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 paper addresses the challenge of assigning heterogeneous sensors (i.e., robots with varying sensing capabilities) for multi-target tracking. We classify robots into two categories: (1) sufficient sensing robots, equipped with range and bearing sensors, capable of independently tracking targets, and (2) limited sensing robots, which are equipped with only range or bearing sensors and need to at least form a pair to collaboratively track a target. Our objective is to optimize tracking quality by minimizing uncertainty in target state estimation through efficient robot-to-target assignment. By leveraging matroid theory, we propose a greedy assignment algorithm that dynamically allocates robots to targets to maximize tracking quality. The algorithm guarantees constant-factor approximation bounds of 1/3 for arbitrary tracking quality functions and 1/2 for submodular functions, while maintaining polynomial-time complexity. Extensive simulations demonstrate the algorithm’s effectiveness in accurately estimating and tracking targets over extended periods. Furthermore, numerical results confirm that the algorithm’s performance is close to that of the optimal assignment, highlighting its robustness and practical applicability.

This paper proposes a low-complexity tracking control framework for uncertain nonlinear systems in strict feedback and normal forms, respectively. By leveraging a smooth scaling function, these control schemes ensure unified prescribed performance for the output tracking error of strict feedback nonlinear systems and the full-state tracking errors of normal form nonlinear systems. The notion of unified prescribed performance allows for different performance behaviors via performance functions, which can be either constant or time-varying with arbitrarily large initial values. The main contribution is achieving unified prescribed performance for full-state tracking errors without imposing feasibility conditions, a limitation of existing approaches. To eliminate these strict conditions, we introduce a uniform transformation independent of initial conditions. Additionally, the proposed control schemes are low-complexity since they do not require adaptive mechanisms or function approximation to deal with uncertainties and disturbances. The effectiveness of these frameworks is demonstrated through comparative analysis.

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 high-gain observer (HGO)-based differentiator is proposed to approximate the derivatives of the virtual control to ease the "explosion of complexity" problem in backstepping for the second-order strict-feedback systems (SOSFSs) and high-order strict-feedback systems (HOSFSs). Unlike the existing high-order command-filtered backstepping or extended dynamic surface control that needs to tune a large number of parameters, this proposed high-order HGO-based backstepping (HOHGOB) scheme can improve the derivative approximation performance by only tuning a single parameter, i.e., the observer gain. A further advantage of the proposed HOHGOB scheme, in addition to its simplicity and ease of implementation, is that the estimation error of the derivatives shrinks to zero as the observer gain grows to infinity. We have also rigorously established that the states of the closed-loop system achieve uniform ultimate boundedness under the designed high-order backstepping controller. Additionally, the output tracking error can be made arbitrarily small by the designer. The efficacy of the proposed scheme is numerically validated through a benchmark application to a single-link robot arm.

Although the literature on control of overhead crane systems is extensive and relatively mature, there is still a need to develop strategies that can simultaneously handle factors such as the double pendulum effect, variable cable length, input saturation, input dead zones, and external disturbances. This article is concerned with adaptive tracking control for underactuated overhead cranes in the presence of the above-mentioned challenging effects. The proposed controller is composed of the following two components. First, a tracking signal vector that effectively reduces system swing magnitudes is constructed to improve the transient performance and guarantee smooth operation of the system. Second, an adaptive law is designed to estimate and compensate for the overall effects of the friction, the external disturbances, and certain nonlinearities. The system stability has been proved rigorously via the Lyapunov method and Barbalat's lemma. Extensions to the cases with input saturation and dead zones have also been discussed. Extensive numerical simulations have been conducted to verify the performance and robustness of the proposed controller, in comparison to some existing methods.

This work deals with the complicated problem of constrained fixed-time attitude control for flexible spacecraft in view of actuator saturations and fault. The proposed controller is composed of two parts. The first part provides fast fixed-time convergence of system trajectories using a novel nonsingular terminal sliding mode control. The second part offers the desired performance specification, such as the rate of convergence, overshoot, and steady-state bounds for attitude/rotation velocity to improve attitude-pointing accuracy and pointing stability. The constrained control method ensures the desired performance in the transient/steady-state phases. It obtains a much simpler structure in comparison with other constrained controls. The simulations on a flexible spacecraft validate the efficacy of the planned scheme.

The rapid attitude stabilization problem of flexible spacecraft with uncertain inertia and disturbances is investigated. In this article, a sliding mode-based fixed-time control approach is presented with a new fixed-time surface ensuring a faster convergence rate incorporated. This surface has no singularity and can guarantee the settling time to be independent of initial states. An adaptive fixed-time attitude control law is then synthesized, which is continuous and chattering free. It is rigorously proved that the states of the spacecraft attitude system can converge into a small neighborhood after fixed time. A numerical example is presented to validate that the designed scheme is efficient to perform attitude stabilization maneuvers rapidly, whereas high control accuracy is still provided.