A globally convergent direct adaptive pole‐placement controller for nonminimum phase systems with relaxed excitation assumptions

In this paper, we propose the first solution to the long‐standing problem of designing a globally convergent direct adaptive pole‐placement controller for linear, time‐invariant discrete‐time systems with arbitrary zeros that does not rely on persistency of excitation assumptions. As is well known, the main difficulty of this design is that it involves the estimation of parameters that enter nonlinearly in the regression model. This problem can be overcome introducing an overparameterized representation of the system, which imposes very strict persistency of excitation conditions to prove the parameter convergence. The latter is avoided here using a new version of the dynamic regressor extension and mixing parameter estimator recently proposed in the literature. The main feature of this estimator is that it generates, out of an m‐dimensional vector regression, m scalar regression models. This property allows us to estimate only the controller parameters of interest for the adaptive implementation, whose convergence is ensured under assumptions that are strictly weaker than the classical persistency of excitation requirement. Simulation results that illustrate the performance of the proposed scheme are also presented.     

Decentralized adaptive control for a class of large‐scale systems with multiple delays in the interconnections

In this paper, we consider the decentralized stabilization problem of a class of large‐scale systems subject to uncertain parameters and multiple time‐varying delays in the interconnections and non‐linear inputs. The interconnection matrices are subject to perturbations whose bounds are unknown. Decentralized memoryless adaptive controllers are synthesized within an LMI framework to guarantee that the state trajectories of the large‐scale system are uniformly exponentially convergent towards a ball with any prespecified exponential convergence rate. The problem is formulated as an optimization problem with LMI constraints. Finally, an example is included to illustrate the results developed in this paper. Copyright © 2004 John Wiley & Sons, Ltd.     

Observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances

This paper studies the problem of observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances. Based on mean value theorem and convex combination method, a adaptive neural observer with virtual control coefficients is designed to estimate the systems states. Then, by using funnel Lyapunov function and backstepping method, a finite time control scheme is designed in the presence of disturbances and actuator faults. The stability analysis proves that tracking errors can converge to the prescribed performance bound in a finite time and all signals are uniformly ultimately bounded. Finally, simulation results verify efficiency of the studied approach.     

Finite‐time synchronization and adaptive synchronization of memristive recurrent neural networks with delays

This paper solves the finite‐time synchronization and adaptive synchronization problems of drive‐response memristive recurrent neural networks with delays under two control methods. First, the state‐feedback control rule containing delays and the adaptive control rule are designed for realizing synchronization of drive‐response memristive recurrent neural networks in finite time. Then, on the basis of the Lyapunov stability theory, many algebraic sufficient conditions are obtained to guarantee finite‐time synchronization and adaptive synchronization of drive‐response memristive recurrent neural networks via two control methods, which are easily verified. In addition, the estimation of the upper bounds of the settling time of finite‐time synchronization is obtained. Lastly, to illustrate the effectiveness of the obtained theoretical results, two examples are given.     

Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

This paper investigates the global adaptive finite‐time stabilization of a class of switched nonlinear systems, whose subsystems are all in p (p≤1) normal form with unknown control coefficients and parametric uncertainties. The restrictions on the power orders and the nonlinear perturbations are relaxed. By using the parameter separation technique, the uncertain parameters are separated from nonlinear functions. A systematic design procedure for a common state feedback controller and a switching adaptive law is presented by employing the backstepping methodology. It is proved that the closed‐loop system is finite‐time stable under arbitrary switching by utilizing the common Lyapunov function. Finally, with the application to finite‐time control of chemical reactor systems, the effectiveness of the proposed method is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

模型不确定的下肢康复机器人轨迹跟踪自适应控制

为了实现康复训练过程中高精度的轨迹跟踪控制,针对下肢康复机器人的模型参数和外界干扰等不确定性因素对其轨迹跟踪造成严重影响,提出一种模型不确定的下肢康复机器人轨迹跟踪自适应控制方法。根据所提方案,设计了相应的轨迹跟踪自适应控制器;并进行了轨迹跟踪控制仿真实验对比分析,结果表明,计算力矩控制方法在系统模型不确定时,膝关节的最大角度跟踪误差高达11.3°,髋关节最大稳态误差4.6°;而轨迹跟踪自适应控制方法在模型不确定的情况下,髋关节和膝关节的角度跟踪稳态误差均收敛于零;轨迹跟踪自适应控制方法可以显著提高下肢康复机器人轨迹跟踪的精度。     

Finite time adaptive fault-tolerant controller based on neural networks for switched stochastic nonlinear systems with actuator failures and disturbance

This article investigates the novel finite time adaptive neural fault-tolerant controller (FTC) for strict-feedback switched stochastic systems under arbitrary switching signals and takes into actuator failures including loss of effectiveness faults and bias faults consideration concurrently. Neural networks are utilized to approximate the unknown external disturbance and internal dynamics. On the basis of Itô differential equation and backstepping technique, an adaptive neural finite time FTC method is put forward. It is attested that the closed-loop systems are semiglobal practical finite time stable in probability and the tracking effects are great. Finally, to further demonstrate the high efficiency of proposed control method, two simulation examples are given.     

A robust solution to the admissibility problem in indirect adaptive control without persistency of excitation

This paper deals with adaptive control based on explicit identification. The problem of admissibility of the identified model is solved without requiring persistently exciting inputs. This solution is robust with respect to process variations, unstructured disturbances and model order errors. Finally, this approach is not restricted to a particular class of control laws.     

Adaptive control of complex systems with unknown dynamics and input constraint: Applied to a chaotic elastic beam

Owing to the limitations of system identification and modeling techniques, there is usually some unknown dynamics in the mathematical models of the complex systems. In addition, external perturbations can affect the chaotic systems' responses and may destroy the desired control purpose. Consideration of such uncertain dynamics and external fluctuations in control applications is important in research and practice. On the other hand, because of the limited operation of control actuators, most of the practical implementations of control systems are forced with some input constraints. Therefore, this paper investigates the control problem of uncertain autonomous and/or nonautonomous complex chaotic systems in the presence of input saturation. The upper bounds of the unknown dynamics, modeling uncertainties, external perturbations, and the parameters of the saturation function are assumed to be unknown in advance. To make a fast control response, an adaptive nonsingular terminal variable structure controller is proposed to assure the finite‐time stability of the equilibrium states. Rigorous stability analysis is performed to prove the correct performance of the designed control algorithm. Numerical simulations on the unified system and a chaotic elastic beam model are developed to demonstrate the usefulness of the introduced adaptive control strategy. It is worth to notice that the derived adaptive nonsmooth sliding mode approach is general and it can be easily adopted for controlling of a wide class of uncertain MIMO nonlinear systems.     

On the asymptotic property analysis for a class of adaptive control systems with σ‐modification

With the effect of σ‐modification in adaptive control systems, robustness is achieved at the potential expense of destroying some of the convergence properties. This paper proposes a qualitative analysis method for the situations where the σ‐modification may lead to perfect tracking and also, given the prior knowledge of system parameters, may allow proper modification of the adaptive algorithm. The applicability of the proposed analysis method is illustrated by two examples, where the system control gains that lead to global asymptotic convergence are given explicitly. Further, simulations are performed to verify the qualitative analysis results. Copyright © 2012 John Wiley & Sons, Ltd.