In this paper, the problem of prescribed-time tracking control with unified prescribed performance is studied for multi-input multi-output (MIMO) nonlinear systems with mismatched nonvanishing disturbances, actuator faults, and time-varying control coefficients whose sign and magnitude are both unknown. On the one hand, a novel prescribed-time stability criterion using Nussbaum functions is proposed to deal with the issues raised by the presence of mismatched nonvanishing disturbances, actuator faults, and time-varying control coefficients. This criterion is of independent interest and can be used beyond the control problem addressed in this paper. On the other hand, based on the proposed stability criterion, a prescribed-time tracking control framework is developed so that the tracking error converges to zero within a prescribed time, in the presence of the aforementioned complicating factors. Compared with existing asymptotic stability results for uncertain MIMO nonlinear systems subject to unknown control coefficients, the proposed framework guarantees that the tracking error remains within the unified prescribed performance boundary, which is uniform with respect to different initial tracking errors, thereby eliminating the need for controller redesign and stability reanalysis. The proposed control method is verified via an electromechanical system and a robot manipulator system in numerical simulation.

In this article, a prescribed-time output feedback controller is proposed for a class of uncertain nonlinear systems with unknown control coefficients and mismatched nonvanishing disturbances. Both unknown control coefficients and mismatched disturbances are tricky to address by the existing prescribed-time output feedback control frameworks. Differently, a novel prescribed-time control criterion in conjunction with Nussbaum functions is proposed, and prescribed-time stability is achieved. Furthermore, design methods for a state observer and a prescribed-time output feedback controller are developed. With the proposed control design, both the system output and observer errors are rigorously proved to converge to zero within a prescribed time. Moreover, the unified prescribed performance (UPP) of the system output and the satisfaction of output constraints are simultaneously achieved. Numerical simulations and experiments are provided to illustrate the effectiveness of the proposed control design.

This article studies the global asymptotic neural network (NN) tracking problem for full-state error constrained spacecraft attitude systems with actuator faults, inertia uncertainties, and external disturbances. In the literature, most existing NN control schemes can only achieve semiglobally bounded stability since the approximation capability of NNs is confined to a compact domain called the approximation domain. Differently, an attitude tracking control strategy in conjunction with a modified smooth switching mechanism is proposed to ensure the global asymptotic stability. Specifically, an adaptive NN controller is developed within the approximation domain to address unknown nonlinearities, and a robust controller is activated outside the approximation domain to drive back the system states. With the proposed design, both attitude and angular velocity errors (collectively defined as the full-state errors) are rigorously proven to globally asymptotically converge to zero. Moreover, the full-state errors are preserved within the unified prescribed performance constraints, which are uniform with respect to any initial conditions, thereby eliminating the requirement for offline computation of the performance boundary. In addition, the undesirable feasibility conditions on virtual control laws are completely eliminated. Theoretical analysis and numerical simulations validate the effectiveness of the proposed method.

This paper proposes an adaptive tracking control framework for nonlinear systems with unmodeled dynamics, ensuring both practical prescribed-time convergence and prescribed performance for full-state errors. Existing methods often depend on unbounded gains, focus only on output tracking error, or rely on initial conditions, restricting their practical applicability. To overcome these issues, we propose a novel adaptive control framework that constrains full-state errors independent of initial conditions and drives them to a prescribed region within a predefined time. This is achieved by using a bounded, continuously differentiable, prescribed-time gain. An adaptive mechanism with a dissipating term is designed to handle unmodeled dynamics and guarantee zero tracking error even under nonvanishing disturbances. Moreover, a smooth scaling function is introduced to enforce desired transient and steady-state performance while reducing large initial control effort. Numerical simulations demonstrate the superiority of the proposed method compared to existing approaches.

This paper studies the prescribed-time tracking control problem for nonlinear systems with unknown time-varying parameters, mismatched nonvanishing uncertainties, unknown control coefficients, and potential actuator faults. The proposed control strategy employs a prescribed-time adjustment function to guarantee that state errors converge to zero within a specified time, despite the presence of nonvanishing mismatched uncertainties. The proposed controller avoids the need to use adaptive mechanisms and is therefore simple to implement. Moreover, the proposed control strategy does not require the control coefficient bounds to be known. Based on a prescribed-time scaling function and a barrier function, prescribed performance for state errors is guaranteed, which is uniform with respect to initial conditions, eliminating the need for an offline optimization algorithm to determine the controller gains. The simulation results demonstrate the effectiveness of the proposed control framework.

In this article, a trajectory tracking control strategy is proposed for robot manipulators via a fully actuated system (FAS) approach, which has shown its simplicity and flexibility for most of the nonlinear controller design. However, the motion control for robot manipulators is more complicated since unknown dynamical model, external disturbances, friction forces, and various physical constraints are required to be considered. Therefore, the FAS approach cannot be straightforwardly applied. To address these challenges, the dynamic model of robot manipulators is established via model identification methods. Furthermore, based on the identified model, an FAS composite control strategy with simple structure is designed, which is achieved by integrating a high-order disturbance observer (HODO) in the inner loop, with an FAS trajectory tracking controller in the outer loop. Specifically, the HODO is utilized for handling the uncertain dynamics and external disturbances. Moreover, the controller gains are optimized using a gradient-based optimal parameter tuning method (OPTM). By imposing joint angle constraints, joint angular velocity constraints, and input torque limits into the formulation, the OPTM also ensures the satisfaction of these physical constraints. Numerical simulations and experiments are provided to validate the performance of the proposed controller.