Adaptive dynamic surface control of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics

In this paper, the issue of adaptive neural control is discussed for a class of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics. A dynamic signal produced by the first-order auxiliary system is employed to deal with the dynamical uncertain terms. Radial basis function neural networks are used to reconstruct unknown nonlinear continuous functions. With the help of the mean value theorem and Young's inequality, only one learning parameter is adjusted online at recursive each step. Using the hyperbolic tangent function as nonlinear mapping, the output constrained stochastic nonstrict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained stochastic nonstrict-feedback system. Based on dynamic surface control technology and the property of Gaussian function, adaptive neural control is developed for the transformed stochastic nonstrict-feedback system. The output abides by stochastic constraints in probability. By the Lyapunov method, all signals of the closed-loop control system are proved to be semi-global uniform ultimate bounded (SGUUB) in probability. The obtained theoretical findings are verified by two numerical examples.     

Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint

This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed‐loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated.     

Decentralized adaptive output‐feedback control for stochastic interconnected systems with stochastic unmodeled dynamic interactions

In this paper, we consider the problem of decentralized adaptive output‐feedback regulation for stochastic nonlinear interconnected systems with unknown virtual control coefficients, stochastic unmodeled dynamic interactions. The main contributions of the paper are as follows: (1) This paper presents the first result on decentralized output‐feedback control for stochastic nonlinear systems with unknown virtual control coefficients; (2) For stochastic interconnected systems with stochastic integral input‐to‐state stable unmodeled dynamics, and more general nonlinear uncertain interconnections which depend upon the outputs of subsystems and the stochastic unmodeled dynamics, a decentralized output‐feedback controller is designed to drive the outputs and states to the origin almost surely. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive control of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics

This paper focuses on the problem of adaptive control for a class of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics. By introducing a one-to-one nonlinear mapping, the constrained pure-feedback nonlinear system with state and input unmodeled dynamics is transformed into unconstrained pure-feedback system. The controller design based on the transformed novel system is proposed by using a modified dynamic surface control method. Dynamic signal and normalization signal are designed to handle dynamical uncertain terms and input unmodeled dynamics, respectively. By adding nonnegative normalization signal into the whole Lyapunov function and using the introducing compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded, and all states can obey the time-varying constraint conditions. A numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

In this paper, an adaptive neural output‐feedback control approach is considered for a class of uncertain multi‐input and multi‐output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K‐filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high‐frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time‐varying delays, so that the offered control approach is free of common assumptions on derivative of time‐varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed‐loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Fuzzy adaptive control of a class of nonlinear systems with unmodeled dynamics

This paper investigates the tracking control problem for a class of pure‐feedback systems with unmodeled dynamics. The useful properties of the fuzzy basis functions and membership are explored to be used for stability analysis, and an alternative Lyapunov function depending on both control input and system state is utilized. Then, an adaptive fuzzy controller is designed to ensure that the tracking error is within a small adjustable neighborhood of the origin, where some conventional assumptions imposed on the unmodeled dynamics have been relaxed. Finally, simulation results are given to validate the theoretical results.     

Adaptive neural network control for stochastic constrained block structure nonlinear systems with dynamical uncertainties

Stochastic adaptive dynamic surface control is presented for a class of uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems with unmodeled dynamics and full state constraints in this paper. The controller is constructed by combining the dynamic surface control with radial basis function neural networks for the MIMO stochastic nonlinear systems. The nonlinear mapping is applied to guarantee the state constraints being not violated. The unmodeled dynamics is disposed through introducing an available dynamic signal. It is proved that all signals in the closed‐loop system are bounded in probability and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four‐moment and the state constraints are confirmed in probability. Simulation results are offered to further illustrate the effectiveness of the control scheme.     

An adaptive dynamic surface control of output constrained stochastic nonlinear systems with unknown control directions

This article is concerned about an adaptive dynamic surface control (DSC) of output constrained stochastic nonlinear systems with unknown control directions and unmodeled dynamics. Nonlinear mapping-based backstepping control design is presented for stochastic nonlinear systems with output constraint. The explosion of complexity exists in tradition backstepping method is avoided by using the DSC technique. The radial basis function neural networks are employed to deal with unknown nonlinear functions. Nussbaum gain technique is employed to handle the unknown control directions. And a dynamic signal is employed to dominate the unmodeled dynamics. The adaptive controller is designed can ensure that the tracking error converges on a small region of the origin. And all signals of the closed-loop systems are semiglobal uniformly ultimately bounded. Finally, the results of the simulation cases are provided to show the effectivity of the designed controller scheme.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Robust adaptive output feedback control of nonlinearly parameterized systems

The ideas of adaptive nonlinear damping and changing supply functions were used to counteract the effects of parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The high-gain observer was used to estimate the state of the system. A robust adaptive output feedback control scheme was proposed for nonlinearly parameterized systems represented by input-output models. The scheme does not need to estimate the unknown parameters nor add a dynamical signal to dominate the effects of unmodeled dynamics. It is proven that the proposed control scheme guarantees that all the variables in the closed-loop system are bounded and the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately. Simulation results have illustrated the effectiveness of the proposed robust adaptive control scheme. Translated from Journal of Sichuan University (Engineering Science Edition), 2006, 38(4): 136–140 [译自: 四川大学学报 (工程科学版)]     

Adaptive fuzzy FTC design of nonlinear stochastic systems with actuator faults and unmodeled dynamics

This paper investigates an adaptive fuzzy control method for accommodating actuator faults in a class of uncertain stochastic nonlinear systems with both immeasurable states and unmodeled dynamics. The considered faults are modeled as both loss of effectiveness and lock‐in‐place. To deal with the immeasurable states, a novel state observer containing the actuator faults is designed. Combining with the backstepping technique and stochastic small‐gain theorem, an adaptive fuzzy output feedback control method is developed. The presented design scheme can guarantee that the closed‐loop system is input‐to‐state practically stable in probability. Finally, a simulation example is shown to verify the effectiveness of the proposed control method.     

Global output‐feedback control of systems with dynamic nonlinear input uncertainties through singular perturbation‐based dynamic scaling

A general class of uncertain nonlinear systems with dynamic input nonlinearities is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions, coupled uncertain nonlinear appended dynamics, and uncertain nonlinear input unmodeled dynamics. The control design is based on dual controller/observer dynamic high‐gain scaling with an additional dynamic scaling based on a singular perturbation‐like redesign to address the non‐affine and uncertain nature of the input appearance in the system dynamics. The proposed approach yields a constructive global robust adaptive output‐feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive finite-time output feedback control for Markov jumping nonlinear systems

In this article, the problem of output feedback tracking control for uncertain Markov jumping nonlinear systems is studied. A finite-time control scheme based on command filtered backstepping and adaptive neural network (NN) technique is given. The finite-time command filter solves the problem of differential explosions for virtual control signals, the NN is utilized to approximate the uncertain nonlinear dynamics and the adaptive NN observer is applied to restructure the state of system. The finite-time error compensation mechanism is established to compensate the errors brought by filtering process. The proposed finite-time tracking control algorithm can ensure that the solution of the closed-loop system is practically finite-time stable in mean square. Two simulation examples are employed to demonstrate the effectiveness of the proposed control algorithm.     

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 148–153 (in Chinese)     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Small-gain technique-based adaptive fuzzy command filtered control for uncertain nonlinear systems with unmodeled dynamics and disturbances

This article studies the adaptive tracking control problem for a class of uncertain nonlinear systems with unmodeled dynamics and disturbances. First, a fuzzy state observer is established to estimate unmeasurable states. To overcome the problem of calculating explosion caused by the repeated differentiation of the virtual control signals, the command filter with a compensation mechanism is applied to the controller design procedure. Meanwhile, with the help of the fuzzy logic systems and the backstepping technique, an adaptive fuzzy control scheme is proposed, which guarantees that all signals in the closed-loop systems are bounded, and the tracking error can converge to a small region around the origin. Furthermore, the stability of the systems is proven to be input-to-state practically stable based on the small-gain theorem. Finally, a simulation example verifies the effectiveness of the proposed control approach.