Practical tracking results have been reported in the literature for high-order odd-rational-power nonlinear dynamics (a chain of integrators whose power is the ratio of odd integers). Asymptotic tracking remains an open problem for such dynamics. This note gives a positive answer to this problem in the framework of prescribed performance control, without approximation structures (neural networks, fuzzy logic, etc.) being involved in the control design. The unknown system uncertainties are first transformed to unknown but bounded terms using barrier Lyapunov functions, and then these terms are compensated by appropriate adaptation laws. A method is also proposed to extract the control terms in a linear-like fashion during the control design, which overcomes the difficulty that virtual or actual control signals appear in a nonaffine manner. A practical poppet valve system is used to validate the effectiveness of the theoretical findings.

This article attempts to realize zero-error constrained tracking for hypersonic flight vehicles (HFVs) subject to unknown control directions and asymmetric flight state constraints. The main challenges of reaching such goals consist in that addressing multiple unknown control directions requires novel conditional inequalities encompassing the summation of multiple Nussbaum integral terms, and in that the summation of conditional inequality may be bounded even when each term approaches infinity individually, but with opposite signs. To handle this challenge, novel Nussbaum functions that are designed in such a way that their signs keep the same on some periods of time are incorporated into the control design, which not only ensures the boundedness of multiple Nussbaum integral terms but preserves that velocity and altitude tracking errors eventually converge to zero. Fuzzy-logic systems (FLSs) are exploited to approximate model uncertainties. Asymmetric integral barrier Lyapunov functions (IBLFs) are adopted to handle the fact that the operating regions of flight state variables are asymmetric in practice, while ensuring the validity of fuzzy-logic approximators. Comparative simulations validate the effectiveness of our proposed methodology in guaranteeing convergence, smoothness, constraints satisfaction, and in handling unknown control directions.

This article solves the fixed-time trajectory tracking problem for hypersonic flight vehicles (HFVs) encountered with diverse actuator faults and asymmetric envelope constraints. In contrast to the state of the art, the crucial characteristics of our design lie in obviating the explosion of complexity of the conventional recursive design, and in realizing satisfactory preselected tracking qualities for flight states in the sense of guaranteeing asymmetric envelope constraints. More precisely, by exploiting the fixed-time command filters to produce certain command signals and their derivatives, a modified command-filtered control algorithm is formulated to circumvent heavy computation burden caused by repetitive derivative of intermediate control laws. A two-step control methodology is devised based on an auxiliary compensating dynamics, which is capable of compensating for the actuator faults completely without the need for prior knowledge about the lumped disturbances and the actuator faults. Time-varying asymmetric barrier Lyapunov functions are introduced to confine the flight state tracking errors within the corresponding time-varying compact sets all the time provided their initial values remain therein. The effectiveness of the proposed method is validated by comparative simulation results.

Compared with most existing results concerning unmanned aerial vehicles (UAVs) wherein two-degree or only attitude/longitudinal dynamics are considered, this paper proposes an event-based fault-tolerant coordinated control (FTC) for multiple fixed-wing UAVs such that the consensus tracking of velocity and attitude is achieved in the presence of actuator faults, external disturbances and modeling uncertainties. More precisely, as opposed to static event-triggered communication mechanisms, a dynamic event-triggered communication mechanism (DECM) is devised to schedule the connected communications while avoiding the unnecessary information exchanges among UAVs, which reduces the communication burden and saves on the network resources. Meanwhile, the Zeno phenomenon is excluded in terms of guaranteeing that the period between two consecutive triggering communication is lower bounded by a positive constant. Moreover, the actuator fault, external disturbance as well as model uncertainty are treated as the lumped disturbances and estimated via the disturbance observer technique. By strict Lyapunov arguments, all closed-loop signals are proved to be uniformly ultimately bounded (UUB) and the tracking errors of velocity and attitude converge to a residual set around origin. Finally, simulation results are presented to illustrate the validity and superiority of proposed event-based control scheme.

Prescribed-performance control (PPC) for high-power dynamics with time-varying unknown control coefficients requires to address two open problems: (a) given a Nussbaum function, which properties hold for the power of the Nussbaum function? (b) to avoid high gains, how to design a switching gain that increases only when the tracking error is close to violate the performance bounds? To address the first problem, we show with a counterexample and a positive example that only some Nussbaum functions are suited to handle time-varying unknown control coefficients for high-power dynamics. To address the second problem, we propose a new switching conditional inequality.

This article proposes a fixed-time adaptive fault-tolerant control methodology for a larger class of high-order (powers are positive odd integers) nonlinear systems subject to asymmetric time-varying state constraints and actuator faults. In contrast with the state-of-the-art control methodologies, the distinguishing features of this study lie in that: (a) high-order asymmetric time-varying tan-type barrier Lyapunov function (BLF) is devised such that the state variables can be convergent to the preassigned compact sets all the time provided their initial values remain therein, which not only preserves the constraints satisfaction, but warrants the validity of the adopted neural network approximator; (b) the proposed control design ensures the tracking errors converge to specified residual sets within fixed time and makes the size of the convergence regions of tracking errors adjustable a priori by means of a new BLF-based tuning function and a projection operator; (c) a variable-separable lemma is delicately embedded into the control design to extract the control terms in a “linear-like” fashion which not only overcomes the difficulty that virtual control signals appear in a non-affine manner, but also solves the problem of actuator faults. Comparative simulations results finally validate the effectiveness of the proposed scheme.

This article proposes a fuzzy adaptive design solving the finite-time constrained tracking for hypersonic flight vehicles (HFVs). Actuator dynamics and asymmetric time-varying constraints are considered when solving this problem. The main features of the proposed design lie in 1) introducing a novel piecewise but differentiable switching control law, with an appropriate design thought to avoid the singularity issues typical of finite-time control; 2) handling actuator magnitude, bandwidth, and rate constraints, thanks to the introduction of an auxiliary compensating system counteracting the adverse effects caused by actuator physical constraints, while guaranteeing the closed-loop stability; and 3) handling asymmetric time-varying state constraints, thanks to the introduction of tan-type barrier Lyapunov functions working for both constrained and unconstrained scenarios. Comparative simulation results illustrate the effectiveness of the proposed strategy over existing methods for HFVs in terms of convergence, smoothness, actuator performance, and constraints satisfaction.

In contrast with most existing results concerning unmanned aerial vehicles (UAVs) wherein material points or only attitude/longitudinal dynamics are considered, this article proposes a distributed fixed-time fault-tolerant control methodology for networked fixed-wing UAVs whose dynamics are six-degree-of-freedom with twelf-state-variables subject to actuator faults and full-state constraints. More precisely, state transformations with the scaling function are devised to keep the involved velocity and attitude within their corresponding constraints. The fixed-time property is obtained in the sense of guaranteeing that the settling time is lower bounded by a positive constant, which is independent of initial states. The actuator faults as well as the network induced errors are handled via the bound estimation approach and well-defined smooth functions. By strict Lyapunov arguments, all closed-loop signals are proved to be semiglobally uniformly ultimately bounded, and the tracking errors of velocity and attitude converge to the residual sets around origin within a fixed time.

In contrast with most existing results concerning unmanned aerial vehicles (UAVs) wherein two-degree or only attitude/longitudinal dynamics are considered, this article proposes an event-triggered cooperative synchronization fault-tolerant control (FTC) methodology for multiple fixed-wing UAVs whose dynamics are six-degree-of-freedom (DOF) with twelf-state-variables subject to actuator faults, modeling uncertainties, and external disturbances. More precisely, an event-triggering mechanism is devised to determine the time instants of updating control signals, which reduces the signal transmission burden, while saving on system resources. The Zeno phenomenon is excluded in the sense of guaranteeing that the time between two consecutive switchings is lower bounded by a positive constant. The actuator faults as well as the network induced errors are handled via the bound estimation approach and some well-defined smooth functions. By strict Lyapunov arguments, all closed-loop signals are proved to be semi-globally uniformly ultimately bounded (SGUUB) and the synchronization tracking errors of speed and attitude converge to a residual set around origin whose size can be made arbitrarily small through selecting appropriate design parameters.

This article aims to realize event-triggered constrained consensus tracking for high-order nonlinear multiagent networks subject to full-state constraints. The main challenge of achieving such goals lies in the fact that the standard designs [e.g., backstepping, event-triggered control, and barrier Lyapunov functions (BLFs)] successfully developed for low-order dynamics fail to work for high-order dynamics. To tackle these issues, a novel high-order event-triggered mechanism is devised to update the actual control input, lowering the communication and computation burden. More precisely, compared with the conventional event-triggered mechanism, not only the amplitudes of control signals and a fixed threshold are considered but a monotonically decreasing function is introduced to allow a relatively big threshold, while guaranteeing consensus tracking error to be small. Then, a high-order tan-type BLF working for both constrained and unconstrained scenarios is incorporated into the distributed adding-one-power-integrator design for the purpose of confining full states within some compact sets all the time. A finite-time convergent differentiator (FTCD) is introduced to circumvent the ``explosion of complexity.'' The consensus tracking error is shown to eventually converge to a residual set whose size can be adjusted as small as desired through choosing appropriate design parameters. Comparative simulations have been conducted to highlight the superiorities of the developed scheme.

A new fixed-time fuzzy adaptive fault-tolerant control methodology is proposed for the longitudinal dynamics of hypersonic flight vehicles (HFVs) in the presence of actuator faults, uncertain dynamics, and external disturbances. In contrast with the conventional fixed-time control schemes that typically contain the fractional powers of errors in their designs, this work develops a low-complexity control structure in the sense of removing the dependence on the need of abovementioned fractional power terms by means of prescribed performance control (PPC) method. Different from the most existing PPC approaches where the initial conditions of tracking errors are required to be known, the newly proposed prescribed performance function (PPF) can relax such restrictions through choosing properly small initial values of PPF. Fuzzy logic systems (FLSs) are employed to handle unknown dynamics, and minimal learning parameter (MLP) technique is incorporated into the design for the purpose of alleviating computation burden. Closed-loop stability is rigorously proved via Lyapunov stability theory, and simulation results are eventually given to validate the effectiveness of the proposed control strategy.

This work studies logic-based distributed switching control for nonlinear agents in power-chained form, where logic-based (switching) control arises from the online estimation of the control directions assumed to be unknown for all agents. Compared to the state-of-the-art logic-based mechanisms, the challenge of power-chained dynamics is that in general asymptotic tracking cannot be obtained, even for a single agent. To address this challenge, a new logic-based mechanism is proposed, which is orchestrated by a dynamic boundary function. The boundary function is decreasing in-between switching instants and monotonically increasing at the switching instants, depending on the jumps of an appropriately designed Lyapunov-like function. To remove chattering (i.e. two or more switching instants occurring consecutively with zero dwell time), a dynamic threshold is proposed, based on selecting the maximum values of the Lyapunov-like function before and after switching.

This article proposes an output-feedback fixed-time trajectory tracking control methodology for hypersonic flight vehicles subject to asymmetric output constraints. In contrast to the state of the art, the most distinguishing feature of our control design lies in avoiding using conventional recursive design methods (e.g., backstepping technique, dynamic surface control, etc.) and in not relying on full-state availability. In the velocity control loop, an asymmetric integral barrier Lyapunov function is adopted to confine velocity variable within a well-defined compact set all the time. In the altitude control loop, after utilizing its cascaded property and proposing a novel scaling function, the original constrained system is transformed to an unconstrained one, which facilitates the control design and stability analysis. Moreover, the proposed control algorithm only involves one fuzzy logic approximator as well as one fixed-time differentiator in the transformed system and guarantees that the tracking errors of velocity and altitude converge into the user-defined residual sets within fixed time. Several comparative simulations have been conducted to highlight the superiorities of the developed method.

This work investigates a reduced-complexity adaptive methodology to consensus tracking for a team of uncertain high-order nonlinear systems with switched (possibly asynchronous) dynamics. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping methods successfully developed for low-order systems fail to work. Even the adding-one-power-integrator methodology, well explored for the single-agent high-order case, presents some complexity issues and is unsuited for distributed control. At the core of the proposed distributed methodology is a newly proposed definition for separable functions: this definition allows the formulation of a separation-based lemma to handle the high-order terms with reduced complexity in the control design. Complexity is reduced in a twofold sense: the control gain of each virtual control law does not have to be incorporated in the next virtual control law iteratively, thus leading to a simpler expression of the control laws; the power of the virtual and actual control laws increases only proportionally (rather than exponentially) with the order of the systems, dramatically reducing high-gain issues.

This paper investigates the problems of modeling and control of the morphing aircraft. Henceforth, a nonlinear dynamic model of a wing-sweep morphing aircraft is first established in this work. This model is suitable for larger envelopes by elaborating the variation of aerodynamic coefficients, air density, mass distribution at different altitudes, Mach numbers, and sweep angles. Considering the alterations in the dynamic characteristics of the morphing aircraft owing to the various flight conditions, we design the switching adaptive backstepping controllers for the altitude subsystem and velocity subsystem. The actuator dynamics have been explicitly included in the process of the controller design to alleviate the chattering problem caused by the switching. Furthermore, the closed-loop stability is rigorously proved via the Lyapunov stability theory and the technique of compact set. Comparative results from the simulations finally validate the effectiveness of the proposed scheme.

This article investigates the stability of continuous-time switched linear systems with dwell-time constraints. A fresh insight into this established problem is provided via novel stability conditions that require the solution to a family of differential Lyapunov equations and algebraic Lyapunov equations. The proposed analysis, which leads to a peculiar Lyapunov function that is decreasing in between and at switching instants, enjoys the following properties: it achieves the same dwell time as the well-known result in the research 'stability and stabilization of continuous time switched linear systems' by Geromel and Colaneri; it removes the increasing computational complexity of the linear interpolation method; it leads to a straightforward counterpart for discrete-time switched linear systems.We show the application of this methodology to the problem of adaptive control of switched linear systems with parametric uncertainties.

This paper proposes a novel set-invariance adaptive dynamic surface control (DSC) design for a larger class of uncertain large-scale nonlinear input-saturated systems. The peculiarity of this class is that no a priori bound on the continuous control gain functions is assumed (i.e., their boundedness cannot be assumed before obtaining system stability). This requires a new design. Differently from the available methods, the proposed design involves the construction of appropriate invariant sets for the closed-loop trajectories, which allows to remove the restrictive assumption of a priori bounds of the control gain functions. Furthermore, we show that such set-invariance design can handle input constraints in the form of input saturation. In line with the DSC methodology, semi-globally uniformly ultimate boundedness is proven: however, differently from the standard methodology, stability analysis requires the combination of Lyapunov and invariant set theories.

This work proposes a nonsingular adaptive fixed-time switching control method for a class of strict-feedback nonlinear dynamics subject to full state constraints. The peculiarity of this design lies in overcoming the singularity issue that typically appears in the existing backstepping-based fixed-time control methods caused by the iterative differentiation of fractional power terms as tracking errors approach to zero, while guaranteeing the nonviolation of full state constraints. Crucial in solving such singularity issue is to skillfully introduce a smooth switching between fractional power and integer power terms, which guarantees that fractional power term is confined within a positive interval all the time. An asymmetric time-varying barrier Lyapunov function is delicately incorporated into control design, rendering state variables to be within prescribed time-varying bounds. Besides, radial basis function neural network is employed to handle system unknown nonlinearities. It is rigorously proved that all the closed-loop signals eventually converge to small regions around origin within fixed-time. Comparative simulation results are finally given to validate the effectiveness and superiority of the proposed control strategy.