Output feedback controller for hysteretic time-delayed MIMO nonlinear systems

In this paper, an H ^?? output feedback controller is developed for a class of time-delayed MIMO nonlinear systems, containing backlash as an input nonlinearity. Particularly, a state observer is proposed to estimate unmeasurable states. The control law can be divided into two elements: An adaptive interval type-2 fuzzy part which approximates the uncertain model. The second part is an H ^??-based controller, which attenuates the effects of external disturbances and approximation errors to a prescribed level. Furthermore, the Lyapunov theorem is used to prove stability of proposed controller and its robustness to external disturbance, hysteresis input nonlinearity, and time varying time-delay. As an example, the designed controller is applied to address the tracking problem of 2-DOF robotic manipulator. Simulation results not only verify the robust properties but also in comparison with an existing method reveal the ability of the proposed controller to exclude the effects of unknown time varying time-delays and hysteresis input nonlinearity.     

Event-triggered output-feedback tracking of a class of nonlinear systems with unknown time delays

A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.

     

Finite-time synchronization control for a class of perturbed nonlinear systems with fixed convergence time and hysteresis quantizer: applied to Genesio–Tesi chaotic system

In the present article, a terminal sliding mode control strategy has been proposed in order to address the synchronization problem for a class of perturbed nonlinear systems with fixed convergence time and input quantization. The proposed protocol guarantees the fixed-time convergence of the sliding manifold to the origin, which means that the convergence time of the proposed sliding manifold does not change on the variations of initial values, different from typical control methods. Here, the hysteresis quantizer, as a specific type of quantizer with nonlinear sector-bounded, is applied in order to quantize the input signal. The proposed quantized control scheme vigorously prevents the potential adverse chattering phenomenon which is experienced in the common quantization methods. The proposed controller does not need the limiting criteria related to considered parameters of quantization compared to recent control approaches. Finally, the designed controller is implemented on the perturbed Genesio–Tesi (G–T) chaotic systems to verify effectiveness and strength of the proposed method.

     

Controller design for fractional-order interconnected systems with unmodeled dynamics

This paper focuses on the output feedback tracking control for fractional-order interconnected systems with unmodeled dynamics. The reduced order high gain K-filters are designed to construct the estimation of the unavailable system state. Unmodeled dynamics is extended to the general fractional-order dynamical systems for the first time which is characterized by introducing a dynamical signal r(t). An adaptive output feedback controller is established using the fractional-order Lyapunov methods and proposed by novel dynamic surface control strategy. Then, it is confirmed that the considered system is semi-globally bounded stable and the errors between outputs and the desired trajectories can concentrate to a small neighborhood of the origin. Finally, a simulation example is introduced to demonstrate the correctness of the supplied controller.

     

控制存在时滞的线性系统主动控制的滑移模态方法

本文研究控制存在时滞的线性系统的滑模控制方法。在控制时滞量为采样周期的整数倍和非整数倍的两种情况下，通过采用零阶保持器，将包含时滞的连续系统转化为形式上不包含时滞的标准离散线性系统，然后分别进行切换函数和控制律的设计。所得出的切换面和控制律表达式中，除了含有当前的状态反馈外，还包含有前若干步控制项的线形组合。最后对某三自由度结构模型进行仿真计算，验证了所给控制方法的有效性。     

T–S fuzzy control design for a class of nonlinear networked control systems

This paper is devoted to controlling a class of nonlinear systems over a communication network in the presence of packet transmission delays, packet losses, quantization errors, and sampling-related phenomena. Specifically, based on the Takagi–Sugeno (T–S) fuzzy approach, this paper presents a way of designing a quantized controller that allows all the states of nonlinear NCSs to converge exponentially to a bounded ellipsoid. In particular, this paper provides a method capable of exploiting fully the time-varying delay term d(t), induced by Jensen inequality, for nonlinear NCSs.     

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

This paper is concerned with the stabilization problem of uncertain chaotic systems with input nonlinearity. The slope parameters of this nonlinearity are unmeasured. A new sliding function is designed, then an adaptive sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time and finite-time reachability is theoretically proved. Using a virtual state feedback control technique, sufficient condition for the asymptotic stability of sliding mode dynamics is derived via linear matrix inequality (LMI). Then the results can be extended to uncertain chaotic systems with disturbances and adaptive sliding mode H _∞ controllers are designed. Finally, a simulation example is presented to show the validity and advantage of the proposed method.     

Adaptive neural network-based saturated control of robotic exoskeletons

In this paper, novel adaptive neural network (NN) controllers with input saturation are presented for n-link robotic exoskeletons. The controllers consist of a state feedback controller and an output feedback controller. Through utilizing auxiliary dynamics, the controllers provide a new framework for input saturated control of these robotic systems which can feature the global stability for state feedback control. To compensate for the unknown dynamics of the system, adaptive schemes based on NNs are exploited. Furthermore, adaptive robust terms are utilized to deal with unknown external disturbances. Stability studies show that the closed-loop system is globally uniformly ultimately bounded (UUB) with the state feedback controller, where the global property of the NN-based controller is achieved exploiting a smooth switching function and a robust control term. Also, the system is semi-globally UUB with the output feedback controller. Effectiveness of the controllers is validated by simulations and experimental tests.     

{L}_{2}-gain analysis and output feedback control for continuous-time switched systems with actuator saturation

This paper is concerned with the problem of \(L_2\) -gain analysis for a class of continuous-time switched systems with actuator saturation. Different from the existing results using the state-dependent switching approach, a linear parameter-varying output feedback controller with the time-dependent switching mechanism is designed such that the overall system is exponentially stable and with disturbance tolerance capacity and \(L_2\) gain. Further, the proposed controller is insured by introducing the slack matrices to have less conservatism, which maximizes the ellipsoid where the state trajectories starting from the origin will remain. Sufficient conditions for the existence of the switching and output feedback control law are derived in terms of linear matrix inequalities. Finally, a practical example is given to show the effectiveness of the proposed method.     

H ∞ control for uncertain switched nonlinear singular systems with time delay

This paper investigates the H _∞ control problem for a class of uncertain switched nonlinear singular systems with time delay. By appropriately introducing some auxiliary variables and using a Lyapunov–Metzler inequality approach, some sufficient conditions for finding a suitable state-dependent switching law guaranteeing the switched system meets the desired control objective are firstly given. Then, these results are extended to construct a state feedback controller. Based on the derived results, the existence conditions of an observer-based output feedback H _∞ controller for the switched system are provided and formulated by using a combination of a linear matrix inequality (LMI) approach and a linear search algorithm. Finally, some numerical examples are performed to show the effectiveness and superiority of the proposed methods.     

Robust stabilization and l 2-gain control of uncertain discrete-time constrained piecewise-affine systems

In this paper, the robust stabilization and l ₂ gain control are investigated for a class of uncertain discrete-time piecewise-affine systems with input saturation and state constraints. By introducing some auxiliary feedback matrices, the LMI-based local stabilization condition is firstly proposed, where the designed controller can be saturated, and meanwhile, the domain of attraction is well estimated. Under energy bounded disturbance, the disturbance tolerance condition is proposed under which all trajectories starting from the origin will remain inside a bounded state region, then the l ₂-gain controller is designed in the restricted region. Finally, numerical examples and simulations illustrate the effectiveness and the reduced conservativeness of the proposed results.     

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.     

Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems

The output-feedback control problem of a class of uncertain SISO nonlinear systems is investigated based on an indirect adaptive fuzzy approach. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. Compared with the existing results in the observer design, the main advantages of the proposed adaptive fuzzy output-feedback control approach are as follows: (1) It does not require to assume that the sign of the control gain coefficient is known and Nussbaum-gain technique is utilized to control the nonlinear systems with both the unknown control direction and the unmeasured states; (2) The observer in this paper is designed for the states rather than the tracking errors, then it is convenient to compute; (3) The controller singularity problem is perfectly avoided. The stability of the closed-loop system is analyzed by using Lyapunov method. A simulation example is given to verify the feasibility of the proposed approach.     

Truncated predictor stabilization control for interconnected nonlinear systems with time-varying input delay

This paper deals with control design for interconnected nonlinear systems with time-varying input delay. Based on the truncated prediction of the system state over the delay period, the state feedback control law is constructed. In the framework of the Lyapunov–Krasovskii function, the stability equations of closed-loop system under state feedback law are established, and the feasibility of the controller is transformed into the problem of establishing a set of linear matrix inequality (LMI) conditions. Based on the Lyapunov stability theorem, it is proved that the closed-loop system is asymptotically stable. Finally, a simulation example is provided to demonstrate the effectiveness of the control scheme.

     

Ride quality analysis of a tracked vehicle suspension with a preview control

The feasibility of a preview control is examined for tracked vehicle’s suspension systems to improve the performance of tracked vehicle systems. Numerical results are compared with LQ, robust H_∞, reference model tracking and hybrid preview control methods. The ride quality analysis is performed based on the vertical acceleration at the driver’s position. On the simulations, it is proven that the hybrid preview controller is the most efficient and practical method.     

Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot

In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i)?the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii)?the problem of ??explosion of complexity?? is avoided.     

Guaranteed cost nonlinear sampled-data control: applications to a class of chaotic systems

Nonlinear Dynamics - This paper addresses the guaranteed cost sampled-data controller synthesis and analysis problems with application to nonlinear chaotic systems. A linear parameter-varying (LPV)...     

Decentralized direct adaptive output feedback fuzzy H ∞ tracking design of large-scale nonaffine nonlinear systems

A novel H _∞ tracking-based decentralized direct adaptive output feedback fuzzy controller is developed for a class of interconnected nonaffine uncertain nonlinear systems in this paper. By virtue of the proper filtering of the observation error dynamics to assure its strictly positive realness, the observer-based decentralized direct adaptive fuzzy control (DAFC) scheme is presented for a class of large-scale nonaffine nonlinear systems by the combination of H _∞ tracking technique, implicit function theorem, a state observer and a fuzzy inference system. The output feedback and adaptation mechanisms for each subsystem depend upon local measurements not only to achieve asymptotical tracking of a reference trajectory but to guarantee arbitrary small attenuation level of the mismatched errors and external disturbances on the tracking error. Simulation results confirm the effectiveness of the proposed decentralized output feedback scheme.     

Improving the performance of UDE-based controller using a new filter design

Robust control of uncertain systems has been a field of active research and the technique of uncertainty and disturbance estimator (UDE) has proved itself as a viable tool in the design of a robust control strategy for systems having uncertainties and acted upon by disturbances. Though the technique is quite efficient for ensuring robustness under slow-varying disturbances, the presence of steady-state tracking and estimation errors cannot be ruled out for fast-varying or sinusoidal disturbances. To address this issue, a new form of filter in UDE-based controller is proposed in this work and it is shown that the errors can be kept within acceptable limits by means of appropriate choice of the design parameter \(\alpha \) . Closed-loop stability and simulation results for wing-rock motion control problem employing an UDE-based controller using the new filter are carried out to demonstrate its efficacy against fast-varying uncertainties and disturbances.     

连续时间线性约束LQ控制问题的时程精细积分方法

本文基于连续时间线性约束LQ控制问题,给出时段的消元公式。由于消元过程与消元次序无关,故可在此过程中引入2N类高精度时程积分方法,求出Riccati方程后,对状态向量进一步采用时程精细积分法,可确定系统非常精确的状态向量,该方法不仅保证了系统的计算精度,而且有很好的数值稳定性,数值例题说明了本文方法的有效性。