Discrete sliding mode control for nonlinear systems using feedback linearization

A self-organizing fuzzy controller to augment a sliding-mode control (SOFSMC) scheme for a class of nonlinear systems is proposed. The motivation behind this scheme is to combine the best features of self-organizing fuzzy control and sliding-mode control to achieve rapid and accurate tracking control of a class of nonlinear systems. The chatter encountered by most sliding-mode control schemes is greatly alleviated without sacrificing invariant properties. A stability analysis is presented; the design guidelines and the class of applicable systems are clearly identified. To verify the scheme, the authors performed experiments on its implementation in a magnetic levitation system. The results show that both alleviation of chatter and robust performance are achieved; the advantages of the scheme are indicated in comparison with the conventional sliding-mode design. >

In this paper, an optimal control scheme for a class of nonlinear systems with time delays in both state and control variables with respect to a quadratic performance index function is proposed using a new iterative adaptive dynamic programming(ADP) algorithm.By introducing a delay matrix function, the explicit expression of the optimal control is obtained using the dynamic programming theory and the optimal control can iteratively be obtained using the adaptive critic technique.Convergence analysis is presented to prove that the performance index function can reach the optimum by the proposed method.Neural networks are used to approximate the performance index function, compute the optimal control policy, solve delay matrix function, and model the nonlinear system, respectively, for facilitating the implementation of the iterative ADP algorithm.Two examples are given to demonstrate the validity of the proposed optimal control scheme.

This paper modifies the prototype model-free adaptive control (PMFAC) approach in which system output fluctuation and overshoot (SOFO) is easy to occur. Targeting a class of nonlinear discrete-time single-input single-output systems, historical input/output sensor data are utilized to online construct equivalent explicit data model for control design, making the controller model-free. Then, a novel compensation input term including a compensation gain and a signum function parameterized by incremental output is proposed to soften system inputs, which can in turn restrain the SOFO. Numerical simulations and a speed control experiment for a direct current motor verify that the modified approach can restrain the SOFO successfully and reduce response time compared with the PMFAC.

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

The author presents a robust technique for designing compensators for a certain class of nonlinear systems following the philosophy behind input-output linearization and sliding mode control. The technique takes advantage of a robust equivalent feedback linearization using sliding mode theory and then superimposes linear design algorithms in order to shape the loop operator (loop transfer function) of the feedback linearized system. Robustness issues are addressed; when the external disturbances to the system and modeling parameter uncertainties are bounded and satisfy the matching conditions, the nonlinear system can be robustly linearized. The proposed scheme has enough parameters to give flexibility in the choice of the desired closed-loop characteristics. At the same time, it leaves the designer with the responsibility of selecting the following parameters: boundary layer, strength of attraction to the sliding surface, and bandwidth.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This study proposes a new adaptive output feedback sliding mode control (SMC) for mismatched uncertain time-delay systems. First, sufficient conditions in terms of linear matrix inequalities are derived such that the equivalent reduced-order system in the sliding mode is asymptotically stable. Second, based on a new lemma and a novel adaptive law, an adaptive sliding mode controller is designed to guarantee the finite-time reachability of the system states using output feedback only. The proposed method is not limited by the following conditions: (1) the exogenous disturbances must be bounded by a known function of the outputs or by a known function of the state and delayed state variables, and (2) the norm of unmeasured states must be bounded by a constant value. As these conditions are required for the application of most existing SMC approaches for time-delay systems, the proposed approach can be applied to a more generalized system, making it a valuable contribution to the field.

Neural network-based H∞ sliding mode control for nonlinear systems with actuator faults and unmatched disturbances

In this paper, an novel active safety monitoring system is constructed for a class of nonlinear discrete-time systems. The considered nonlinear system is subjected to unknown inputs, external disturbances, and possible unknown deception attacks, simultaneously. In order to secure the safety of control systems, an active attack estimator composed of state/output estimator, attack detector and attack/attacker action estimator is constructed to monitor the system running status. The analysis and synthesis of attack estimator is performed in the $H_{\infty}$ performance optimization manner. The off-line calculation and on-line application of active attack estimator are summarized simultaneously. The effectiveness of the proposed results is finally verified by an numerical example.

A multilayer neural-network (NN) controller is designed to deliver a desired tracking performance for the control of a class of unknown nonlinear systems in discrete time where the system nonlinearities do not satisfy a matching condition. Using the Lyapunov approach, the uniform ultimate boundedness of the tracking error and the NN weight estimates are shown by using a novel weight updates. Further, a rigorous procedure is provided from this analysis to select the NN controller parameters. The resulting structure consists of several NN function approximation inner loops and an outer proportional derivative tracking loop. Simulation results are then carried out to justify the theoretical conclusions. The net result is the design and development of an NN controller for strict-feedback class of nonlinear discrete-time systems.

In this paper, the observer-based output feedback sliding mode control (SMC) problem is investigated for discrete delayed nonlinear systems subject to packet losses under the event-triggered strategy. It is assumed that the packet losses may occur in the control channel from the sensor to the observer. A suitable compensation strategy via the Bernoulli distributed random variable is used to reduce the effects of packet losses. In order to avoid the phenomenon of network congestion during the networked transmission, an event-triggered mechanism is introduced to determine if the last released measurement needs to be updated. Based on the zero-order-hold (ZOH) measurement, an output feedback observer is designed to reconstruct the system state. This method can facilitate the design of the discrete-time sliding surface. A sufficient condition is proposed to guarantee the stochastic stability of sliding mode dynamics systems by using linear matrix inequality (LMI) method, and a novel observer-based sliding mode controller is synthesized to force the trajectories of the error systems onto the pre-designed sliding mode surface within finite time. Finally, an example is given to illustrate the validity of the proposed theoretical result.

In this study, the problem of output feedback sliding mode control of linear sampled‐data multi‐input–multi‐output systems is considered. Existing sliding mode control schemes can attenuate the influence of an external disturbance by driving system states onto a sliding surface. However, they can exhibit high gains during transients, which can be where T is the sampling time period. To address this problem, a new strategy, which employs disturbance approximation, is proposed so that the control effort will be . The new method avoids deadbeat phenomena and hence, it will be less sensitive to noise. Theoretical analysis is provided to show the convergence and robustness of the proposed method. Simulations were conducted to show the efficiency of the proposed approach.

In this paper, decoupled neural fuzzy sliding-mode control design method for highly nonlinear systems is proposed. The decoupled control method provides a simple way to achieve asymptotic stability for a class of fourth-order nonlinear system into two second-order subsystems by a separate control objective expressed in terms of a sliding surface for each subsystems. Using the proposed method the second subsystem is successfully incorporated into the first one via a two-level decoupling strategy. In the controller design method, reaching mode and sliding mode control of sliding mode control is approximated based on neural network control and fuzzy logic control method respectively. Two simulation results of a cart-pole and ball-beam systems are shown to demonstrate the effectiveness of the proposed method.

This paper proposes a robust supertwisting algorithm (STA) design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.

NN-adaptive predictive control for a class of discrete-time nonlinear systems with input-delay

This paper deals with the stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> static output feedback controller is developed. It consists on a sufficient condition, formulated as an LMI optimization convex problem. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. Numerical example is provided to illustrate the effectiveness of the proposed conditions.