Nonlinear PI control of uncertain systems: an alternative to parameter adaptation

This article presents a global adaptive asymptotic tracking control method, capable of guaranteeing prescribed transient behavior for uncertain strict-feedback nonlinear systems with arbitrary relative degree and unknown control directions. Unlike most existing funnel controls that are built upon time-varying feedback gains, the proposed method is derived from a tracking error-dependent normalized function and a barrier function, together with a time-varying scaling transformation, leading to an improved prescribed performance control solution with the following features: 1) the developed control is embedded with normalized error based adaptive parameter tuning and is able to ensure asymptotic tracking; 2) given transient performance is guaranteed in that the tracking error preserves in the prescribed boundary for <inline-formula><tex-math notation="LaTeX">$\forall t\geq 0$</tex-math></inline-formula>; and 3) it is able to cope with nonlinear systems with arbitrary relative degree, mismatched uncertainties, and unknown control directions. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

This study reports adaptive quantized control for a class of uncertain strict‐feedback nonlinear systems with unknown control directions. Combining backstepping technique and Lyapunov stability theory, a systematic analysis method is designed. Based on the disintegration of the hysteresis quantizer, a Nussbaum‐based scheme can be developed to get over the obstacle of the quantized input signal and unknown control directions. Moreover, the number of adaptive laws is small, thereby reducing the computational burden. Then we testify the boundedness of all signals in the closed‐loop system. Besides, the tracking error can converge to an arbitrarily small domain of origin. Finally, a simulation example is provided to verify the feasibility of the control scheme.

Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities

This study investigates a formation control problem of autonomous underwater vehicles (AUVs) with unknown control directions. By employing the Nussbaum gain technique to deal with the unknown control directions, a finite‐time formation control approach is proposed. To deal with the so‐called ‘explosion of complexity’ issue in backstepping control, a compensator‐based command filter technique is introduced to realise the derivative of virtual control signals. With the proposed method, the formation can be achieved within a finite settling time and all signals in the closed‐loop system are uniformly bounded. The effectiveness and performance is demonstrated by numerical simulations.

SummaryThis paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper.

Adaptive vibration control for flexible satellite with output constraint and unknown control direction

A novel strategy for gain adaptation of higherorder sliding mode (HOSM) based differentiators is developed, considering that the upper bound for the higher timederivatives of the output tracking error exist but they are unknown. Differently of earlier approaches, the proposed adaptive method is based on switching monitoring functions, which assures global stability and exact tracking when applied to output feedback. The challenging class of uncertain nonlinear plants of arbitrary relative degree handled in the paper includes time-varying and state-dependent disturbances with unknown bounds as well as unknown control directions. The unmeasured state is norm bounded through an adaptive state-norm estimator with hybrid dynamics. Simulations illustrate the potential applicability for control design and estimation in sliding mode schemes.

Adaptive passivity-based control extended for unknown control direction

This work focuses on the finite-time synchronization control (FTSC) for fractional-order chaotic systems (FOCSs) subject to uncertain dynamics, unknown parameters and input nonlinearities. In the control law design, the uncertain dynamics of the FOCSs are addressed by using fuzzy logic systems (FLSs), while the unknown control direction caused by unknown input nonlinearity is handled through applying the Nussbaum gain function (NGF) method. Parameter adaptive laws are derived to estimate the unknown parameters of the given FOCSs, the parameter vectors of the FLSs, and unknown bounded constants, respectively. By integrating these parameter-adaptive laws with the FT backstepping control framework and FO Lyapunov direct method, an adaptive fuzzy FTSC strategy is developed. This strategy ensures that the synchronization error (SE) can converge to a small neighborhood of zero (SNoZ) within a FT and all signals of the closed-loop system (CLS) remain ultimately bounded. In the end, three simulation cases are utilized to demonstrate the efficiency of the proposed control method.

Event-triggered adaptive prescribed performance tracking for nonlinear time-varying systems with unknown control directions

Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions

In this paper, an adaptive dynamic event-triggered output-feedback control scheme is proposed for a class of uncertain nonlinear systems. Specifically, a parameter estimator and a Nussbaum function are incorporated into the dynamic event-triggered control scheme to compensate for serious uncertainties, including the completely unknown parameter allowed in system nonlinearities and the unknown control coefficients (both signs and magnitudes are unknown). Importantly, an additional internal dynamic variable is introduced into the event-triggering mechanism, enabling the control scheme to save network resources more efficiently compared with the static ones in the related works. In addition, by skillfully designing the dynamics of this variable, the influence of the execution error can be fully counteracted. It is shown that, with the proposed control scheme, the system states can asymptotically converge to zero, instead of to a residual set, while excluding the Zeno phenomenon. To validate the effectiveness and superiority of the proposed scheme, two simulation examples are provided.

Command filtered neural control of multi-agent systems with input quantization and unknown control direction

In this article, we present an adaptive decentralized control scheme for a class of interconnected uncertain systems with subsystems having different yet unknown control directions and involving static nonlinear interactions as well as input and output dynamic interactions. A new form of K-filters is designed for each subsystem, and only local information is employed to generate control signals. A new Nussbaum-type function is developed with a key property that allows for the quantification of the interconnections among multiple Nussbaum-type functions for the subsystems with different control directions in a single inequality. By using appropriately chosen Lyapunov functions, global stability of the resulting closed-loop system is rigorously established. Simulation results are included to demonstrate the effectiveness of the proposed methodology.

Neuro-adaptive tracking control of non-integer order systems with input nonlinearities and time-varying output constraints