It is an interesting problem to achieve adaptive asymptotic control for strict-feedback nonlinear systems with fast time-varying parameters, particularly in the presence of substantial parameter uncertainties without the availability of a priori knowledge. In this paper, a solution to this problem is presented with a two-level adaptive estimator and a new form of event-triggered control mechanism. Specifically, three adaptive laws (two for the uncertain parameters in the feedback path and one for the uncertain parameters in the input path), two sets of tuning functions, and a dynamic event-triggering mechanism are integrated and strategically designed within a controller to ensure that higher control precision can be obtained in the presence of time-varying parameters. It is shown that, with the derived dynamic event-triggered adaptive asymptotic control strategy, the closed-loop system is globally uniformly asymptotically stable. Furthermore, the inter-event intervals are guaranteed to be lower-bounded by a positive constant. The benefits and effectiveness of the proposed scheme are validated through two numerical simulations.

This article investigates the prescribed-time leader-following consensus problem for heterogeneous multiagent systems (MASs) with unknown sensor sensitivity. Considering a connected undirected topology, we introduce a time-varying dual observer/controller design framework that leverages both regular local and inaccurate feedback to achieve consensus tracking within a prescribed time. The proposed analytical framework applies to MASs equipped with sensors exhibiting uncertain sensitivities. A key innovation of our design is the framework of a distributed matrix pencil formulation based on the worst case sensor, leading to control parameters that exhibit sufficient robustness and relatively low conservativeness. Additionally, we establish a bounded time-varying feedback (TVF) scheme that extends the prescribed-time distributed protocol to an infinite time domain without compromising final control accuracy. This includes a detailed discussion of the analytical relationship between switching time and the upper bound of the time-varying gain. In particular, we employ the proportional coefficient obtained from several matrix pencil formulations along with a monotonically increasing time-varying (blow-up) function to derive the feedback gain, simplifying the complexity of control design. Simulations validate the effectiveness of the methodology through a series of electromechanical systems and single-link robot manipulators.

The control of a humanoid robot equipped with one arm and multiple fingers, designed primarily for grasping and manipulating various objects, is investigated. Synchronizing the movements of the fingers is a challenging task, as each joint must reach the desired angle simultaneously to ensure a firm grasp. The success of this task hinges on the synchronization of convergence times for each finger joint; otherwise, the object may slip or escape. This challenge is further intensified by uncertainties in the dynamics of the hand or the object. We present decentralized prescribed-time tracking control strategies for the dynamical system comprising the arm-finger combination. In this system, the fingers are primarily used for grasping the object while the arm is responsible for moving, tilting, or flipping it. To streamline the controller structure and simplify the stability analysis, we design a linear controller based on the maximum eigenvalue of a parameter matrix and establish a new technical lemma, which paves the way for the stability analysis of the prescribed-time tracking and the reduction of the input efforts of the actuator. We develop robust and decentralized adaptive control schemes separately for the arm and fingers, achieving better transient performance with less prior knowledge and lower computation costs. Finally, we validate the proposed controller's performance through kinematic simulations of grasping and moving tasks in 3-D, alongside numerical simulations that demonstrate the tracking performance of our algorithm in the joint space.

It is nontrivial to achieve exponential stability even for time-invariant nonlinear systems with matched uncertainties and persistent excitation (PE) condition. In this article, without the need for PE condition, we address the problem of global exponential stabilization of strict-feedback systems with mismatched uncertainties and unknown yet time-varying control gains. The resultant control, embedded with time-varying feedback gains, is capable of ensuring global exponential stability of parametric-strict-feedback systems in the absence of persistence of excitation. By using the enhanced Nussbaum function, the previous results are extended to more general nonlinear systems where the sign and magnitude of the time-varying control gain are unknown. In particular, the argument of the Nussbaum function is guaranteed to be always positive with the aid of nonlinear damping design, which is critical to perform a straightforward technical analysis of the boundedness of the Nussbaum function. Finally, the global exponential stability of parameter-varying strict-feedback systems, the boundedness of the control input and the update rate, and the asymptotic constancy of the parameter estimate are established. Numerical simulations are carried out to verify the effectiveness and benefits of the proposed methods.

It is still an open problem to achieve asymptotic tracking meanwhile maintaining specific performance for nonlinear systems with structurally mismatched uncertainties and strictly constrained inputs. In this work, we present a solution to this problem by using neural network (NN)-based adaptive control embedded with the robust integral of the sign of the error (RISE) technique. Most existing prescribed performance control (PPC) can only ensure uniformly ultimately bounded stability, and the RISE-based control, although capable of achieving asymptotic stability, does not guarantee transient behavior (especially, when the system is in strict-feedback form with saturated input). Here, in this study, we make use of NNs to accommodate the unknown nonlinearities, where the NN approximation error, together with other uncertainties, is fully compensated by using a RISE unit. The constraints imposed on the inputs are addressed by the hyperbolic tangent function, resulting in a solution capable of guaranteeing asymptotic tracking with prescribed transient performance, in the presence of mismatched modeling uncertainties and actuation saturation. A numerical simulation is carried out to verify the effectiveness of the proposed method.

Prescribed-time (PT) control for nonlinear systems, originated from Song et al., has gained increasing attention among the control community. The salient feature of PT control lies in its ability to achieve system stability within a finite settling time user-assignable in advance irrespective of initial conditions. It is such a unique feature that has enticed many follow-up studies on this technically important area, motivating numerous research advancements. In this article, we provide a comprehensive survey on the recent developments in PT control. Through a concise introduction to the concept of PT control, and a unique taxonomy covering: 1) from robust PT control to adaptive PT control; 2) from PT control for single-input–single-output (SISO) systems to multi-input–multioutput (MIMO) systems; and 3) from PT control for an isolated system to multiagent systems, we present an accessible review of this interesting topic. We highlight key techniques, and fundamental assumptions adopted in various developments as well as some new design ideas. We also discuss several possible future research directions toward PT control.

For systems in canonical form with nonvanishing uncertainties/disturbances, this work presents an approach to full-state regulation within prescribed time irrespective of initial conditions. By introducing the smooth hyperbolic-tangent-like function, a nonlinear and time-varying state-feedback control scheme is constructed, which is further extended to address output-feedback-based prescribed-time regulation by invoking the prescribed-time observer, all are applicable over the entire operational time zone. As an alternative to full-state regulation within the user-assignable time interval, the proposed method analytically bridges the divide between linear and nonlinear feedback-based prescribed-time control and is able to achieve asymptotic stability, exponential stability, and prescribed-time stability with a unified control structure.