QFT design of multi-loop nonlinear control systems

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

In this article, a novel self-evolving data cloud-based proportional integral derivative (PID) (SEDCPID) like controller is proposed for uncertain nonlinear systems. The proposed SEDCPID controller is constructed by using fuzzy rules with nonparametric data cloud-based antecedence and PID-like consequence. The antecedent data clouds adopt the relative data density to represent the fuzzy firing strength of input variables instead of the explicit design of the membership functions in the classical sense. The proposed SEDCPID controller has the advantages of evolving structure and adapting parameter concurrently in an online manner. The density and distance information of data clouds are proposed to achieve the addition and deletion of data clouds and also a stable recursive method is proposed to update the parameters of the PID-like subcontrollers for the fast convergence performance. Based on the Lyapunov stability theory, the stability of the proposed controller is proven and the proof shows the tracking errors converge to a small neighborhood. Numerical and experimental results illustrate the effectiveness of the proposed controller in handling the uncertain nonlinear dynamic systems.

This paper deals with the problem of robust control for Uncertain Nonlinear System via fuzzy control approach. First, a fuzzy controller with robust control capability is proposed. For avoiding complex controller parameters adjustment, Multi-objective particle swarm Optimization (PSO) algorithm is adopted during the controller design. Secondly, the multi-model is employed to represent the nonlinear system with norm-bounded parameter uncertainties. Finally, a simulation example illustrates the effectiveness and the feasibility of the proposed approach.

A two-step controller synthesis method is proposed in this article for a class of uncertain non-linear systems described by piecewise affine differential inclusions. In the first step, a robust linear controller is designed for the linear differential inclusion that describes the dynamics of the non-linear system close to the equilibrium point. In the second step, a stabilising piecewise affine controller is designed that coincides with the linear controller in a region around the equilibrium point. The proposed method has two objectives: global stability and local performance. It thus enables us to use well-known techniques in linear control design for local stability and performance while delivering a global piecewise affine controller that is guaranteed to stabilise the non-linear system. To construct the required theoretical framework, a stability theorem for non-smooth Lyapunov functions is presented and proved. The new method will be applied to two examples.

Optimal control methods have gained significant attention due to their promising performance in nonlinear systems. In general, an optimal control method is regarded as an optimization process for solving the optimal control laws. However, for uncertain nonlinear systems with complex optimization objectives, the solving of optimal reference trajectories is difficult and significant that might be ignored to obtain robust performance. For this problem, a double-closed-loop robust optimal control (DCL-ROC) is proposed to maintain the optimal control reliability of uncertain nonlinear systems. First, a double-closed-loop scheme is established to divide the optimal control process into a closed-loop optimization process that solves optimal reference trajectories and a closed-loop control process that solves optimal control laws. Then, the ability of the optimal control method can be improved to solve complex uncertain optimization problems. Second, a closed-loop robust optimization (CL-RO) algorithm is developed to express uncertain optimization objectives as data-driven forms and adjust optimal reference trajectories in a close loop. Then, the optimality of reference trajectories can be improved under uncertainties. Third, the optimal reference trajectories are tracked by an adaptive controller to derive the optimal control laws without certain system dynamics. Then, the adaptivity and reliability of optimal control laws can be improved. The experimental results demonstrate that the proposed method can achieve better performance than other optimal control methods.

This paper presents the open-source stochastic model predictive control framework GRAMPC-S for nonlinear uncertain systems with chance constraints. It provides several uncertainty propagation methods to predict stochastic moments of the system state and can consider unknown parts of the system dynamics using Gaussian process regression. These methods are used to reformulate a stochastic MPC formulation as a deterministic one that is solved with GRAMPC. The performance of the presented framework is evaluated using examples from a wide range of technical areas. The experimental evaluation shows that GRAMPC-S can be used in practice for the control of nonlinear uncertain systems with sampling times in the millisecond range.

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

RGA-based on-line tuning of BMF fuzzy-neural networks for adaptive control of uncertain nonlinear systems

Combined adaptive backstepping-SMC schemes to design both static and dynamical adaptive controllers for uncertain nonlinear systems have been presented. It has been shown that, for the class of nonlinear systems with parametric uncertainties entering linearly in the system dynamics and transformable into FGOCF, adaptive dynamical SMC may be designed via an adaptive input-output linearization procedure, based upon the fundamental ideas of the backstepping algorithm. This control design method is applicable to uncertain nonlinear systems without explicit transformations to parametric-pure or parametric-strict feedback forms. The proposed controlled strategy has been applied to the output tracking control of the average Buck-Boost converter model and it has been shown to be remarkably robust with respect to external stochastic bounded perturbation input signals.

This paper presents novel Takagi-Sugeno (T-S) fuzzy model-based robust finite time control methods for a class of uncertain nonlinear systems. First, the nonlinear system is approximated by a suitable T-S fuzzy model in which most of the parameters can be computed offline. Then, a T-S fuzzy model-based nonsingular terminal sliding mode control (TS-NTSMC) method is designed based on a proposed nonsingular terminal sliding mode (NTSM) surface. This method not only alleviates the online computational burden, but also preserves the advantages of fast and finite time convergence, high tracking precision, and robustness to uncertainties and disturbances. However, the discontinuous function [Formula: see text] causes the chattering phenomenon, which is unavoidable. In order to attenuate the chattering, maintain the key properties of the TS-NTSMC method and achieve higher control performance, a novel T-S fuzzy model-based super-twisting higher order nonsingular terminal sliding mode control (TS-STHONTSMC) method is proposed. The global finite time stability of the resulting closed-loop systems is analytically proven herein. Two numerical simulations are presented to illustrate the effectiveness and applicability of the proposed control methods and to validate the theoretical results.

This paper investigates the guaranteed cost control problem of uncertain non-linear systems with time-varying delays via the Takagi–Sugeno fuzzy model approach. Based on the Lyapunov–Krasovskii functional theory and the linear matrix inequality technique, a state feedback controller is proposed to stabilise the non-linear systems and minimise the guaranteed cost of the closed-loop systems. Both delay-dependent and delay-independent stability criteria are derived to guarantee the asymptotic stability of closed-loop systems. Furthermore, the supplementary requirement that the time-derivative of time-varying delays must be smaller than one is released for the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the validity of the results developed in this paper.

In this paper a robust dynamic controller design algorithm for nonlinear systems with unmatched uncertainties and an input time delay is provided. For many practical systems, the existence of time delay is common in control practice. Therefore the problem of controlling such systems becomes more complex and sometimes degrades the control performance. We will propose a feasible method to deal with the problem of unmatched uncertainties and an input time delay. Based on the Lyapunov theory and the concept of functional analysis, the conditions of the robust stability of the overall closed-loop system with unmatched uncertainties and an input time delay will be derived. Finally, some examples and simulation results are provided to illustrate the versatility and performance of the proposed method.

Takagi-Sugeno (T-S) fuzzy model is a system described by a set of fuzzy if-then rules which give local linear representations of the underlying nonlinear system. Usually, a fuzzy control law is constructed by a set of controllers for each local linear representation to carry out the control of a T-S fuzzy system. While, simultaneous control addresses the stability and performance of multiple plants under a single feedback controller. In this paper, simultaneous linear control for nonlinear uncertain systems described by general T-S fuzzy model is considered. A procedure for simultaneous control of T-S fuzzy systems with parametric uncertainties is presented, by which robust reliability method is adopted to deal with uncertainties. Simultaneously linear controller design for an uncertain T-S fuzzy system is carried out by solving a problem of robust reliability based optimization, in which, both the robustness with respect to uncertainties and the control cost can be taken into account simultaneously. It is demonstrated by numerical simulation of the chaotic Lorenz system control that the presented method is effective and feasible.