Articulating crane (AC) is used in various industrial activities. The articulated multisection arm exacerbates nonlinearities and uncertainties, making the precise tracking control challenging. This study proposes an adaptive prescribed performance tracking control (APPTC) for AC to robustly fulfill the task of precise tracking control, with adaptation to resist time-variant uncertainties, whose bounds are unknown but lie in prescribed fuzzy sets. Particularly, a state transformation is applied to simultaneously track the desired trajectory and satisfy the prescribed performance. Adopting the fuzzy set theory to describe uncertainties, APPTC does not invoke any IF-THEN fuzzy rules. There is no linearizations, or nonlinear cancelation for APPTC, thus making it approximation free. The performance of the controlled AC is twofold. First, deterministic performance in fulfilling the control task is ensured by the Lyapunov analysis using uniform boundedness and uniform ultimate boundedness. Second, fuzzy-based performance is further improved by an optimal design, which seeks the optima of control parameters by formulating a two-player Nash game. The existence of Nash equilibrium is theoretically proved, and its acquisition process is given. The simulation results are provided for validations. This is the first endeavor that explores the precise tracking control for fuzzy AC.

Articulating crane (AC), a widely used crane, plays an essential role in various industrial activities. Owing to its strong nonlinearity and uncertainty, its tracking control remains challenging, particularly for precise dynamic tracking control. This paper proposes an adaptive diffeomorphism-constraint-based control (ADCBC) for a nonlinear AC to robustly achieve trajectory tracking while guaranteeing desired dynamic control performance (DDCP), considering (possibly rapid and irregular) time-variant uncertainty with unknown bounds. A user-definable hard-limiting function was used to guarantee the DDCP, including the requirement for steady-state tracking error and dynamic convergence speed. The desired trajectories and DDCP were formulated as equality and inequality servo constraints, respectively. A diffeomorphism approach was adopted to incorporate inequality servo constraints into equality servo constraints, yielding new equality servo constraints. Thus, the control task was converted to enable the transformed AC to follow the new equality servo constraints and was completed by a constraint-based control (CBC) scheme, where an adaptive law was established for the estimation of online uncertainty bounds to compensate for uncertainty. No approximations or linearizations were invoked. The effectiveness and robustness of the proposed ADCBC were confirmed through rigorous proofs and simulation results. To the best of our knowledge, this is the first endeavor in tracking control while guaranteeing the DDCP for uncertain AC-like systems.

A tiltrotor aircraft (TRA) can both hover in the air (hover flight state) and cruise quickly (level flight state). Transition flight is a transitional state between these two flight states, during which tiltable rotors rotate, forming a unique state for TRA. Revolving of the tiltrotor shaft leads to strong nonlinearity and time-varying uncertainty, which weakens the stability of attitude control with linearization in transition flight. The safety of TRA is critical, but it can be easily harmed due to the weak control stability. This study is to regulate the TRA attitudes agilely and precisely simultaneously, by ensuring fast convergence speed and small convergence error, i.e., a prescribed transient and steady state performance (PTSSP). A constraint-based adaptive robust prescribed performance control (CARPPC) is proposed for TRA to follow the desired attitude while guaranteeing PTSSP, with no approximations or linearizations invoked. The desired attitudes and PTSSP are respectively described as equality and inequality servo constraints. A constraint-based control with state transformation is introduced to render both equality and inequality constraint-following. An adaptive law is established for online estimation of unknown uncertainty bounds to compensate time-varying uncertainty. Both theoretical proofs and simulation results demonstrated that CARPPC can realize agile and precise attitude control robustly in transition flight.