Fuzzy sliding mode control design of Markovian jump systems with time-varying delay

This paper studies the robust stochastic stabilization problem for a class of fuzzy Markovian jump systems with time-varying delay and external disturbances via sliding mode control scheme. Based on the equivalent-input-disturbance (EID) approach, an online disturbance estimator is implemented to reject the unknown disturbance effect on the considered system. Specifically, to obtain exact EID estimation Luenberger fuzzy state observer and a low-pass filter incorporated to the closed-loop system. Moreover, novel fuzzy EID-based sliding mode control law is constructed to ensure the stability of the closed-loop system with satisfactory disturbance rejection performance. By employing Lyapunov stability theory and some integral inequalities, a new set of delay-dependent robust stability conditions is derived in terms of linear matrix inequalities (LMIs). The resulting LMI is used to find the gains of the state-feedback controller and the state observer a for the resulting closed-loop system. At last, numerical simulations based on the single-link arm robot model are provided to illustrate the proposed design technique.     

High-gain fractional disturbance observer control of uncertain dynamical systems

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs. The proposed fractional PI-like structure yields precise conditions for feedback gain tuning. Remarkably, the resulting controller rejects non-differentiable disturbances with a smooth controller, guaranteeing robustness, an outstanding features for tracking tasks, under a prescribed practical stability regimen. A comparison to a fractional sliding mode observer is conducted via simulations to highlight the reliability of the proposed scheme.     

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.     

Model predictive tracking control with disturbance compensation for wheeled mobile robots in an environment with obstacles

This paper explores the trajectory tracking control problem for a wheeled mobile robot (WMR) in an environment with obstacles and unknown disturbances. A fixed-time extended state observer is presented, which is utilized to estimate unknown disturbances and improve the convergence speed of estimation errors. By introducing the obstacle avoidance cost, a model predictive controller with disturbance compensation is proposed to guarantee desired tracking performance in the presence of obstacles. The proposed method is analyzed for recursive feasibility and closed-loop system stability subject to unknown disturbances and obstacles. Finally, both simulation and experiment are conducted to express the satisfactory tracking effect of the developed approach.     

Additive-state-decomposition-based model predictive tracking control for PMSM servo system with multiple disturbances

This paper presents an additive-state-decomposition-based model predictive tracking control and disturbance rejection method for a permanent magnet synchronous motor (PMSM) servo system subject to unknown parameter perturbations, unmodeled dynamics, and time-varying load torque. The basic idea of this method is to equivalently decompose the original system into a primary system for handling the tracking control subproblem and a secondary system for dealing with the robust stabilization subproblem. A model predictive controller is designed for the primary system to achieve high-accuracy tracking of the reference speed. As for the secondary system, a novel high-order generalized extended state observer (HGESO) is constructed to estimate the multiple disturbances simultaneously, and a state feedback control law incorporating a disturbance compensator is developed to eliminate the adverse effect of the multiple disturbances on the system output. By combining the control inputs of the two subsystems together, the control objectives of the original system can be achieved. Both the stability criterion and design procedure of the closed-loop control system are developed. Finally, hardware-in-the-loop-based comparative experiments are conducted to demonstrate that the proposed method effectively suppresses the influence of the multiple disturbances on motor speed tracking accuracy and that the control system has both satisfactory dynamic performance and robustness.     

Robust tube-based MPC with enlarging the region of attraction for tracking of switched systems

This paper addresses a robust tube based model predictive control (RTBMPC) strategy for tracking problem of piecewise affine (PWA) linear systems. The core idea of the RTBMPC strategy is to robustly control an uncertain system through its nominal system and an additional feedback term which rejects a bounded additive disturbance. In tracking problem, RTBMPC strategy should be capable to steer the uncertain system to a given setpoint fulfilling the constraints. But if the setpoint changes, the controller may not success due to the loss of feasibility of the optimization problem. This paper employs several novel features to deal with tracking problem. First, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function. Then, the feasibility region is enlarged for given setpoint without increasing the prediction horizon by changing the terminal constraint set at different steps of RTBMPC problem solving. Simulation examples, including two different case studies, are presented to illustrate the effectiveness of the proposed RTBMPC.     

一类线性切换系统的鲁棒跟踪控制

文章研究了线性切换系统的鲁棒跟踪控制,并提出可解性的充分条件。设计切换控制规则使得切换线性系统满足加权H∞参考模型,并采用平均驻留时间法和Lyapunov函数来处理稳定性分析和控制器设计。通过使用线性矩阵不等式,控制器设计问题可以得到很好的解决。     

Design of PID controller based on a self-adaptive state-space predictive functional control using extremal optimization method

In proportional-integral-derivative (PID) controller design, obtaining high stability and desired closed-loop response are of great importance for system engineers. Most existing methodologies, which have validated their excellent control performance on the accurate mathematical model, face significant difficulties in the unavoidable model mismatches and disturbance. To overcome these drawbacks, this paper proposes a self-adaptive state-space predictive functional control (APFC) based on extremal optimization method to design PID controller called EO-APFC-PID, wherein, the self-adaptive means, i.e., a forgetting factor recursive least squares (FFRLS) mechanism is embedded into state-space predictive functional control (PFC), and the proposed EO is exploited to alleviate the challenging problem that the elements in weighting factors of APFC technique are lacking analytical knowledge. The performance of the proposed EO-APFC-PID control scheme is demonstrated and compared with one classic PID tuning method and two state-of-the-art control strategies on the chamber pressure control for a coke furnace. The experimental results fully illustrate that the proposed method is more effective and efficient than other existing control strategies for achieving a desired behavior on the most test cases considered in this paper in terms of set point tracking, input disturbance rejection and output disturbance rejection.     

Robust H∞ control of an observer-based repetitive-control system

This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H_∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.     

Resilient observer-based sliding mode control of connected vehicles with denial-of-service attacks

This paper investigates an observer-based sliding mode control (SMC)) for connected vehicles under denial-of-service attacks. The attacks refer to interrupting communication channels between vehicles. Firstly, a reduced order observer is used to estimate the relative acceleration between neighbor vehicles, and a switching communication topology is introduced to model the attack. Then, an observer based sliding mode controller is proposed to achieve desired stability performance. Moreover, a quadratic cost performance is also defined and the cost upper bound is proved. Some sufficient conditions are provided such that the connected vehicles can achieve robust tracking performance, and input-to-state string stability is guaranteed under zero initial errors. Finally, numerical simulations are given to illustrate the validity of the designed controller.     

Inverse-Dynamics- and disturbance-Observer-Based tube model predictive tracking control of uncertain robotic manipulator

A novel robust hierarchical multi-loop composite control scheme is proposed for the trajectory tracking control of robotic manipulators subject to constraints and disturbances. The inner loop based on inverse dynamics control is used to reduce the nonlinear tracking error system to a set of decoupled linear subsystems to alleviate the computational effort during the sequel optimization. The feasible regions of the equivalent state and control input of each subsystem can be computed efficiently by choosing an appropriate inertia matrix estimate. The external loop, relying on a set of separate disturbance-observer-based tube model predictive composite controllers, is used to robustly stabilize the decoupled subsystems. In particular, the disturbance observers are designed to compensate for the disturbances actively, while the tube model predictive controllers are used to reject the residual disturbances. The robust tightened constraints are obtained by calculating the outer-bounding-tube-type residual disturbance invariant sets of the closed-loop subsystems. Furthermore, the recursive feasibility and input-to-state stability of the closed-loop system are investigated. The effectiveness of the proposed control scheme is verified by the simulation experiment on a PUMA 560 robotic manipulator.     

Design of a H∞ model reference tracking control for interconnected nonlinear systems by decentralized dynamic output-feedback

This study investigates the problem of robust tracking control for interconnected nonlinear systems affected by uncertainties and external disturbances. The designed H_∞ dynamic output-feedback model reference tracking controller is parameterized in terms of linear matrix inequalities (LMIs), which is formulated within a convex optimization problem readily implementable. The resolution of such a problem, guarantying not only the quadratic stability but also a prescribed performance level of the resulting closed-loop system, enables to calculate concurrently the robust decentralized control and observation gain matrices. The established LMI conditions are computed in a single-step resolution to obtain all the controller/observer parameters and therefore to overcome the problem of iterative algorithm based on a multi-stage resolution leading in most cases to conservative and suboptimal solutions. Numerical simulations on diverse applications ranging from a numerical academic example to coupled inverted double pendulums and a 3-strongly interconnected machine power system are provided to corroborate the merit of the proposed control scheme.     

Finite-time command filter-based adaptive fuzzy tracking control for stochastic nonlinear induction motors systems with unknown backlash-like hysteresis

In this article, an adaptive fuzzy control method is proposed for induction motors (IMs) drive systems with unknown backlash-like hysteresis. First, the stochastic nonlinear functions existed in the IMs drive systems are resolved by invoking fuzzy logic systems. Then, a finite-time command filter technique is exploited to overcome the obstacle of “explosion of complexity” emerged in the classical backstepping procedure during the controller design process. Meanwhile, the effect of the filter errors generated by command filters is decreased by utilizing corresponding error compensating mechanism. To cope with the influence of backlash-like hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. The finite-time control technology is adopted to accelerate the response speed of the system and reduce the tracking error, and the stochastic disturbance and backlash-like hysteresis are considered to improve control accuracy. It’s shown that the tracking error can converge to a small neighborhood around the origin in finite-time under the constructed controller. Finally, the availability of the presented approach is validated through simulation results.     

A novel adaptive three stages model predictive control based on fuzzy systems: Application in MIMO controlling of MED-TVC process

In the present study, a novel technique is suggested for the adaptive non-linear model predictive control based on the fuzzy approach in three stages. In the presented approach, in the first stage, the prediction and control horizons are obtained from a fuzzy system in each control step. Another fuzzy system is employed to determine the weight factors before the optimization stage of developing new controller. The proposed controller gives the parameters of the model predictive control (MPC) in each control step in order to improve the performance of nonlinear systems. The proposed control scheme is compared with the traditional MPC and Generic Model Control for controlling MED-TVC process. The performances of the three proposed controllers have been investigated in the absence and presence of disturbance in order to evaluate the stability and robustness of the proposed controllers. The results reveal that the novel adaptive controller based on fuzzy approach performs better than the two other controllers in set-point tracking and disturbance rejection with lower IAE criteria. In addition, the average computational time for the adaptive MPC exhibits a decline of 34% in comparison with the traditional MPC.     

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

Output regulation control for stochastic systems with additive noise

This paper investigates the robust output regulation problem for stochastic systems with additive noises. As is known, for the output regulation control problem, a general method is to regard that the system is disturbed by an autonomous exosystem (which is consisted by external disturbances and reference signals), and for the system disturbed by the white noise, the stochastic differential equations (SDEs) should be utilized in modeling, accordingly, a controller with a feedforward regulator is constructed for the stochastic system with an exosystem, which can not only cancel the external disturbance, but also transform the trajectory tracking problem into the stabilization problem; In consideration of the state variables in stochastic systems cannot be measured completely, we embed an observer to the controller, such that the random interference can be suppressed, and the trajectory tracking can be achieved. Based on the stochastic control theory, the criteria of the exponential practical stability in the mean square is presented for the closed-loop system, finally, through tuning the controller parameters, the mean square of the tracking error can converge to an arbitrarily small neighborhood of the origin.     

Sum-of-squares-based robust H∞ controller design for discrete-time polynomial fuzzy systems

This paper investigates a robust H_∞ controller design for discrete-time polynomial fuzzy systems based on the sum-of-squares (SOS) approach when model uncertainties and external disturbances are simultaneously considered. At the beginning of the controller design procedure, a general discrete-time polynomial fuzzy control system proposed in this paper is used to represent a nonlinear system containing model uncertainties and external disturbances. Subsequently, through use of a nonquadratic Lyapunov function and the H_∞ performance index, the novel SOS-based robust H_∞ stability conditions are derived to guarantee the stability of the entire control system. By solving those stability conditions, control gains of the robust H_∞ polynomial fuzzy controller are obtained. Because the model uncertainties and external disturbances are considered simultaneously in the controller design procedure, the closed-loop control system achieves greater robustness and H_∞ performance against model uncertainties and external disturbances. Moreover, the novel operating-domain-based robust H_∞ stability conditions are derived by considering the operating domain constraint to relax the conservativeness of solving the stability conditions. Finally, simulation results demonstrated the availability and effectiveness of the proposed stability conditions, which are more general than those used in existing approaches.     

Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle

This paper is concerned with the adaptive sliding mode control (ASMC) design problem for a flexible air-breathing hypersonic vehicle (FAHV). This problem is challenging because of the inherent couplings between the propulsion system, the airframe dynamics and the presence of strong flexibility effects. Due to the enormous complexity of the vehicle dynamics, only the longitudinal model is adopted for control design in the present paper. A linearized model is established around a trim point for a nonlinear, dynamically coupled simulation model of the FAHV, then a reference model is designed and a tracking error model is proposed with the aim of the ASMC problem. There exist the parameter uncertainties and external disturbance in the model, which are not necessary to satisfy the so-called matched condition. A robust sliding surface is designed, and then an adaptive sliding mode controller is designed based on the tracking error model. The proposed controller can drive the error dynamics onto the predefined sliding surface in a finite time, and guarantees the property of asymptotical stability without the information of upper bound of uncertainties as well as perturbations. Finally, simulations are given to show the effectiveness of the proposed control methods.     

Barrier function-based nonsingular prescribed performance terminal sliding mode tracker for under-actuated nonlinear systems: Experimental study

In this paper, an adaptive concave barrier function scheme coupled with the non-singular terminal sliding mode control technique is proposed for finite-time tracking control of the under-actuated nonlinear system in the existence of model uncertainty, external disturbance and input saturation. Firstly, the dynamical equation of under-actuated nonlinear n-order system is expressed under model uncertainty, external disturbance and input saturation. Secondly, for the improvement of stability performance of the system in the existence of input saturation, a compensation system is designed to overcome the constraint on the control input. Afterward, the tracking errors between actual states of the system and differentiable reference signals are defined and the sliding surface based on the defined tracking errors is presented. Then, for gaining the better transient and steady-state performance of the closed-loop system, the prescribed performance control scheme is adopted. Based on this method, the transformed prescribed form of the previous determined sliding surface is obtained to ensure that the sliding surface can reach to a predefined region. Afterward, for assurance of the finite-time reachability of transformed sliding surface, the nonsingular terminal sliding surface is recommended. In addition, for the compensation of the model uncertainty and external disturbance existed in the system, the adaptive-based concave barrier function technique is used to estimate the unknown bounds of uncertainty and exterior disturbance. Finally, for demonstration of the proposed control method, the simulations and experimental implementation are done on the air levitation system.     

A new method for fault prediction of model-unknown nonlinear system

In this paper, the subspace identification based robust fault prediction method which combines optimal track control with adaptive neural network compensation is presented for prediction the fault of unknown nonlinear system. At first, the local approximate linear model based on input-output of unknown system is obtained by subspace identification. The optimal track control is adopted for the approximate model with some unknown uncertainties and external disturbances. An adaptive RBF neural network is added to the track control in order to guarantee the robust tracking ability of the observation system. The effect of the system nonlinearity and the error caused by subspace modeling can be overcome by adaptive tuning of the weights of the RBF neural network online without any requisition of constraint or matching conditions. The stability of the designed closed-loop system is thus proved. A density function estimation method based on state forecasting is then used to judge the fault. The proposed method is applied to fault prediction of model-unknown fighter F-8II of China airforce and the simulation results show that the proposed method can not only predict the fault, but has strong robustness against uncertainties and external disturbances.