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This paper studies the problem of adaptive fuzzy asymptotical quantized tracking control of non-strict-feedback systems with unmodeled dynamics. A dynamic signal is used to cope with the unmodeled dynamics and fuzzy systems are introduced to approximate the packaged unknown nonlinearities. Based on backstepping technique and fuzzy approximation property, a systemic fuzzy adaptive control scheme is proposed. By the utilization of Lyapunov theory, the semi-globally uniformly ultimate boundedness of all closed-loop system signals and asymptotical tracking performance are guaranteed. The main contributions of this work are two aspects: (i) a backstepping-based quantized control algorithm is firstly extended to nonlinear systems with unmodeled dynamics and non-strict-feedback structure; (ii) the semi-globally asymptotic tracking control scheme is independent of the quantized parameter. Simulation results verify the presented control approach.

This article discusses the tracking control problem of full-state constrained nonlinear systems with unknown time-varying powers. With the help of a nonlinear state-dependent transformation, by introducing lower and higher powers in control design and skillfully combining the adding a power integrator method with the dynamic gain method, a full-state constrained tracking control design is developed without frequently used feasibility conditions. It is rigorously proved that all the signals of the closed-loop system are bounded, full-state constraints are not violated, and the tracking error converges to a compact set around the origin in a finite-time.

This article studies full-state constrained control for high-order nonlinear systems with unknown multiple time-varying powers and serious parameter unknowns. Due to the simultaneous existence of unknown powers and full-state constraints, we construct a log-type quadratic barrier Lyapunov function (BLF) rather than a quadratic Lyapunov function. By skillfully combining the log-type BLF, adding a power integrator technique and adaptive technique, an adaptive state feedback controller is developed. Under feasibility conditions, which are provided as sufficient conditions for the existence of proposed full-state constrained control, it is proved that all the signals of the closed-loop system are bounded, original system states converge to zero and full-state constraints are not violated.

In this article, tracking control is considered for a class of uncertain multi-input–multi-output (MIMO) nonlinear systems, where the time-varying parameters, the time-varying control coefficient and the time-varying disturbance are assumed to be unknown but to be bounded. Three stable adaptive tracking schemes for a given reference signal are proposed by devising different control algorithms. In the first scheme, bounded-error tracking is achieved in the sense that the tracking error converges exponentially to an adjustable region around the origin, where the $\sigma $ -modification adaptive laws are used to ensure the boundedness of all closed-loop signals. In the second scheme, asymptotic tracking is obtained in the sense that the tracking error converges to zero asymptotically, where the strictly positive and integral functions are employed in the control law to ensure the signal boundedness and zero-error tracking. In the third scheme, exponential tracking is gotten in the sense that the tracking error exponentially converges to zero with a given convergence speed, where exponential functions are incorporated into control law and adaptive laws to ensure system stability and the faster convergence. Three adaptive tracking schemes are, respectively, applied to nonlinear chaotic Chua’s circuit with control inputs. The parametric model is developed for Chua’s circuit with uncertain parameters and external disturbances. The effectiveness of the proposed control algorithms is demonstrated by comparative simulation studies.

In this paper, for uncertain nonlinear systems with time-varying full state constraints, input saturation and unknown control direction, time-varying asymmetric barrier Lyapunov functions, the auxiliary subsystem, and the Nussbaum gain technique are employed. It is shown that all the closed-loop signals are bounded in the semi-global sense, error signals converge to bounded compact sets, and time-varying full state constraints and input saturation are not violated.

This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme.

This paper investigates practical preassigned finite-time tracking control for state-constrained high-order nonlinear systems. Fuzzy systems are utilised to remove frequently used growth assumption...

We propose an approach which is different from the usual Lyapunov-Krasovskii function method to analyze asymptotic stability of nonlinear time-varying systems with bounded and unbounded delays. For the case of unbounded delay, new delay-independent criteria are provided when the involved nonlinear terms satisfy linear and nonlinear growth conditions. For the case of bounded delay, we establish a new delay-dependent criterion based on a model transformation. Numerical examples are given to demonstrate the effectiveness of the obtained results.

This paper investigates adaptive finite-time fuzzy control for full-state constrained high-order nonlinear systems. Fuzzy logic systems are employed to relax growth assumptions imposed on unknown system nonlinearities. By integrating a nonlinear state-dependent transformation into control design, full-state constraints can be handled without imposing feasibility conditions on virtual controllers. It is rigorously proved that fuzzy approximation is valid based on a compact set, full-state constraints aren’t violated for all time. Besides, the solution of the closed-loop system is semi-global practical finite-time stable, and the tracking error converges to an adjustable compact set around the origin in finite-time. Two examples show the advantages of this control scheme.

This paper studies the problem of global output feedback control for a class of feedforward nonlinear systems with the unknown output function and input matching uncertainty, whose nonlinearities s...

This paper investigates state feedback stabilization problem of a class of stochastic cascade nonlinear time-delay systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with stochastic input-to-state stability condition, without imposing any growth condition on time-delay system nonlinearities, a delay-independent, dynamic state feedback controller is constructed. It is shown that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability.

This paper investigates the problem of observer-based decentralized control for a class of large-scale stochastic high-order feedforward systems with multi time delays. By using the homogeneous domination idea and constructing the implementable observer, the decentralized output-feedback controller design scheme is firstly proposed. Then, with the aid of stochastic time delay system stability theory, the globally asymptotically stable in probability of the closed-loop system is verified by selecting an appropriate Lyapunov–Krasoviskii functional. Finally, an example is provided to demonstrate the efficiency of the proposed design method.

This paper investigates the semi-global stabilisation problem of high-order nonlinear systems with full-state constraints and input saturation. By constructing the high-order barrier Lyapunov funct...

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.

This paper aims to solve the finite-time stabilization problem for stochastic high-order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability (FT-SISS), borrowing from some ideas of the Lyapunov function, sign function, backstepping and FT-SISS methods, and using stochastic finite-time stability theory, a new design and analysis method is given to guarantee global finite-time stability in probability of the closed-loop stochastic systems.

In this paper, an adaptive neural-network-based tracking control strategy is proposed for a class of nonlinear switched non-lower triangular systems with the completely unknown nonlinearities and unmodeled dynamics. The design difficulties arise mainly from the fact that the intercoupling between the non-lower triangular functions and the unmodeled dynamics leads the switched system under consideration has a very complex structure. In order to get the desired adaptive state feedback controller, a mild assumption associated with a dynamic signal is utilized to deal with the unmodeled dynamics, and a separating variable method is presented to handle the system nonlinearities with all state variables in the framework of adaptive backstepping technique, respectively. The obtained results show that all signals of the switched closed-loop system are semi-global bounded with the output tracking error can be guaranteed to enter a small region around the origin. In the end, two simulation examples are given to demonstrate the feasibility and practicability of the presented design strategy.

This work considers robust adaptive neural-based control of pure-feedback stochastic nonlinear systems with the generalized Prandtl–Ishlinskii hysteresis. The mean-value theorem is employed to handle the non-affine difficulties from the generalized Prandtl–Ishlinskii hysteresis and the pure-feedback systems. By using the radial basis function (RBF) neural networks’ universal approximation capability and backstepping technique, an adaptive neural control scheme with minimum adaptive parameter is developed. The presented controller can guarantee the semi-global boundedness in fourth-moment of all signals of the resulting closed-loop system. Furthermore, the system output is ensured to converge to a small domain of the given trajectories. Simulation results are presented to demonstrate the effectiveness of the scheme.

This paper deals with the problem of state bounding for a class of nonlinear time-varying systems with delay and bounded disturbance. By using a model transformation and an approach developed in positive systems, new delay-dependent explicit conditions have been established to guarantee all the state trajectories of the system converge exponentially within a ball. Two illustrative examples are given to show that the obtained results can be applied to some cases not covered by preceding results.

This paper studies the problem of global output feedback control for a class of feedforward nonlinear systems with unknown multiple time-varying delays and unknown output function under more genera...

This article investigates the tracking control for input and full-state-constrained nonlinear time-delay systems with unknown time-varying powers, whose nonlinearities do not impose any growth assumption. By utilizing the auxiliary control signal and nonlinear state-dependent transformation (NSDT) to counteract the effect of input saturation and cope with full-state constraints, respectively, and then introducing lower and higher powers and Lyapunov-Krasovskii (L-K) functionals in control design together with the adaptive neural-networks (NNs) method, an adaptive neural tracking control design is provided without feasibility conditions. It is proved that NNs approximation is valid, all the closed-loop signals are semiglobally bounded, and input and full-state constraints are not violated.

This paper investigates adaptive fuzzy control for full-state constrained high-order nonlinear systems. Fuzzy systems are employed to approximate unknown system nonlinearities. By integrating nonlinear transformed functions into control design, full-state constraints can be handled without imposing feasibility conditions on virtual controllers. It is rigorously proved that fuzzy approximation is valid on a crucial compact set, full-state constraints aren’t violated for all time, and the tracking error converges to a small compact set around zero. A simulation example shows the effectiveness of this control scheme.

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov-Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system.

This paper studies adaptive finite-time control problem of a class of nonlinear systems with dynamic and parametric uncertainties. The power of systems in this paper is any positive odd rational number but not necessary equal to or greater than one. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterise the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, adding a power integrator, adaptive control and FTISS methods, an adaptive state feedback controller is designed to drive the states to the origin in finite time while maintaining all the closed-loop signals bounded.

Input–output finite-time stability (IO-FTS) of fractional-order positive switched systems (FOPSS) is investigated in this paper. First of all, the concept of IO-FTS is extended to FOPSS. Then, by using co-positive Lyapunov functional method together with average dwell time approach, some sufficient conditions of input–output finite-time stability for the considered system are derived. Furthermore, the state feedback controller and the static output feedback controller are designed, and sufficient conditions are presented to ensure that the corresponding closed-loop system is input–output finite-time stable. These conditions can be easily obtained by linear programming. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

In this paper, the problem of output feedback stabilization for high-order nonlinear systems with more general low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate is studied. By constructing the novel Lyapunov function and observer, based on the homogeneous domination and adding a power integrator methods, an output feedback controller is developed to guarantee that the equilibrium of the closed-loop system is globally uniformly asymptotically stable.

This paper studies the problem of output feedback disturbance attenuation for a class of nonlinear systems with input matching uncertainty, whose nonlinearities are bounded by unmeasured states multiplying unknown input and output polynomial functions. Combining the technique of dynamic gain and extended state observer, an adaptive output feedback controller is designed to guarantee that the states of the closed-loop system are globally bounded, and the disturbance attenuation is achieved in the L2-gain sense.

We study the input-to-state stability (ISS) of switched nonlinear input delay systems under asynchronous switching. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. By making a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and allowing the increase of the Lyapunov–Krasovskii functional (LKF) on all the switching times, the extended stability criteria for switched delay systems in generally nonlinear setting are derived first. Then, we focus on switched nonlinear input delay systems where the presence of the input delay leads to the instability of some subsystems of it. By explicitly constructing input-to-state stable LKF, the sufficient conditions for ISS of switched nonlinear input delay systems under asynchronous switching are presented. Finally, two examples are given to illustrate the effectiveness of the proposed theory.

This paper investigates the problem of global exponential tracking control for switched nonlinear systems with linear uncertain parameters and without persistency of excitation. A switched model reference adaptive control technique, using the mode-dependent average dwell time method and a concurrent learning approach, is proposed for the first time. A sufficient condition is provided to ensure that the dynamics of the state tracking error and the adaptive weight error converge to zero exponentially rapidly. Consequently, the relationship among the average dwell time of each subsystem, the concurrent learning algorithm, and the performance of uncertain switched systems is established. Furthermore, the transient performance bounds of the state tracking error and the adaptive weight error are studied. Finally, an illustrative numerical example is provided to demonstrate the effectiveness of the proposed method.

In this note, we study the stabilization problem of positive switched linear system (PSLS) with disturbance. By introducing a class of weak common linear copositive Lyapunov functions, we design time-dependent switching rules under which the system is asymptotically stable. Both continuous-time and discrete-time PSLS are taken into consideration, and the obtained results are also extended to nonpositive switched systems. Finally, the theoretical results are applied to consensus problem of multiagent systems with switching topologies and disturbance.

This paper investigates the consensus problem for third-order discrete-time multi-agent systems in directed networks. For the case when each agent can only receive the information of position and velocity from its neighbors, necessary and sufficient conditions for consensus have been proposed. In contrast to the preceding work, we not only present the exact consensus value, but also illustrate the influence of scaling parameters and nonzero eigenvalues of the involved Laplacian matrix on consensus. Two numerical examples are given to demonstrate the effectiveness of the obtained results.

Summary This paper studies the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with state and input delays and the unknown output function. For stochastic feedforward nonlinear systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and C2 Lyapunov-Krasovskii functional and using the homogeneous domination method, an output feedback controller can be developed to guarantee the closed-loop system globally asymptotically stable in probability.

This paper studies the problem of global output feedback stabilisation for a class of nonlinear time-delay systems with the unknown output function. By constructing the appropriate Lyapunov–Krasovskii functional and observer, skillfully combining generalised adding a power integrator technique, sign function and homogeneous domination approach, an output feedback controller is designed to guarantee globally uniformly asymptotical stability of nonlinear time-delay systems with the unknown output function.

Based on stochastic time-delay system stability criterion and a homogeneous domination approach, the output-feedback stabilization problem for a class of more general stochastic upper-triangular systems with state and input time-delays has been solved in this paper. Firstly, the initial system is changed into an equivalent one with a designed scalar by introducing a set of coordinate transformations. After that, by designing an implementable homogeneous reduced-order observer, and tactfully selecting a suitable Lyapunov–Krasoviskii functional and a low gain scale, a delay-independent output-feedback controller is explicitly constructed. Finally, the globally asymptotically stability in probability of the closed-loop system is ensured by rigorous proof. The simulation results demonstrate the efficiency of the proposed design scheme.

This paper studies the problem of output feedback stabilisation for a class of stochastic nonlinear time-delay systems with the unknown output function. For stochastic nonlinear time-delay systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and Lyapunov– Krasovskii functional and using the homogeneous domination method, an output feedback controller can be developed to guarantee the closed-loop system globally asymptotically stable in probability.

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker a...

Summary This paper deals with the problem of continuous output-feedback stabilization for a class of switched high-order planar systems under arbitrary switchings. Based on the common Lyapunov function design method, by using the adding a power integrator technique and designing an implementable observer, a continuous output-feedback controller is constructed such that the closed-loop system is global stabilization and the output can be regulated to the origin. As an application, the developed strategy is utilized to the control design for the continuous stirred tank reactor with two modes feed stream. The simulation results verify the efficiency of the proposed design scheme. Copyright © 2017 John Wiley & Sons, Ltd.

This paper studies the output feedback control problem for high-order nonlinear feedforward time-delay systems. Systems become more general due to both low-order and high-order in nonlinearities taking any value in certain intervals. By constructing the new Lyapunov–Krasovskii functional and reduced-order observer, based on the homogeneous domination theory, an output feedback controller is developed to guarantee high-order nonlinear feedforward time-delay systems globally asymptotically stable. A simulation example demonstrates the theoretical result.

Summary This paper considers semi-global output feedback control for more general nonlinear systems with unknown time-delay and output function whose derivative is unbounded from above. By introducing a new observer and using the backstepping design method and the Razumikhin stability theorem, an output feedback controller is constructed to achieve a semi-global stability. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies the problem of finite-time stabilisation of more general high-order nonlinear systems with dynamic and parametric uncertainties. By characterising the unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), skillfully combining Lyapunov function, sign function, backstepping, adaptive control and FTISS approaches, and using finite-time stability theory, an adaptive state feedback controller is designed to guarantee high-order uncertain nonlinear systems globally finite-time stable.

To deal with a class of uncertain nonlinear systems with time-varying full state constraints, input saturation and unknown control direction, a Nussbaum gain adaptive control scheme is provided in this paper. Time-varying asymmetric barrier Lyapunov functions (TVABLFs) are employed to prevent the transgression of state constraints. An auxiliary subsystem is utilized to analyze the effect of input saturation. Nussbaum gain technique is introduced to compensate the influence of unknown control direction and nonlinear terms arising from input saturation. It is shown that all the closed-loop signals are bounded in the semi-global sense, error signals converge to bounded compact sets around origin, and time-varying full state constraints and input saturation aren’t violated. The effectiveness of this method is indicated by a simulation example.

This paper studies the problem of global output feedback control for a class of feedforward nonlinear systems with unknown multiple time-varying delays and unknown output function. We allow that system nonlinearities satisfy the linear growth condition on unmeasured states multiplying the unknown constant, input function and polynomial-of-output growth rates. By skillfully introducing dynamic gain method, backstepping method and Lyapunov-Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain to guarantee the boundedness of closed-loop system signals and the convergence of original system states and their corresponding observer states.

This paper solves finite-time stabilization problem of stochastic low-order nonlinear systems with time-varying orders and stochastic inverse dynamics. Due to stochastic low-order systems being merely continuous but not smooth, and the appearance of time-varying orders and stochastic inverse dynamics, all of control methods of stochastic nonlinear systems are inapplicable. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability (FT-SISS) and applying more general stochastic finite-time stability theory, a new design and analysis method is proposed to guarantee almost sure boundedness of all the closed-loop signals and stochastic finite-time stability of stochastic low-order nonlinear systems with time-varying orders and FT-SISS inverse dynamics.

This paper solves the problem of output feedback stabilisation for nonlinear systems with unknown output function and control coefficients. Since output function is Lipschitz continuous but not necessary derivable, the maximal sector region of output function is given. As long as output function belongs to the sector, an output feedback controller can be designed to render the closed-loop system globally asymptotically stable. The effectiveness of controller is demonstrated by two examples.

This paper considers the problem of global finite-time stabilization in probability for stochastic high-order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite-time stability, via the combined adding one power integrator and sign function method, constructing a C2 Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system globally finite-time stable in probability.

This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a C2 Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

This paper studies a class of random nonlinear systems with time-varying delay, in which the r -order moment of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time-delay systems. Secondly, some criteria on noise-to-state stability in the moment sense and in probability sense are given by Lyapunov method respectively. Finally, an adaptive output feedback regulation controller is constructed for a class of random nonlinear time-delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example.

Under a weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems globally finite-time stable.