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

This paper investigates the problem of adaptive fault-tolerant control for a class of nonlinear parametric strict-feedback systems with multiple unknown control directions. Multiple sensor faults are first considered such that all real state variables are unavailable. Then, a constructive design method for the problem is set up by exploiting a parameter separation and regrouping technique. To circumvent the main obstacle caused by the coupling effects of multiple unknown control directions and sensor faults, a region-dependent segmentation analysis method is proposed. It is proven that the closed-loop system is globally exponentially stable. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

We consider the problem of finite-time stabilization for nonlinear systems. In the previous work, it was proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system could be achieved by non-Lipschitz continuous state feedback. The proof was based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method proposed in, for the control of nonlinear systems that are impossible to be dealt with by any smooth feedback. A simpler design algorithm is given for the construction of a non-Lipschitz continuous, global finite-time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function that guarantees finite-time stability.

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.

Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

Finite-time stability is investigated for a class of nonlinear systems and a new design is presented for globally finite-time stabilising feedback, extending the results obtained in Huang, Lin, and Yang (2005) [‘Global Finite-time Stabilization of a Class of Uncertain Nonlinear Systems’, Automatica, 41, 881–888]. The new method may achieve accelerated convergence speed and reduced settling time. An example verifies the feasibility and effectiveness of the proposed design.

H finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

The problem of global finite-time stabilization for p-normal nonlinear systems subject to uncertain time-varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated in this paper. By virtue of the technique of homogeneous domination, a new dual-layer adaptive approach is presented to address the uncertainties and nonlinearities of the system. For one layer of the adaptive mechanism, a nonlinear adaptive parameter estimator is proposed to reconstruct the upper bounds of the unknown uncertainties. For the other, an explicit construction approach of a new adaptive dynamic gain mechanism is presented for the first time to cope with the uncertain time-varying control coefficients of the p-normal nonlinear systems. It is shown that the global boundedness of the systems under consideration is guaranteed by the presented approach, and in addition the time taken to converge to the equilibrium is rendered to be finite time.

This paper discusses the problem of global finite-time stabilization in probability for a class of stochastic high-order nonlinear systems whose drift and diffusion terms satisfy lower-triangular growth conditions. By adopting adding one power integrator technique and constructing twice continuous differential Lyapunov functions, a continuous state-feedback controller is recursively designed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Several simulation examples are given to illustrate the effectiveness of the proposed design procedure.

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

ABSTRACTThis paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.

General fuzzy adaptive fault-tolerant control based on Nussbaum-type function with additive and multiplicative sensor and state-dependent actuator faults

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.

International audience

Robust finite-time output feedback control of perturbed double integrator