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The adaptive tracking control is extended to the nonlinear system with multiple uncertainties consisting of input saturation, unknown parameter and full-state constraints. To deal with the input saturation, a distinctive method of introducing an auxiliary system is used instead of directly approximating it by a smooth function. Then, the adaptive backstepping technique is combined with the barrier Lyapunov function (BLF) to solve the parametric nonlinearities and give a systematic design procedure. Based on this design procedure, an adaptive state-feedback controller is obtained with rigourous stability analysis. It is verified that all the signals are uniformly ultimately bounded, the tracking error is bounded in a compact set of the origin, and the full-states are not violated. Finally, the proposed controller is used to a mass-spring mechanical system, and demonstrates the proposed scheme is effective.

This paper investigates the adaptive tracking control problem of stochastic nonlinear systems under the conditions of full-state constraints and input saturation. The barrier Lyapunov function (BLF) is applied to handle the full-state constraints. To deal with the input saturation, a distinctive method of introducing an auxiliary system is adopted. Then, a systematic controller design procedure is given by combining a novel radial basis function neural network (RBF NN) approximation approach with backstepping technique.By this way, an adaptive state-feedback controller with only one adaptive law is obtained, which renders the closed-loop system semi-globally uniformly ultimately bounded. Meanwhile, the tracking error is bounded by an explicit function of the design parameters and saturated input error. In addition, the full-states are not violated. Finally, a simple pendulum system and a numerical example are simulated to demonstrate the effectiveness of the proposed scheme.

This paper is concerned with the practically finite-time (PFT) control problem for a class of more general nonlinear systems subject to mismatching time-varying disturbances. Without any extra assumptions on system nonlinearities, a composite controller is developed by introducing a disturbance observer and finite-time control technique. Based on the designed controller and Lyapunov stability theory, the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance. Furthermore, as a byproduct of the proposed design method, the disturbance observer-based PFT control for high-order nonlinear systems is also shown to be possible. To the best of the authors’ knowledge, it is the first PFT control result for high-order nonlinear systems with external disturbances. Finally, an application example of a single-link robot system with disturbances and a numerical example are presented to demonstrate the effectiveness of the proposed scheme, respectively.

This paper investigates adaptive attitude control for quadrotor unmanned aerial vehicle (UAV) with dead zone and external disturbance. A attitude controller is designed based on backstepping, and adaptive law is designed to compensate the influence of input dead zone and external disturbance. The designed controller guarantees that attitude angle of quadrotor UAV can trace the desired attitude angle. Finally, simulation results have demonstrated the effectiveness of the designed scheme.

This paper aims to solve the position control problem for quadrotor unmanned aerial vehicle (UAV). In order to be closer to the real UAV system, we consider the UAV with input delay. A barrier Lyapunov function is introduced to ensure that the tracking error is limited within a predetermined range. Pade approximation and an intermediate variable are applied to compensate the effect of the input delay. By using the designed control method, the UAV can track the desired trajectory. Finally, the simulation example is given to verify the effectiveness of the proposed approach.

This paper investigates the state-feedback stabilization problem in the smooth case for a class of high-order nonlinear systems with time delays. By generalizing a novel radial basis function neural network (RBF NN) approximation approach to high-order nonlinear systems, we successfully remove the power order restriction and the growth conditions on system nonlinearities. It should be pointed out that the knowledge of NN nodes and weights does not need to be known a priori and operate on-line, and the adaptive parameter is only one. Furthermore, without imposing any growth assumptions on system nonlinearities, we construct a smooth adaptive state-feedback controller which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, we apply the proposed scheme to a single-link robot system and a numerical example to demonstrate the effectiveness of the controller.

This paper focuses on the state-feedback control problem for a class of high-order nonlinear systems with unknown time delay and control coefficients. Based on a novel dynamic gain-based backstepping technique and radial basis function neural network (RBF NN) approximation approach, the restrictions on high-order and nonlinearities are removed or further relaxed. Under these weaker conditions, a smooth state-feedback controller is skillfully constructed with only one adaptive parameter. In addition, the knowledge of time delay, NN nodes and weights is not necessary to be known a priori. It is proven that the designed controller can render the closed-loop system be semi-globally uniformly ultimately bounded. Finally, both practical and numerical examples are shown to demonstrate the effectiveness of the proposed scheme.

This study is concerned with the output-feedback control problem for a class of stochastic high-order non-linear systems with time-varying delays. A distinctive feature of the control scheme is that the restrictions on delay-dependent drift and diffusion terms are greatly relaxed by using radial basis function neural network (NN) approximation approach. Furthermore, with the approach, the specific knowledge of NN nodes and weights is not required. Under some weaker conditions, by combining dynamic surface control technique with proper Lyapunov–Krasovskii functional, an adaptive NN output-feedback controller is designed constructively such that the closed-loop system is 4-moment (or mean square) semi-globally uniformly ultimately bounded. Finally, the control scheme is applied to both a practical stochastic robot system and a numerical system to demonstrate the effectiveness of the proposed approach.

This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability. The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded (SGUUB) and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.

This paper studies the state feedback control problem for a class of nonlinear systems with integral input-to-state stability (iISS) unmodeled dynamics and unknown control direction. By using the properties of iISS and the backstepping technique, the design function of the state feedback controller and the updating rule of parameters are selected to obtain the appropriate controller. Theoretical analysis proves that the designed controller can ensure that all signals of the system are bounded and the state can be gradually adjusted to zero. Simulation results show the effectiveness of the proposed method.

This paper addresses the neural network-based output-feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control DSC technique with radial basis function neural network RBF NN approximation approach, we construct an adaptive output-feedback controller to guarantee the closed-loop system to be mean square semi-globally uniformly ultimately bounded M-SGUUB. A simulation example demonstrates the effectiveness of the proposed scheme.

This paper solves the decentralized state-feedback control problem for a class of large-scale stochastic high-order nonlinear systems. By generalizing neural network (NN) approximation approach to this kind of systems, we completely remove the growth conditions on system nonlinearities and the power order restriction. It is shown that through using dynamic surface control (DSC) and backstepping technique, an adaptive state-feedback controller is constructed, which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme.

This paper considers the state-feedback control for high-order stochastic nonlinear time-delay system that is additionally driven by the noise of unknown covariance. Without any assumptions imposing on nonlinear functions, an adaptive composite controller is skillfully obtained on the basis of the Lyapunov-Krasovskii functional and recursive backstepping technique. Through using stochastic stability theory to give the analysis, the proposed adaptive controller can render the closed-loop system globally uniformly ultimately bounded (GUUB). The effectiveness and performance of the proposed scheme is verified by numerical simulation results.

This paper focuses on investigating the issue of adaptive state-feedback control based on neural networks (NNs) for a class of high-order stochastic uncertain systems with unknown nonlinearities. By introducing the radial basis function neural network (RBFNN) approximation method, utilizing the backstepping method and choosing an approximate Lyapunov function, we construct an adaptive state-feedback controller which assures the closed-loop system to be mean square semi-global-uniformly ultimately bounded (M-SGUUB). A simulation example is shown to illustrate the effectiveness of the design scheme.

This paper is concerned with the state-feedback control for a class of stochastic high-order nonlinear systems with multiple time delays. A distinctive novelty lies in the removal of the traditional growth assumptions imposed on the delay-dependent nonlinear terms. Then, without any extra assumptions, a state-feedback controller is explicitly constructed based on the Lyapunov-Krasovskii functionals and recursive backstepping design, which guarantees the closed-loop system to be globally uniformly ultimately bounded (GUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed scheme.

This paper focuses on solving the output-feedback tracking problem for a class of nonlinear time-delay systems in the presence of unmeasurable states and input saturation. A distinctive feature is that the growth assumptions imposed on system nonlinearities are proven to be unnecessary and can be removed. Based on this, by constructing a full-order state observer to handle unmeasurable states and introducing an auxiliary system to compensate for input saturation, an output-feedback controller is explicitly constructed with the help of Lyapunov-Krasovskii functional method and backstepping technique. It is proven that the designed controller can render the closed-loop system be globally uniformly ultimately bounded. Particularly, instead of converging to an arbitrarily small neighborhood of zero as in related results, the tracking error is ensured to be tuned by design parameters and input saturation error in the mean sense. Finally, a simulation example is provided to validate the effectiveness of the proposed scheme.

This paper investigates the adaptive state-feedback control problem of a two-stage chemical reactor system. Firstly, by using a direct radial basis function neural network (RBF NN) approximation approach, the nonlinear terms are handled under much weaker conditions. Then, with the help of a novel dynamic gain-based backstepping technique and appropriate Lyapunov-Krasovskii functionals, a smooth controller with only one adaptive parameter is constructed, which successfully overcomes the obstacles generated by time delay, control coefficients and nonlinear restrictions. It is proven that the constructed controller can render the closed-loop system semi-globally uniformly ultimately bounded. Finally, the simulation results of the chemical reactor system are shown to demonstrate the effectiveness of the control scheme.

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

In this study, we propose a variant of Particle Swarm Optimization (PSO) algorithm for chaotic synchronization based on PID control. The new method, called Improved Particle Swarm Optimization (IPSO) algorithm employs the global best position to execute a global searching strategy such that the position updating is well finished. In addition, the IPSO introduces a mutation operation in terms of the personal best positions. By combining the global searching strategy and mutation operation, the global searching capacity of the IPSO is enhanced, and it can easily get rid of the local optimums. The performance of the IPSO is investigated on four test examples and its results are compared with those of the PSO. The empirical analysis of the experimental results demonstrates the efficiency of the IPSO.

For a class of stochastic high-order nonlinear systems, by introducing the combined homogeneous domination and sign function design approach, this technical note solves the problem of output-feedback control under the weaker high-order and nonlinear growth conditions.

In this paper, a combined homogeneous domination and sign function design approach is presented to state feedback control for a class of stochastic high-order nonlinear systems with time-varying delay. The use of the combined approach relaxes the restriction on nonlinear functions and makes the closed-loop system globally asymptotically stable in probability.

In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system.

Contrast and analysis of the influence that synchronous rotor mixer’s two phase angles 90° and 180° to the mixing effect using special visco-elasticity fluid software--Polyflow. The results show that 90° phase angle rotor could promote compound mixing, and improve mixing rubber’s uniformity, and its mixing effect is better than synchronous rotor with 180° phase angle.

This paper addresses the problem of adaptive output-feedback control for more general class of stochastic time-varying delay nonlinear systems with unknown control coefficients and perturbations. By using Lyapunov–Krasovskii functional, backstepping and tuning function technique, a novel adaptive neural network (NN) output-feedback controller is constructed with fewer learning parameters. The designed controller guarantees that all the signals in the closed-loop system are 4-moment (or mean square) semi-globally uniformly ultimately bounded (SGUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed control scheme.

This notes focuses on the state-feedback stabilization problem for a class of high-order nonlinear parameterized systems in presence of time-varying control coefficient. The conditions on parameterized nonlinear functions and time-varying control coefficient are further relaxed by adopting Nussbaum function approach and backsetpping technique. In addition, the uniform ultimate boundedness of the closed-loop system is guaranteed by designing an adaptive state-feedback controller. Finally, a simulation example is given to illustrate the effectiveness of the proposed scheme.

The output tracking problem is considered for a class of stochastic nonlinear systems with unknown control coefficients in this paper. By combining the radial basis function neural network (RBF NN) approximation method with backstepping technique, an adaptive state-feedback controller is successfully constructed to guarantee the solution process to be bounded in probability. In addition, the tracking error signal is 4th-moment semi-globally uniformly ultimately bounded, which can also be regulated into a small neighborhood of the origin in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

This paper solves the partial-state-feedback control problem for a class of stochastic high-order nonlinear systems with the drift and diffusion terms depending on system states and stochastic inverse dynamics. The homogeneous domination approach is successfully introduced to this class of systems to relax the restrictions on nonlinear functions and guarantee the closed-loop system to be globally asymptotically stable (GAS) in probability.

This paper further discusses output-feedback regulation for more general nonlinear systems with integral input-to-state stability (iISS) inverse dynamics and unknown control direction. By using the adaptive backstepping method, an output feedback controller is given to drive the output to the origin while maintaining other closed-loop signals bounded.

This paper further considers more general high-order stochastic nonlinear system driven by noise of unknown covariance and its adaptive state-feedback stabilization problem. A smooth state-feedback controller is designed to guarantee that the origin of the closed-loop system is globally stable in probability.

This technical note considers a class of high-order stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics, and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states. A new design and analysis approach to the problem of state-feedback global regulation is developed to guarantee that all the signals of the closed-loop system are bounded almost surely and the states can be regulated to zero almost surely.

For a class of stochastic nonlinear systems in which the drift and diffusion vector fields depend on the unmeasurable states besides the measurable output, the research purpose of this technical note is to find the maximum value interval of observer gain for the desired control performance. For this interval, the designed output-feedback controller ensures that the equilibrium at the origin is globally asymptotically stable in probability, and the inverse optimal stabilization in probability is achieved.

This paper further considers a more general class of stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics and drift and diffusion terms depending upon the other states besides stochastic inverse dynamics and the first state. By skillfully choosing the designed functions and the update laws of parameters, and using the important mathematical tools established in IEEE Trans. Automat. Contr. 2010; 55(2):304–320, a unifying framework of state feedback controller is proposed to guarantee that all the signals of the closed-loop system are bounded almost surely and the states can be regulated to zero almost surely. A simulation example demonstrates the effectiveness of the control scheme. Copyright © 2011 John Wiley & Sons, Ltd.

This paper investigates the small-gain type conditions on stochastic iISS (SiISS) systems and makes full use of these conditions in the design and analysis of the controller. The contributions are as follows: (1) A new proof of the stochastic LaSalle theorem is provided; (2) The small-gain type conditions on SiISS are developed and their relationship is discussed; (3) Based on the stochastic LaSalle theorem and SiISS small-gain type conditions, the adaptive controllers are designed to guarantee that all of the closed-loop signals are bounded almost surely and the stochastic closed-loop systems are globally (asymptotically) stable in probability.

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance (e. g., asymptotical stability) and reducing the control effort. By introducing a new rescaling transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs an improved output-feedback controller. The output-feedback controller guarantees the globally asymptotical stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and rescaling transformation parameter are obtained to effectively reduce the control effort.

This paper designs an improved output-feedback controller from the viewpoint of reducing the control effort at the premise of maintaining the desired control performance for a concrete example. The output-feedback controller guarantees the globally asymptotical stability of the closed-loop system by introducing a new rescaling transformation, adopting an effective reduced-order observer, and choosing ingenious Lyapunov function and appropriate design parameters. Simultaneously, from both the theoretical analysis and a concrete example, smaller critical values for gain parameter and rescaling transformation parameter are obtained to effectively reduce the control effort and the rate of change of controller than the design of the related papers.

Nussbaum-type gain function and neural network (NN) approximation approaches are extended to investigate the adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear time-delay systems. The distinct features of this paper are listed as follows. Firstly, the power order condition is completely removed; the restrictions on system nonlinearities and time-varying control direction are greatly weakened. Then, based on Lyapunov-Krasovskii function and dynamic surface control technique, an adaptive NN controller is constructed to render the closed-loop system semiglobally uniformly ultimately bounded (SGUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed control scheme.

The adaptive stabilization scheme based on tuning function for stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics is investigated. By combining the stochastic LaSalle theorem and small-gain type conditions on SiISS, an adaptive output feedback controller is constructively designed. It is shown that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally stable in probability.

This paper considers a concrete stochastic nonlinear systems with stochastic unmeasurable inverse dynamic. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is introduced. A constructive strategy is proposed to design a dynamic output-feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

This paper investigates the problem of state-feedback regulation for a class of nonlinear systems with iISS unmodeled dynamics. Using the backstepping technique and the properties of iISS, we give the design procedure of a state-feedback controller, by appropriately choosing the designed functions and update laws of parameters. The designed controller guarantees that all the signals of the closed-loop system are bounded, and the states can be regulated asymptotically to zero. A simulation example demonstrates the effectiveness of the control scheme.

This paper considers a concrete example, and designs an improved output-feedback controller from the viewpoint of reducing the control effort at premise of maintaining the desired control performance (e.g., asymptotical stability). By introducing a new rescaling transformation, adopting an effective reduced-order observer, and choosing ingenious Lyapunov function and appropriate design parameters, the output-feedback controller guarantees the globally asymptotical stability of the closed-loop system. Simultaneously, from both the theoretical analysis and a concrete example, the smaller critical values for gain parameter and rescaling transformation parameter are obtained to reduce effectively the control effort and the rate of change of controller than the design of the related papers. At last, simulations are given to compare the control effort of two control schemes.