Robust adaptive neural control of uncertain pure-feedback nonlinear systems

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.     

Universal stabilisation design for uncertain nonlinear system with sign-switching unknown control direction

A universal robust control approach is proposed to stabilise a class of nonlinear systems. The system contains both nonlinear dynamics uncertainty and an unknown control direction, which is the multiplier of the control term. Being different from most previous studies, the unknown control direction is allowed to switch its sign in this article. A new Nussbaum gain technique is designed and integrated with robust controller to tackle the sign-switching unknown control direction. It is proven that the proposed control approach can yield asymptotic stabilisation and guarantee the boundedness of the closed-loop signals. In addition, these results can be readily extended to tracking problems under a different assumption.     

Digital self-triggered robust control of nonlinear systems

In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.     

Robust adaptive control for nonlinear uncertain systems

A direct robust adaptive control framework for nonlinear uncertain systems with constant linearly parameterized uncertainty and nonlinear state-dependent uncertainty is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic robust stability of the closed-loop system; that is, asymptotic robust stability with respect to part of the closed-loop system states associated with the plant. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.     

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.     

Robust control of a class of uncertain nonlinear systems

This paper considers the robust control of a class of nonlinear systems with real time-varying parameter uncertainty. Interest is focused on the design of linear dynamic output feedback control and two problems are addressed. The first one is the robust stabilization and the other is the problem of robust performance in an H_∞ sense. A technique is proposed for designing stabilizing controllers for both problems by converting them into ‘scaled’ H_∞ control problems which do not involve parameter uncertainty.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers

In this paper, a novel robust adaptive control scheme for a class of uncertain nonlinear systems is proposed using disturbance observer and backstepping method.Firstly, a disturbance observer is developed using radial basis function(RBF) neural network.The parameter updated law of the RBF neural network is given for monitoring subsystem disturbance well.The robust adaptive control scheme is then presented with backstepping method based on the designed disturbance observer.Semiglobal uniform ultimate bounded...     

Distributed cooperative stabilisation of continuous-time uncertain nonlinear multi-agent systems

This paper addresses the distributed cooperative stabilisation problem of continuous-time uncertain nonlinear multi-agent systems. By approximating the uncertain dynamics using neural networks, a distributed adaptive cooperative controller, based on the state information of the neighbouring agents, is proposed. The control design is developed for any undirected connected communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case. An observer-based distributed cooperative controller is devised and a parameter dependent Riccati inequality is employed to prove stability of the overall multi-agent systems. This design is less complex than the other design methods and has a favourable decouple property between the observer design and the controller design for uncertain nonlinear multi-agent systems. For both cases, the developed controllers guarantee that all signals in the closed-loop network are uniformly ultimately bounded, and the states of all agents cooperatively converge to a small neighbourhood of origin. A comparative study is given to show the efficacy of the proposed method.     

不确定串联非线性系统H∞鲁棒自适应控制

针对一类含有未知参数和干扰的非最小相位串联非线性系统,结合H∞控制和自适应控制方法并利用李雅普诺夫函数递推设计方法设计了状态反馈H∞自适应控制器,避免了求解Hamilton-Jacobi-Isaacs不等式设计控制器的困难.该控制器不仅保证闭环系统ISS(input-to-state)稳定,而且使得系统对于所有允许的参数不确定从干扰输入到可控输出的 L 2增益不大于给定的值.最后,给出了一个仿真例子,仿真结果充分表明了所设计的控制器的可行性和有效性.     

Simplified robust control for nonlinear uncertain systems: a method of projection and online estimation

Robust control based on an online estimation of uncertainty is presented for a class of nonlinear uncertain systems. The estimation is done via a robust observer after the uncertainty vector is projected onto a one-dimensional subspace. The proposed combination of dynamics projection and online estimation is to relax the knowledge about the size of uncertainty and required in the robust control design, to make robust control less conservative while being effective, and to ensure robust stability without undue complexity.     

Model reference adaptive robust fuzzy control for ship steering autopilot with uncertain nonlinear systems

A novel model reference adaptive robust fuzzy control algorithm is presented for ship steering autopilot, which is an uncertain nonlinear system. In the proposed algorithm, fuzzy logic systems have been used to approximate lumped unknown function in the ship steering systems and the adaptive mechanism with minimal learning parameter, i.e. only one parameter, has been achieved by use of Lyapunov approach. The proposed methodology is verified using the simulation mode of the Dalian Maritime University's ocean-going training ship named Yulong. It is shown that the proposed algorithm guarantees that the ship steering autopilot system is asymptotically stable and its tracking error can approach to zero.     

Adaptive fault diagnosis and fault-tolerant control of MIMO nonlinear uncertain systems

This article presents an integrated fault diagnosis and fault-tolerant control (FTC) methodology for a class of nonlinear multi-input–multi-output systems. Based on the fault information obtained during the diagnostic procedure, an FTC component is designed to compensate for the effect of faults. In the presence of a fault, a baseline controller guarantees the boundedness of all the system signals until the fault is detected. After fault detection and then again after isolation, the controller is reconfigured to improve the tracking performance using online fault diagnostic information. Under certain assumptions, the stability and tracking performances of the closed-loop system are rigorously investigated. It is shown that the system signals always remain bounded and the output tracking error converges to a neighbourhood of the origin of the state space.     

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.     

一类不确定参数系统鲁棒稳定界的解析分析与应用

研究一类具有不确定参数系统鲁棒性稳定界的解析分析方法.在定义了鲁棒稳定界的基础上,证明了鲁棒稳定界只与标称系统的最小特征值有关.利用这一结论不仅可以方便地分析多项式的稳定性,而且可以根据系统的不确定性设计闭环控制系统的期望极点,并进行极点配置.     

Output tracking control of uncertain nonlinear second-order systems

The solution of a tracking problem for a secondorder nonlinear system with uncertain dynamics and incomplete state measurement is obtained by means of a procedure directly inspired by the solution of the classical minimum-time optimal control problem. Two different types of uncertainty are considered in the paper: in the first case a constant bound on the uncertain dynamics is assumed to be known; in the second case, the bound is a function of both the measurable and the unmeasurable state variable of the system. In both cases, the possibility of applying the proposed control algorithms is proved to be determined by a proper choice of the control signal features. The resulting system is characterized by a suitable feedback switching logic and the convergence of the system trajectory to the desired one (or to a δ-vicinity of this latter) is proved also in the uncertain case.     

Robust adaptive fuzzy controller for non‐affine nonlinear systems with dynamic rule activation

This paper describes the design of a robust adaptive fuzzy controller for an uncertain single‐input single‐output nonlinear dynamical systems. While most recent results on fuzzy controllers considers affine systems with fixed rule‐base fuzzy systems, we propose a control scheme for non‐affine nonlinear systems and a dynamic fuzzy rule activation scheme in which an appropriate number of the fuzzy rules are chosen on‐line. By using the proposed scheme, we can reduce the computation time, storage space, and dynamic order of the adaptive fuzzy system without significant performance degradation. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as for all other signals in the closed loop. No a priori knowledge of an upper bounds on the uncertainties is required. The theoretical results are illustrated through a simulation example. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

反步方法原理及在非线性鲁棒控制中的应用

介绍了非线性控制中的反步(backstepping)设计方法的基本原理、构成方法及其拓展,综述了该方法在非线性鲁棒控制中的应用,提出并分析了若干关键性问题.     

Design of ‘softer’ robust nonlinear control laws

We show that the Lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily ‘hard’ control laws having undesirable high-gain properties. We present a new Lyapunov function and use it to design ‘softer’ control laws which exhibit the high-gain properties to a much lesser extent. We show that the ‘soft’ designs eliminate the chattering exhibited by the ‘hard’ designs and achieve the same or better performance with less control effort.