Adaptive sliding mode control for uncertain Euler–Lagrange systems with input saturation

In this paper, the tracking control problem of uncertain Euler–Lagrange systems under control input saturation is studied. To handle system uncertainties, a leakage-type (LT) adaptive law is introduced to update the control gains to approach the disturbance variations without knowing the uncertainty upper bound a priori. In addition, an auxiliary dynamics is designed to deal with the saturation nonlinearity by introducing the auxiliary variables in the controller design. Lyapunov analysis verifies that based on the proposed method, the tracking error will be asymptotically bounded by a neighborhood around the origin. To demonstrate the proposed method, simulations are finally carried out on a two-link robot manipulator. Simulation results show that in the presence of actuator saturation, the proposed method induces less chattering signal in the control input compared to conventional sliding mode controllers.     

Disturbance observer-based fixed-time leader-following consensus control for multiple Euler–Lagrange systems: A non-singular terminal sliding mode scheme

This paper focuses on the fixed-time leader-following consensus problem for multiple Euler–Lagrange (EL) systems via non-singular terminal sliding mode control under a directed graph. Firstly, for each EL system, a local fixed-time disturbance observer is introduced to estimate the compound disturbance (including uncertain parameters and external disturbances) within a fixed time under the assumption that the disturbance is bounded. Next, a distributed fixed-time observer is designed to estimate the leader’s position and velocity, and the consensus problem is transformed into a local tracking problem by introducing such an observer. On the basis of the two types of observers designed, a novel non-singular terminal sliding surface is proposed to guarantee that the tracking errors on the sliding surface converge to zero within a fixed time. Furthermore, the presented control algorithm also ensures the fixed-time reachability of the sliding surface, while avoiding the singularity problem. Finally, the effectiveness of the proposed observers and control protocol is further verified by a numerical simulation.     

Fractional-order adaptive neuro-fuzzy sliding mode H∞ control for fuzzy singularly perturbed systems

This paper investigates the fractional-order (FO) adaptive neuro-fuzzy sliding mode control issue for a class of fuzzy singularly perturbed systems subject to the matched uncertainties and external disturbances. Firstly, a novel FO fuzzy sliding mode surface is presented. Secondly, by introducing an appropriate ε-dependent Lyapunov function, some H_∞ performance analysis criteria are given, which also ensure the robust stability of the sliding mode dynamics. Furthermore, a hybrid neuro-fuzzy network system (HNFNS) is introduced to estimate the matched uncertainty. Moreover, an FO adaptive fuzzy sliding mode controller is designed to drive the state trajectories of fuzzy singularly perturbed systems to the predefined FO sliding mode surface within a finite-time. Finally, two verification examples are presented to illustrate the validity of the proposed FO control scheme.     

Model transformation based sliding mode control of discrete-time two-dimensional Fornasini–Marchesini systems

This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time.     

Tracking control of a piezo-hydraulic actuator using input–output linearization and a Cascaded Extended Kalman Filter structure

In this paper, an innovative piezo-hydraulic actuator (PHA) is considered that is intended to realize a fully variable valve control in camless combustion engines. A nonlinear model of the hydraulic system part is presented along with linear models of the remaining system parts. Accurate tracking of desired valve trajectories as well as soft landing despite disturbance forces and measurement noise is achieved using a combined control strategy. It consists of an input–output linearization of the nonlinear part as well as feedforward and linear quadratic integral (LQI) feedback control of the linear system part. Given measurements of the valve spool and engine valve positions, a Cascaded Extended Kalman Filter (CEKF) structure provides estimates for the immeasurable states. Simulation results confirm the effectiveness of the proposed approach.     

SmartRolling: A human–machine interface for wheelchair control using EEG and smart sensing techniques

Smart wheelchairs based on brain–computer interface (BCI) have been widely utilized recently to address certain mobility problems for people with disability. In this paper, we present SmartRolling, an intuitive human–machine interaction approach for the direct control of robotic wheelchair that jointly leverages EEG signals and motion sensing techniques. Specifically, SmartRolling offers two wheelchair-actuation modes for users with different physical conditions: (1) head motion only — people who are severely disabled but able to do basic tasks using eyes and head, and (2) head and hands motion — in addition to type 1, people who can use functioning hands/arms for extra tasks. The system issues operation commands by recognizing different EEG patterns elicited by motor execution (ME) tasks including eye blink, jaw clench, and fist open/close, while at the same time estimates users’ steering intentions based on their facing direction by leveraging inertial measurements and computer vision techniques. The experiment results demonstrate that the proposed system is robust and effective to meets the individual’s needs and has great potential to promote better health.     

H∞ tracking control for a class of asynchronous switched nonlinear systems with uncertain input delay

This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.     

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

In this paper, a sliding-mode approach is proposed for exponential H_∞ synchronization problem of a class of master–slave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov–Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law, which include the master–slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H_∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H_∞ synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.     

Output feedback robust H∞ control for spacecraft rendezvous system subject to input saturation: A gain scheduled approach

In this paper, the problem of output feedback robust H_∞ control for spacecraft rendezvous system with parameter uncertainties, disturbances and input saturation is investigated. Firstly, a full-order state observer is designed to reconstruct the full state information, whose gain matrix can be obtained by solving the linear matrix inequality (LMI). Subsequently, by combining the parametric Riccati equation approach and gain scheduled technique, an observer-based robust output feedback gain scheduled control scheme is proposed, which can make full use of the limited control capacity and improve the control performance by scheduling the control gain parameter increasingly. Rigorous stability analyses are shown that the designed discrete gain scheduled controller has faster convergence performance and better robustness than static gain controller. Finally, the performance and advantage of the proposed gain scheduled control scheme are demonstrated by numerical simulation.     

DSP-based implementation of fast terminal synergetic control for a DC–DC Buck converter

Finite time convergence based on robust synergetic control (SC) theory and terminal attractor techniques is investigated. To this end a fast terminal synergetic control law (FTSC) is applied to drive a DC–DC Buck converter via simulation and through a dSpace based experimental setup to validate the approach. As robust as sliding mode control, the synergetic approach used is chattering free and provides rapid convergence. Efficacy of the proposed fast terminal synergetic controller is tested for step load change and output voltage variation and results compared to classical synergetic and PI control. Experimental validation using dSpace DS1104 confirms the results obtained in simulation showing the soundness of this approach compared to synergetic and PI controllers.     

L’ Hopital’S rule-Based adaptive dynamic surface control for a class of strict-Feedback systems with unknown parameters

In this paper, a L’ Hopital’s rule-based adaptive dynamic surface control (L-ADSC) scheme is developed for a class of strict-feedback systems with unknown parameters using backstepping technique. The L-ADSC-derived backstepping technique is deployed to remove differentiation of complex virtual controller, thereby efficiently avoiding ”exlosion of complexity”. The L’ Hopital’s Rule is resorted to tackle singularity problem within controller synthesis. As a consequence, the proposed L-ADSC scheme guarantees that all signals of the closed-loop control system are semi-globally uniformly ultimately bounded. Simulation results show remarkable effectiveness.     

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

To perform repetitive tasks, this paper proposes an adaptive boundary iterative learning control (ILC) scheme for a two-link rigid–flexible manipulator with parametric uncertainties. Using Hamilton?s principle, the coupled ordinary differential equation and partial differential equation (ODE–PDE) dynamic model of the system is established. In order to drive the joints to follow desired trajectory and eliminate deformation of flexible beam simultaneously, boundary control strategy is added based on the conventional joints torque control. The adaptive iterative learning algorithm for boundary control scheme includes a proportional-derivative (PD) feedback structure and an iterative term. This novel controller is designed to deal with the unmodeled dynamics and other unknown external disturbances. Numerical simulations are provided to verify the performance of proposed controller in MATLAB.     

Legendre wavelet operational matrix of derivative for optimal control in a convective–diffusive fluid problem

We consider the problem of controlling the model of one-dimensional fluid flow through a soil packed tube in which a contaminant is initially distributed. A fluid is pumped through a tube to remove the contaminant. The control problem is to determine the optimal convective velocity due to the fluid being pumped by minimizing a given performance criterion. The performance criterion is chosen to be a combination of the total contaminant at the final time and the cost of the control. The set of orthogonal Fourier trigonometry series is used as a basis function of the Galerkin procedure to lump the distributed parameter system. A Legendre wavelet operational matrix of derivative is used to approximate the control and modal state variables. The main characteristics of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The effectiveness of the proposed approach is illustrated numerically and the results are quite satisfactory.     

Switching PDC control for discrete-time T–S fuzzy system: A membership function ranking approach

In this paper, a new type of switched parallel distributed compensation (PDC) controller is presented, in which a novel switching scheme, namely, membership function ranking (MFR) scheme is proposed. The MFR scheme can be viewed as an improvement and extension of previous results named largest membership function (LMF) scheme concerned with piece-wise quadratic Lyapunov function (PQLF) approach, since it provides a denser subdivision of normalized membership function space and therefore essentially yields less conservative results. Moreover, it shows that MFR scheme covers LMF scheme as a particular case. Based on MFR scheme, a family of _?∞${\mathbf{?}}_{\infty }$ controllers and a switching scheme is designed to ensure the closed-loop system asymptotically stable and has a required _?∞${\mathbf{?}}_{\infty }$ performance. A design example is presented to illustrate the advantages of MFR scheme.     

The approximation of the T–S fuzzy model for a class of nonlinear singular system with derivative of input

In this paper, the approximation problem of T–S fuzzy linear singular system for a class of nonlinear singular system with derivative of input is considered and the nonlinear singular system has impulses. Consider a numerical example and a two-wheel drive robot, the T–S fuzzy singular systems are calculated for original system with derivative of input. According to solvability and steps of solving of the two examples, the results are extended to more generally nonlinear singular system with derivative of input. The theorem and algorithm that are given if input-state system is bounded impulse-free item and separable impulse item, it can be approximated by T–S fuzzy singular system with arbitrary accuracy. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of approximation.     

Adaptive actuator fault-tolerant control for a three-dimensional Euler–Bernoulli beam with output constraints and uncertain end load

This paper studied an adaptive actuator fault-tolerant control scheme for the flexible Euler–Bernoulli beam in the three-dimensional space with output constraints and uncertain end load. The dynamic models are represented by partial differential equations (PDEs) and ordinary differential equations (ODEs). When part of the actuator fails, an adaptive control scheme is designed to regulate the vibration and stabilize the flexible three-dimensional Euler–Bernoulli beam. Barrier Lyapunov Function (BLF) is adopted to realize output constraints of the system. Adaptive control law with projection mapping operator is designed to compensate for the end load which is uncertain and bounded. The goal of this paper is to suppress the displacement of the flexible three-dimensional Euler–Bernoulli beam which can be constrained in given bounds under actuator fault and uncertain, bounded end load. It is confirmed that the proposed control scheme can deal with the vibration, adaptive actuator fault-tolerant control, uncertain and bounded end load and output constraints of the system simultaneously. Finally, numerical simulations illustrate the effectiveness and feasibility of the method.