (GA) under uncertainties. To alleviate the complexity due to the interior-point constraints caused by intermediate GA, a trajectory segmentation strategy is used. The low-thrust trajectory legs before and after GA are segmented into interplanetary transfer phases (ITPs) and approaching phases (APs), respectively, and Markov decision processes with stochastic dynamics are modeled in each phase. Moreover, for the issue of failing to reach the target state of the AP due to the low terminal accuracy of the preceding ITP, a tradeoff factor is defined to modify the nominal initial state of the AP to better guide the exploration of robust policies. In particular, a reachability constraint of the target state of the AP is modeled analytically and incorporated into the reward of the ITP, which can significantly improve the reachability from the end states of RL-based trajectories in the preceding ITP to the target of the AP. Besides, low-thrust robust guidance laws in the AP are trained to deal with the uncertainties over the AP. The promising results in an Earth–Earth–Jupiter mission show that the proposed method can not only effectively deal with various uncertainties but also achieve the desired accuracy for intermediate GA and terminal rendezvous.