Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems

Global adaptive neural network control of nonlinear time-varying systems with unknown control coefficients and model uncertainties

In this paper, a novel event-triggered (ET) adaptive neural tracking control scheme is proposed for uncertain strict-feedback systems subject to asymmetric time-varying full-state constraints, unknown virtual control coefficients and external disturbances. The lower-order time-varying asymmetric barrier Lyapunov function (TVABLF) is constructed to ensure that state constraints are not transgressed. Then, a simple backstepping-based control procedure is developed to remove the existing restrictions on a high power of piecewise TVABLF and high-order differentiability of virtual laws. In particular, a novel adaptive updating law is constructed to co-design the controller and the ET scheme by the combination of the Nussbaum gain technique, thereby solving the ET controller design difficulty resulting from unknown control coefficients. The proposed scheme can guarantee all states within the time-varying constrained areas, achieve the satisfactory tracking ability and save the communication resource. Finally, the effectiveness of the proposed scheme is testified by numerical and practical examples.

For floating production storage and offloading (FPSO) vessels, a dynamic positioning controller is necessary because using only a mooring system is not possible to keep the ship within a predefined region. Position control of the FPSO vessel is extremely challenging due to model uncertainties and unknown control coefficients. This paper develops a new robust adaptive positioning controller consisting of several components: adaptive law, dynamic surface control (DSC) technology, sigmoid tracking differentiator (STD), Nussbaum gain function, and structural reliability index. Model uncertainties can be estimated by the adaptive law derived from the Lyapunov theory. The DSC technology is used to eliminate repeated differentiation by introducing first-order filtering of the virtual control. The chattering-free STD with the characteristics of global fast convergence can estimate the derivatives of model uncertainties that are difficult to calculate directly. Therefore, the DSC and STD techniques make the proposed controller simpler to compute and easier to implement in engineering practice. Most of the traditional controllers require the information about the control coefficients to guarantee the stability of the closed-loop system while the Nussbaum gain function can remove the requirement for a priori knowledge of the sign of control coefficients. The capacity of the mooring system can be fully utilized to position the FPSO vessel by adjusting the structural reliability index on the premise of ensuring the safety of mooring lines, and hence less control effort is needed for the positioning controller. Simulations using two sets of system parameters demonstrate the proposed controller’s effectiveness. In addition, a qualitative comparison with the adaptive backstepping controller shows that our proposed controller is computationally more efficient and does not require a priori knowledge of the sign of control coefficients. A quantitative comparison with robust adaptive controller without the structural reliability shows that less control effort is needed using our proposed controller.

This paper considers a robust adaptive stabilization problem for a class of uncertain nonlinear systems which include an unknown virtual control coefficient, an unknown constant parameter, and a time-varying disturbance whose bound is unknown, We propose a new estimator for an un-known virtual control coefficient and present a robust adaptive backstepping design procedure which results in a smooth state feedback control law, a new two-dimensional parameter update law, and a <TEX>$C^1$</TEX> Lyapunov function which is positive definite and proper.

This paper is concerned with the problem of adaptive neural control for uncertain nonlinear strict-feedback time-delay systems with unknown virtual control coefficients. Radial basis function (RBF) neural networks are employed to directly approximate unknown virtual control signals, and then the adaptive neural control law is constructed by Lyapunov-Krasovskii functionals and backstepping. In order to avoid encountering a large number of adaptive parameters when using RBF neural networks as function approximators, an unknown constant, instead of unknown neural weights themselves, is employed as the estimated parameter. This technique makes only one adaptive parameter tuned online, thus significantly alleviating the burdensome computation. Meanwhile, some continuous functions are introduced to overcome the design difficulty originating from the use of one adaptive parameter. The proposed adaptive control guarantees the boundedness of all the signals in the closed-loop system. Simulation studies are presented to illustrate the effectiveness of the scheme.

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L 2 tracking performance to stabilise the closed-loop system. This L 2 tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.

Hydraulic system is widely used in industry where large actuation forces are needed such as electro-hydraulic positioning system, active suspension control, and so on. One of the main problem in hydraulic system is the nontriviality, for instance, the deadbands in valve operation, frictions of links, saturations, pressure dynamics, etc. both system unknown nonlinearities and external disturbances should be considered in controller design. For underwater hydraulic manipulator, because of the environment of sea and the large nonlinearities of the hydraulic manipulator system, both system unknown nonlinearities and external disturbances should be considered in controller design. A lot of control methods have been proposed to solve the problem properly, such as sliding mode control, adaptive control, fuzzy adaptive control, adaptive robust control, ect. However, due to limited knowledge about hydraulic manipulator system, it is hard to precisely estimate the nonlinearities for a possible higher performance. In this paper, a neural network adaptive robust control method is proposed to help control an underwater hydraulic manipulator. In order to achieve better performance using adaptive robust control strategy, unknown nonlinearities in the system are approximated by the outputs of radial basis function neural network (RBFNNs). A projection law has been used to bound the NN weights when they are tuning on-line to avoid possible adaptive divergence, and the tracking transient performance is guaranteed by robust control law. Simulation results illustrate that manipulator has a good tracking performance.

In this paper, an adaptive neural design is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require the a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semi-global uniformly and ultimately boundedness of all the signals in the closed-loop.

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 &amp; Sons, Ltd.

Novel adaptive neural control design for nonlinear MIMO time-delay systems

In this paper, robust adaptive neural tracking control is developed for a class of uncertain SISO nonlinear systems in a Brunovsky form with unknown nonlinear dead-zone and unknown control gain & its sign. The design is based on the principle of sliding mode control and the use of Nussbaum-type function in solving the problem of the completely unknown function control gain. A novel description of general nonlinear dead-zone, which makes the control system design possible, is introduced by using the mean value theorem. The approach removes the condition of the equal slope with defined region for the dead-zone. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation for the upper bound of the optimal approximation error and the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded

This paper presents a robust adaptive fuzzy neural controller (AFNC) suitable for motion control of multilink robot manipulators. The proposed controller has the following salient features: (1) self-organizing fuzzy neural structure, i.e., fuzzy control rules can be generated or deleted automatically according to their significance to the control system and the complexity of the mapped system and no predefined fuzzy rules are required; (2) fast online learning ability, i.e., no prescribed training models are needed for online learning and weights of the fuzzy neural controller are modified without any iterations; (3) fast convergence of tracking errors, i.e., manipulator joints can track the desired trajectories very quickly; (4) adaptive control, i.e., structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; and (5) robust control, where asymptotic stability of the control system is established using the Lyapunov theorem. Experimental evaluation conducted on an industrial selectively compliant assembly robot arm demonstrates that excellent tracking performance can be achieved under time-varying conditions.

In this paper, we deal with the problem of tracking control for a class of uncertain nonlinear systems in strict-feedback form subject to completely unknown system nonlinearities, hard constraints on full states, and unknown time-varying bounded disturbances. Integral barrier Lyapunov functionals are constructed to handle the unknown affine control gains ( $ {g(\cdot )}$ ) with state constraints simultaneously. This removes the need on the knowledge of control gains for control design and avoids the conservative step of transforming original state constraints into new bounds on tracking errors. Neural networks (NNs) are used to approximate the unknown continuous packaged functions. To enhance the robustness, adapting parameters are developed to compensate the unknown bounds on NNs approximations and external disturbances. Design parameters-dependent feasibility conditions are formulated as sufficient conditions for the existence of feasible design parameters to guarantee the state constraints, and an offline constrained optimization step is proposed to obtain the optimal design parameters prior to the implementation of the proposed control. It is proved that the proposed control can guarantee the semiglobal uniform ultimate boundedness of all signals in closed-loop system, all states are ensured to remain in the predefined constrained state space, and tracking error converges to an adjustable neighborhood of the origin by choosing appropriate design parameters. Simulations are performed to validate the proposed control.

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

A new event-triggered adaptive tracking controller for nonlinear systems with unknown virtual control coefficients