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This paper designs a novel nonsingular terminal sliding mode control (TSMC) scheme for a class of nonlinear systems under binary encoding transmission. To further ease the communication overheads between the plant and the controller, a dynamic event-triggered mechanism is also introduced to the TSMC design. Sufficient conditions are proposed, respectively, for guaranteeing the reachability to a practical sliding mode and the ultimate boundedness of the closed-loop system, in which the effects from the binary encoding and the dynamic event-triggered protocol are quantified clearly. The Zeno phenomena for the developed dynamic event-triggered mechanism is excluded via an explicit analysis. Finally, the feasibility and effectiveness of the proposed scheme are demonstrated by a numerical example and a real experiment on permanent magnet synchronous motor speed regulation system. [ABSTRACT FROM AUTHOR]

High-quality data transmission synchronization process is frequently expected in light of secure communication mechanisms (SCMs), especially for space laser communication among the satellite constellation. To improve security and reliability during the data transmission processes prominently, control problems of chaotic synchronization synchronously at the same time are explored. In this paper, several novel error synchronization control protocols are proposed to solve these problems. First, by introducing a norm-normalized sign function (NNSF), unique (fixed-) time-synchronized stability is manifested, such that all non-zero state elements reach the origin synchronously at the same time. And upper bounds of synchronous resident time calculated by offered protocols are irrelevant/relevant to initial states of the error systems. Second, integrated with the (fixed-) time-synchronized stability theories, the (fixed-) time-synchronized sliding mode controllers with special convergent performance are established for two representative types of chaotic systems. Third, the ratio-persistent performance plays a dominating role for simultaneous convergence of the errors. Further, the innovation of the algorithms is reflected in that the decrypted signal is completely consistent with the transmitted message signal within synchronized settling time. Finally, in the simulation, not only theoretical verifications, but also practical verifications of image encryption and decryption processes verify the effectiveness of the SCMs. [ABSTRACT FROM AUTHOR]

In this paper, a fixed-time backstepping fractional-order sliding mode excitation controller (FTBFOSMEC) is proposed to enhance the performance of multimachine power system. The FTBFOSMEC is designed to achieve semi-global uniform ultimate boundedness of the multimachine power system within an upper limited convergence time irrelated to the initial operating states. The FTBFOSMEC can achieve the attractive qualities of sliding mode control with strong robustness and fast dynamic response, and the merits of backstepping control in globally asymptotic stability for parametric uncertainty. In addition, the FTBFOSMEC can avoid the singularity problem of conventional SMC. Furthermore, the nonlinear first-order filter is carried out to avoid the “explosion complexity” issue of traditional backstepping control. The fractional-order controller is designed to alleviate the chattering phenomenon of the conventional SMC. Meanwhile, the FTBFOSMEC is in a continuous description, which can further eliminate the chattering phenomenon. The Lyapunov function is taken to analyze the stabilization of the multimachine power system under the control of the FTBFOSMEC, and to estimate the upper limit of convergence time. Finally, comparative results, based on the New England 10-machine 39-bus power system, indicate that the power system under the proposed FTBFOSMEC can obtain effective, robust and superior performances compared with the existing control strategies under different operating circumstances. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time sliding mode control issue is studied for a series of semi-Markov jump systems subject to actuator faults, where an asynchronous control method is adopted to overcome the non-synchronous phenomenon between the system mode and controller mode. Additionally, the event-triggered protocol, which determines whether the transmission of data should be performed according to the threshold condition, is introduced to alleviate the burden of data transmission in the communication channel. This paper aims to devise an asynchronous event-triggered sliding mode control law so as to guarantee the trajectories of the resulting closed-loop system can be forced onto the predefined sliding surface in a finite-time interval. Thence, by means of the mode-dependent Lyapunov functions and the finite-time theory, sufficient conditions are derived to assure that the closed-loop system is mean-square finite-time bounded in both reaching and sliding motion phases. Eventually, a numerical example and a tunnel diode circuit model are presented to illustrate the availability and practicability of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with bipartite tracking for double-integrator networked systems with signed communication graphs, where both cooperative and antagonistic interactions coexist. A finite-time bipartite tracking framework is established, where followers track either the state or the opposite state of a leader. Different from some conventional results with convergence over an infinite time horizon, the finite-time convergence in this paper is achieved in an accurate manner. Under structurally balanced signed graphs, an integral sliding mode based finite-time bipartite tracking controller is proposed. The construction of an integral sliding mode variable is to ensure that the system dynamics is driven onto a sliding surface in finite-time. On the sliding surface, neighbouring states are used together with the homogeneous technique to guarantee that bipartite tracking is achieved in finite-time. To further realize fixed-time bipartite tracking, a controller is designed by using the integral sliding mode and the bi-limit homogeneous concept. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

In this paper, a unified framework is proposed to address the synchronization problem of memristor chaotic systems (MCSs) via the sliding-mode control method. By employing the presented unified framework, the finite-time and fixed-time synchronization of MCSs can be realized simultaneously. On the one hand, based on the Lyapunov stability and sliding-mode control theories, the finite-/fixed-time synchronization results are obtained. It is proved that the trajectories of error states come near and get to the designed sliding-mode surface, stay on it accordingly and approach the origin in a finite/fixed time. On the other hand, we develop an image encryption algorithm as well as its implementation process to show the application of the synchronization. Finally, the theoretical results and the corresponding image encryption application are carried out by numerical simulations and statistical performances. [ABSTRACT FROM AUTHOR]

This paper presents a sliding mode dynamic output feedback controller design for Markovian jump systems under a communication network. For the inaccessible states and uncertain parts of Markovian jump systems, a novel integral-type sliding mode output feedback controller combined with system states and dynamic controller states is proposed. An event-triggered mechanism is introduced to reduce network bandwidth and resources requirements. The augmented dynamic system and complete control framework are presented together. The reachability of the novel integral-type sliding mode is proved. Then, based on delay-dependent Lyapunov functions, free-weighting matrices, and a singular value decomposition approach, a less conservative sufficient condition is proposed to ensure exponential stability with a weighted $\mathcal {L}_{2}$ - $\mathcal{ L}_{\infty}$ disturbance performance. Finally, a numerical and a DC-DC switched boost converter circuit simulations that verify the feasibility and effectiveness of the proposed controller are presented. [ABSTRACT FROM AUTHOR]

This paper offers an improved finite time sliding mode controller scheme for a class of robotic manipulators with external disturbances. Since conventional sliding mode controllers have a discontinuous signum function, an important problem called chattering phenomenon can occur in them. The proposed scheme presents a new Lyapunov candidate functional containing an absolute function based on a fractional power of the switching surface such that the designed control law is continuous and smooth. The recommended control technique is designed using the Lyapunov stability theory and satisfies the presence of the sliding mode around designed switching surface in the finite time. The presented method eliminates the chattering problem produced by the switching controller and satisfies high precision action. Besides, the adaptive tuning controllers are designed to approximate the unknown bound of external disturbance. An extension of the proposed control technique based on the barrier function adaptive terminal sliding mode control is also suggested for better performance and robust tracking control of the nonlinear systems with external disturbances. Some simulation and experimental outcomes exhibit the efficacy of the planned technique. [ABSTRACT FROM AUTHOR]

In this paper, a high-order nonlinear disturbance observer-based fractional-order sliding mode control (FOSMC) strategy is proposed for DC/DC buck converters in the presence of mismatched disturbances, ensuring the properties of both stability and dynamic performance. Traditional sliding mode control can deal with matched disturbances while achieving desired closed-loop performance, unfortunately it is particularly sensitive to mismatched disturbances. In the proposed control structure, two nonlinear disturbance observers are constructed to estimate both matched and mismatched disturbances in finite time. Then, the estimated variables are used for the fractional-order sliding mode surface design, where a super twisting sliding mode controller is designed to drive the states of the system to track their desired values. Comparing with the traditional SMC, the proposed method not only reduces the sensitivity of the system to mismatched disturbance, but also improves the transient performance of the system. Simulation and experimental results have comprehensively illustrated the feasibility and effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, the problem of formation control is studied for second-order multi-agent systems with practical issues like mismatched uncertainties and obstacle avoidance. A reference correction algorithm based sliding mode control scheme is proposed to ensure the boundedness of each agent’s position tracking error. Both disturbance observer and artificial potential field are implemented to first tackle the problem of obstacle avoidance with the existence of mismatched uncertainties. The unreachable reference scenarios are then defined to describe the passive correcting behaviours of the multi-agent system when agents are trying to avoid obstacles. A distributed reference correction algorithm is developed for each agent to attenuate the harmful effects of passive correcting behaviours. The effectiveness of obstacle avoidance and boundedness of position tracking error are both verified by Lyapunov stability theory. Finally, multi-robot system based numerical simulations and comparisons are conducted to demonstrate the effectiveness of the proposed algorithm and controller. [ABSTRACT FROM AUTHOR]

To increase lifespan and optimize capacity utilization of lithium-ion (Li-ion) battery, it is imperative to predict its states accurately. This paper primarily focuses on offering an improved solution for estimating one of the most important battery states known as state of charge (SOC). After extensive analysis of the current state-of-the-art methods, we propose a new adaptive observer based approach for precise estimation of battery SOC using super twisting algorithm. The proposed approach avoids overestimation of gains while ensuring finite-time convergence of the states. For choosing the associated adaptive gains, it does not demand any information on upper bounds of the uncertainty and its derivative, except for their existence. Unlike most of the sliding mode methods employed for SOC estimation, the proposed approach provides continuous control injection resulting in reduced chattering and eliminates the need for low pass filter that leads to improved accuracy and response time. Lyapunov stability theory is utilized to prove the robustness and the error convergence of the proposed observer. The presented algorithm is executed on a lithium-polymer battery and the obtained results demonstrate that it outperforms the well-established approaches in terms of accuracy, chattering, robustness, computational complexity, and convergence time. [ABSTRACT FROM AUTHOR]

This paper deals with the $H_{\infty }$ adaptive sliding mode fault tolerant control problem for uncertain Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs) of fractional order $0 < \alpha < 1$ with mismatched disturbances. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms. A sliding surface with reduced dimension is constructed by the method of state transformation. A sufficient condition in terms of linear matrix inequalities (LMIs) is established which guarantees the stability of the sliding motion. Then, a new control law is designed to make the resulting control system reach the sliding surface in a finite time. Both state and output feedback control forms are addressed. The proposed methods are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the decentralized optimal control problem is addressed for a class of large-scale systems subject to injection attacks. All subsystem matrices are considered to be unavailable to the designer. A model-free decentralized sliding mode control (SMC) scheme for each subsystem is designed via just utilizing its own state information and the known bounds of the interconnections and the injection attacks. Moreover, the adaptive dynamic programming (ADP) approach is incorporated to deal with the infinite horizon optimal control problem for the sliding mode dynamics, which is equivalent to the solution of a set of parallel algebraic Riccati equations. Furthermore, a novel parallel policy iteration algorithm is developed to implement the proposed decentralized SMC scheme without using all subsystems dynamics matrices. Specifically, it is shown that during the whole policy iteration steps, the reachability of each sliding variable and the stability of each sliding mode dynamics are guaranteed simultaneously by the online updating decentralized SMC scheme. Finally, the applicability of the proposed novel ADP-based decentralized SMC strategy is illustrated by a two-machine power system subject to three different injection attacks. [ABSTRACT FROM AUTHOR]

In this paper, four control strategies for DC-DC buck converters are proposed, compared and analyzed: a single-loop adaptive control strategy (SA), a double-loop adaptive control strategy (DA), a single-loop disturbance observer-based control strategy (SDOB) and a double-loop disturbance observer-based control strategy (DDOB). First, the nominal system without considering the parametric uncertainties of the DC-DC buck converter is built to help develop the SA and DA. The SA is built by adaptive and backstepping control approaches, and the DA is set up by adaptive and sliding mode control approaches. Additionally, a model considering parametric uncertainties is introduced, giving the opportunity to develop the SDOB and DDOB. The SDOB is developed using a designed disturbance observer and backstepping control technique, and the DDOB is synthesized using a designed disturbance observer and sliding mode control method. Finally, the advantages and disadvantages of the four proposed control strategies are compared and analyzed through experiments. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive second-order sliding mode (SOSM) control method is proposed by combining a new adaptive strategy with the backstepping-like technique. The new adaptive strategy is first constructed by means of the equivalent control for which a sliding-mode-based filter is employed rather than the widely-used low-pass filter such that the parameter restriction under the usage of low-pass filter can be relaxed. Then, by applying the proposed adaptive strategy and the idea of adding a power integrator, an adaptive SOSM method is established to finite-time stabilize the sliding variables. The feature of the proposed SOSM method lies in that the gain will vary with the size of the lumped uncertainty so as to avoid the overestimation of the gain. The stability analysis is given based on the finite-time Lyapunov theory. The theoretical results are finally applied to the voltage regulation problem of a Buck converter. [ABSTRACT FROM AUTHOR]

This paper introduces a new, reference trajectory following, sliding-mode control strategy for disturbed discrete-time systems. The strategy uses an external trajectory generator based on a switching type reaching law. The trajectory following strategy not only ensures all the properties of the quasi-sliding-mode as defined by Gao et al., but with a certain choice of the control parameters it also guarantees a significant reduction of the quasi-sliding-mode band width and the errors of all the state variables. This paper also considers the problem of error calculation in the discrete-time, reaching law based sliding-mode control systems. It is shown that the limitation of the sliding variable in the sliding phase directly results in bounded errors of all state variables. The results are verified with a simulation example. [ABSTRACT FROM AUTHOR]

In the paper, the periodic event-triggered adaptive controller is proposed for attitude stabilization of a rigid spacecraft with model uncertainties, external disturbances, and input saturation. We adopt the periodic state measurement instead of the continuous one, and it is known that the former is more economical and practical than the latter due to the relaxation of continuous measurements. Moreover, new event-triggered adaptation update laws and the periodic event-triggering strategy are proposed for adaptive sliding mode control (SMC) to guarantee the states in the practical sliding mode. It is illustrated that the states of the attitude control system are ultimately bounded. Further, it is proved that the presented periodic event-triggered strategy is without $Zeno$ phenomenon and there exists a uniform lower bound for each interevent time. Some numerical examples are given to demonstrate the validity of the derived control strategy. [ABSTRACT FROM AUTHOR]

This paper studies the high-order sliding mode (HOSM) control for a general class of uncertain nonlinear systems. Firstly, the standard sliding mode system is extended to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the system uncertainties in the control channel and relax the well defined relative degree assumption. Secondly, the conventional constant upper bounds assumption is relaxed to time-varying positive functions, which enables us to obtain a global result. For the new sliding mode system under the new global assumption, a novel HOSM controller, that has a simple relay polynomial form, is then proposed. By introducing a new continuous component in the controller, the discontinuous component of the controller only needs to be selected to suppress the uncertainties and thus a controller with minimal discontinuous component magnitude can be implemented. Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented. [ABSTRACT FROM AUTHOR]

This paper endeavors to investigate the output-feedback sliding mode control (SMC) issue of the networked singularly perturbed systems (SPSs) under fast sampling. In order to improve the reliability of network communication, a redundant channel transmission protocol is introduced in the SMC design. Based on the measurement outputs, a sliding function is constructed with the consideration of the transmission protocol. With the aid of some appropriate Lyapunov functions, the sufficient conditions are derived to ensure the mean-square exponentially ultimately boundedness of the sliding mode dynamics and the reachability of the specified sliding surface. Moreover, a convex optimization algorithm is formulated to solve the output-feedback SMC law by searching the available upper bound of the singularly perturbed parameter. Finally, an operational amplifier circuit is exploited to explore the influences from the redundant channel transmission protocol to the output-feedback SMC performance and the estimated $\varepsilon$ -bound. [ABSTRACT FROM AUTHOR]

In this paper, the receding horizon near-optimal tracking control problem about a class of continuous-time nonlinear systems with fully unknown dynamics is considered. The main challenges of this problem lie in two aspects: 1) most existing systems only restrict their considerations to the state feedback part while the input channel parameters are assumed to be known. This paper considers fully unknown system dynamics in both the state feedback channel and the input channel and 2) the optimal control of nonlinear systems requires the solution of nonlinear Hamilton–Jacobi–Bellman equations. Up to date, there are no systematic approaches in the existing literature to solve it accurately. A novel model-free adaptive near-optimal control method is proposed to solve this problem via utilizing the Taylor expansion-based problem relaxation, the universal approximation property of sigmoid neural networks, and the concept of sliding mode control. By making approximation for the performance index, it is first relaxed to a quadratic program, and then, a linear algebraic equation with unknown terms. An auxiliary system is designed to reconstruct the input-to-output property of the control systems with unknown dynamics, so as to tackle the difficulty caused by the unknown terms. Then, by considering the property of the sliding-mode surface, an explicit adaptive near-optimal control law is derived from the linear algebraic equation. Theoretical analysis shows that the auxiliary system is convergent, the resultant closed-loop system is asymptotically stable, and the performance index asymptomatically converges to optimal. An illustrative example and experimental results are presented, which substantiate the efficacy of the proposed method and verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the actuator fault estimation sliding-mode observer (SMO) design problem of linear continuous-time systems over digital communication channels. This problem frequently occurred in a network environment where data has to be quantized before being transmitted via digital communication channels. Traditional observers (linear Luenberger observer, Walcott–ZaK SMO) are not effective to solve this design issue since the effects of signal quantization will degrade estimation performances evidently. In this paper, a new descriptor SMO method is presented to overcome this difficult problem. It is shown that, if the quantizer density is larger than $\sqrt{2}-1$ , the designed observer can compensate quantization errors completely, and the fault vector can be reconstructed despite of signal quantization. Finally, a simulation example with the F-404 aircraft engine model is proposed to demonstrate the effectiveness of the proposed robust digital observer design approach. [ABSTRACT FROM AUTHOR]

In this paper, a control technique is presented for an undamped, pinned–pinned Euler–Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances. This is achieved in two main steps. First, a backstepping transformation is used to convert the marginally stable Euler–Bernoulli beam system to a new form that has an exponentially stable homogeneous form. Control inputs are needed to fully convert the system to this form; however, since they are distorted by unknown bounded disturbances, the next step implements a sliding mode controller to account for them. The proposed sliding manifolds require a combination of classical and “second order” techniques in order to avoid discontinuous chattering on the physical system. Therefore, the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate, and do so in the presence of unknown bounded disturbances on the boundary. The main contributions of this paper with respect to previous backstepping designs for the Euler–Bernoulli beam are that all three of the following goals are accomplished together: (i) steady-state position is the origin, (ii) decay rate has no theoretical restrictions, and (iii) is robust to bounded disturbances. [ABSTRACT FROM AUTHOR]

This paper deals with the observer-based adaptive sliding mode control (OBASMC) design for nonlinear uncertain singular semi-Markov jump systems. The system satisfies the singular property and follows a stochastic semi-Markov process related to Weibull distribution. Due to the influence of sensor factors in practical systems, the state vectors are not always known. Additionally, the unavoidable measurement errors in the actual system always lead to the model uncertainties and the unknown nonlinearity. Our attention is to design the OBASMC law for such a class of complex systems. First, by the use of the Lyapunov–Krasovskii functional, sufficient conditions are given, such that the sliding mode dynamics are stochastically admissible. Then, the OBASMC law is proposed to guarantee the reachability in a finite-time region. Finally, the practical system about dc motor model is given to verify the validity. [ABSTRACT FROM AUTHOR]

A model-based event-triggered control scheme for nonlinear constrained continuous-time uncertain systems in networked configuration is presented in this paper. It is based on the combined use of model-predictive control (MPC) and integral sliding-mode (ISM) control, and it is oriented to reduce the packet transmission over the network both in the direct path and in the feedback path, in order to avoid network congestion. The key elements of the proposed control scheme are the ISM local control law, the MPC remote controller, a smart sensor, and a smart actuator, both containing a copy of the nominal model of the plant. The role of the ISM control law is to compensate matched uncertainties, without amplifying the unmatched ones. The MPC controller with tightened constraints generates the control component oriented to comply with state and control requirements and is asynchronous since the underlying constrained optimization problem is solved only when a triggering event occurs. In the paper, the robustness properties of the controlled system are theoretically analyzed, proving the regional input-to-state practical stability of the overall control scheme. [ABSTRACT FROM AUTHOR]

By considering the under-actuated characteristics of the quadcopter suspension transportation system and the external disturbance, the effective tracking control of the quadrotor transportation system faces great difficulties and challenges. An adaptive hierarchical sliding mode control (HSMC) scheme based on fixed-time sliding mode disturbance observer (FTSMDO) is developed for the anti-disturbance tracking control of under-actuated quadcopter suspension transportation system (UQSTS). The HSMC is used to deal with the under-actuated characteristics of the UQSTS, and the external disturbance is estimated by designing the FTSMDO. Synchronously, the disturbance estimation error is processed by designing the adaptive law. The stability analysis based on Lyapunov is applied to verify the uniform ultimate boundedness of the closed-loop system. Finally, the comparison of physical experiment upshots shows the effectiveness and potential of the proposed new control techniques. [ABSTRACT FROM AUTHOR]

The efficient driving control of MEMS gyroscopes is an attractive way to improve the precision without hardware redesign. This paper investigates the sliding mode control (SMC) for the dynamics of MEMS gyroscopes using neural networks (NNs). Considering the existence of the dynamics uncertainty, the composite neural learning is constructed to obtain higher tracking precision using the serial–parallel estimation model (SPEM). Furthermore, the nonsingular terminal SMC (NTSMC) is proposed to achieve finite-time convergence. To obtain the prescribed performance, a time-varying barrier Lyapunov function (BLF) is introduced to the control scheme. Through simulation tests, it is observed that under the BLF-based NTSMC with composite learning design, the tracking precision of MEMS gyroscopes is highly improved. [ABSTRACT FROM AUTHOR]

In this paper, a full-regulated neural network (NN) with a double hidden layer recurrent neural network (DHLRNN) structure is designed, and an adaptive global sliding-mode controller based on the DHLRNN is proposed for a class of dynamic systems. Theoretical guidance and adaptive adjustment mechanism are established to set up the base width and central vector of the Gaussian function in the DHLRNN structure, where six sets of parameters can be adaptively stabilized to their best values according to different inputs. The new DHLRNN can improve the accuracy and generalization ability of the network, reduce the number of network weights, and accelerate the network training speed due to the strong fitting and presentation ability of two-layer activation functions compared with a general NN with a single hidden layer. Since the neurons of input layer can receive signals which come back from the neurons of output layer in the output feedback neural structure, it can possess associative memory and rapid system convergence, achieving better approximation and superior dynamic capability. Simulation and experiment on an active power filter are carried out to indicate the excellent static and dynamic performances of the proposed DHLRNN-based adaptive global sliding-mode controller, verifying its best approximation performance and the most stable internal state compared with other schemes. [ABSTRACT FROM AUTHOR]

This paper addresses a finite-time sliding-mode control problem for a class of Markovian jump cyber-physical systems. It is assumed that the control input signals transmitted via a communication network are vulnerable to cyber-attacks, in which the adversaries may inject false data in a probabilistic way into the control signals. Meanwhile, there may exist randomly occurring uncertainties and peak-bounded external disturbances. A suitable sliding mode controller is designed such that state trajectories are driven onto the specified sliding surface during a given finite-time (possibly short) interval. By introducing a partitioning strategy, the stochastic finite-time boundedness over the reaching phase and the sliding motion phase is analyzed, respectively. A key feature is that a set of mode-dependent sufficiently small scalars are introduced into some coupled Lyapunov inequalities such that the feasible solutions are easily obtained for the stochastic finite-time boundedness of the closed-loop systems. Finally, the practical system about a single-link robot-arm model is given to illustrate the present method. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive sliding-mode controller design problem for a class of Markov jump systems with actuator faults. First, a more extensive faults model, which includes actuator loss of effectiveness, outage and stuck, is established. Moreover, a novel sliding surface function is designed and sufficient conditions are established to ensure stochastic stability of the Markov jump systems with known transition probability. Second, based on the adaptive sliding-mode algorithm and the fault compensation algorithm, a comprehensive control law is synthesized not only to overcome the boundary restrictions of actuator loss effectiveness and external disturbances, but also to ensure the properties of stochastic stability and the reachability of the sliding-mode dynamics. Third, an improved stochastically stability criterion, in the case of Markov jump system with uncertain transition probability, is derived based on the homogeneous polynomial matrix technique. Finally, two simulation examples are provided to support the feasibility and effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a feedback controller designed to realize reachability is investigated in a class of nonlinear systems. Different from stability, reachability defines that there exists an input such that a closed-loop system can reach the desired states from any other initial states within finite time. In other words, the state errors can converge to zero in finite time if reachability can be realized. In order to realize reachability, it is proved that the state and all derivatives of the state must simultaneously satisfy a group of functions, called triple constraints. Then, it can be derived that the best approximation to realize the triple constraints is to guarantee the value of the highest order derivatives of the state. As a result, the controller can be obtained by solving a group of algebraic equations described by the highest order derivatives and the input. However, the solution will be difficult to obtain if the system is subjected to unknown parameters and disturbance. An online parameter estimation algorithm is proposed and the highest order derivatives are updated according to the current state to handle the uncertainties. With this newly developed online estimation algorithm and a scheme for updating the highest order derivatives online, reachability can be approximately realized for a class of nonlinear systems with uncertainties. To further illustrate the implementation and effectiveness of the proposed controller based on reachability, numerical simulations are conducted on a two-link robot arm. The results show the proposed controller outperforms conventional controllers such as computed-torque proportional-derivative (PD) control, sliding mode control, and finite-time controller. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of sliding mode control design for nonlinear stochastic singular semi-Markov jump systems (S-MJSs). Stochastic disturbance is first considered in studying S-MJSs with a stochastic semi-Markov process related to Weibull distribution. The specific information including the bound of nonlinearity is known for the control design. Our attention is to design sliding mode control law to attenuate the influences of uncertainty and nonlinear term. First, by the use of the Lyapunov function, a set of sufficient conditions are developed such that the closed-loop sliding mode dynamics are stochastically admissible. Then, the sliding mode control law is proposed to ensure the reachability in a finite-time region. Finally, the practical system about dc motor model is given to verify the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of discrete-time two-dimensional (2-D) sliding mode control (SMC) for Fornasini–Marchesini (FM) systems subject to exogenous nonlinear disturbances. With the introduction of the time instant and global state in the 2-D case, the discrete-time sliding surface function for 2-D systems is constructed. Then, based on the corresponding sliding mode dynamics, the solvability condition for the desired sliding surface function is derived. Subsequently, a sliding mode controller is designed to guarantee that the state trajectories can enter into a neighborhood of the specified sliding surface. Meanwhile, the stability of the 2-D sliding mode dynamics is also ensured. Finally, a simulation example is provided to illustrate the feasibility and the effectiveness of the presented new 2-D SMC design method. Different from existing results, the proposal focuses on the features of multi-dimension and the dynamics of 2-D systems, which is expected to develop a completely different SMC design approach for discrete-time 2-D systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme based on neural networks for predicting the packet disordering and sliding mode control (SMC) to stabilize the nonlinear networked control systems (NCSs). It is assumed that the packet disordering is unknown in the NCSs. The stochastic configuration networks (SCNs), which randomly assign the input weights and biases and analytically evaluate the output weights, are designed to solve the problem of unknown packet disordering. A new SMC scheme is developed by integrating the SCNs algorithm to learn and control the system in advance. Specifically, a novel measurement of packet disordering is constructed for the quantization of the packet disordering. In addition, the newest signal principle leads to the existence of stochastic parameters, thereby resulting in a Markovian jumping system. The effectiveness of the proposed approach is verified by some simulation results. [ABSTRACT FROM AUTHOR]

This article proposes a novel distributed predefined-time sliding mode controller (DPTSMC) to gain exceptional performances of power system under input saturation. Firstly, considering the saturation of excitation input to avoid the overvoltage of the coil, an auxiliary system is taken to compensate the effect of the excitation saturation. Then, the sliding mode control (SMC) and the predefined-time stability theory are taken to devise the DPTSMC to make the power system stable in a predefined time, which has an upper limit and is directly equivalent to an adjustable parameter, thus satisfying the high requirement of the power system for expected convergence time. Meanwhile, the estimated upper bound convergence time of the power system under the proposed DPTSMC is less conservative than some existing fixed-time control strategies. Moreover, the distributed control is taken to devise the DPTSMC and the controller can receive the real-time information from the phasor measurement units (PMU). Hence, the central controller is not required and the communication network is simple, thus releasing the pressure in complicated calculation and communication, and gaining rapid and coordinated response capacity. Next, the stabilization of the power system under the DPTSMC within a predefined upper limited time is proved through the Lyapunov function. Finally, the exceptional performance of the proposed DPTSMC than the existing control methods is verified through the simulation in the IEEE 39-bus 10-machine New England power system under different operation scenarios. [ABSTRACT FROM AUTHOR]

The almost sure finite-time sliding mode control issue is investigated for Markov jump systems. The switching asynchronism between the constructed controller and considered systems is studied. The influence of time-varying delays and disturbances on systems is fully considered, and the sliding mode controller design within a finite time interval is extended to the probability framework. First, the finite time interval is divided into the reaching and the sliding motion phases, and the almost sure finite-time boundedness is analyzed in both phases. Second, the sliding mode controller gain is determined by the provided linear matrix inequality-based criteria. Finally, a numerical example and DC-DC buck converter circuit example verify the effectiveness and less conservativeness of our method. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem for nonlinear Markovian jump systems (MJS) with output disturbances, actuator and sensor faults simultaneously. This kind of plants are common in practical systems, such as mobile manipulators with switching joints. In this paper, a sliding mode observer design scheme is proposed for a new descriptor augmented plant. By employing the developed observer, the effects of actuator and sensor faults can be eliminated. It is shown that the stabilization of the overall closed-loop plant can be guaranteed by the proposed fault tolerant control (FTC) scheme. Finally, an example concerning mobile manipulators with Markovian switching joints is presented to show the effectiveness and applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stabilization of a one-dimensional wave equation with nonlinear van der Pol type boundary condition that covers the antistable boundary, and subject to boundary control matched disturbance on the other side. Due to the nonlinear boundary condition and disturbance, the uncontrolled system may present spatiotemporal chaotic, period-doubling bifurcation, and some other dynamical behaviors. We will deal with this disturbance, which is supposed to be bounded only, by the integral sliding mode control. The well-posedness of the system for the closed-loop system is proved and the “reaching condition” is obtained. Finally, we provide some numerical simulations to illustrate the theoretical outcomes. [ABSTRACT FROM AUTHOR]

This paper studies the data-driven prescribed performance control (PPC) problem for a class of discrete-time nonlinear systems in the presence of tracking error constraints. By using the equivalent dynamic linearization technique and constructing a novel transformed error strategy, an adaptive integral sliding mode controller is designed such that the tracking error converges to a predefined neighborhood. Meanwhile, the presented control scheme can effectively ensure that the convergence rate is less than a predefined value and maximum overshoot is not smaller than a preselected constant. In addition, better tracking performance can be achieved by regulating the design parameters appropriately, which is more preferable in the practical application. Contrary to the existing PPC results, the new proposed control law does not use either the plant structure or any knowledge of system dynamics. The efficiency of the proposed control approach is shown with two simulated examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the sliding mode control (SMC) problem for a class of uncertain discrete-time systems subject to unmatched external disturbances and communication constraints. In order to reduce the bandwidth usage between the controller and the actuators, the stochastic communication protocol (SCP) is utilized to determine which actuator should be given the access to the network at a certain instant. A key issue of the addressed problem is to design both the sliding surface and the sliding mode controller under the SCP scheduling. An updating rule on actuator input is first introduced and then a token-dependent SMC law is designed. Sufficient conditions are established for the resultant SMC systems such that not only the reachability with a sliding domain around the specified sliding surface is ensured, but also the stochastic stability with a prescribed $H_\infty$ performance level is guaranteed. Based on these conditions, a set of coupled matrix inequalities is given to acquire the token-dependent parameter matrices in the proposed SMC law. Finally, a numerical example is presented to illustrate the effectiveness of the proposed $H_\infty$ SMC scheme under the SCP scheduling. [ABSTRACT FROM AUTHOR]

In this paper, we combine a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains with classical model reference adaptive control (MRAC) schemes to solve the relevant and yet open problem of trajectory tracking via output feedback of uncertain plants with arbitrary relative degree in a simple-closed form for the control design. The gains of the differentiator are adapted through state-norm observers for the unmeasured state, whereas the control parametrization explores the input–output filters commonly used in the MRAC design. Global asymptotic stability and robust exact tracking are rigorously demonstrated. Simulations highlight the claimed properties as well as the remarkable simplicity of the proposed adaptive control system using robust exact differentiators when compared to more involved alternatives found in standard approaches. The theoretical results are also illustrated with an application to bilateral teleoperation. [ABSTRACT FROM AUTHOR]

Recently, an extension of the super-twisting algorithm for relative degrees $m\geq {}1$ has been proposed. However, as of yet, no Lyapunov functions for this algorithm exist. This paper discusses the construction of Lyapunov functions by means of the sum-of-squares technique for  $m=1$. Sign definiteness of both Lyapunov function and its time derivative is shown in spite of numerically obtained—and hence possibly inexact—sum-of-squares decompositions. By choosing the Lyapunov function to be a positive semidefinite, the finite time attractivity of the system's multiple equilibria is shown. A simple modification of this semidefinite function yields a positive definite Lyapunov function as well. Based on this approach, a set of the algorithm's tuning parameters ensuring finite-time convergence and stability in the presence of bounded uncertainties is proposed. Finally, a generalization of the approach for $m>1$ is outlined. [ABSTRACT FROM AUTHOR]

Sliding mode control (SMC), which is known to present strong robustness against various disturbances, has been extensively employed on underactuated systems, whose control problem has been a research focus in recent years. However, though received great attention, the study on SMC for underactuated systems still remains quite open since it is very challenging to construct a proper manifold which can simultaneously stabilize both actuated and unactuated system states. Motivated to promote the corresponding research, we propose an improved second-order SMC (IS-SMC) method for a class of nonlinear underactuated systems in this paper, which guarantees that the closed-loop system's equilibrium point is asymptotically stable even in the presence of unknown nondiminishing disturbances. Different from traditional SMC methods presenting with chattering problem, the control inputs of the proposed method are essentially continuous, which brings much convenience for practical applications. Moreover, for the disturbances which are second-order differentiable, an enhanced IS-SMC (EIS-SMC) method is derived to guarantee the smoothness for both the control inputs and their derivatives. Finally, the proposed approach is applied to a practical underactuated system: The overhead crane system, with sufficient simulation results provided to validate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a generalized discrete time reaching law for sliding variables with arbitrary relative degree is proposed. The reaching law is based on Gao's strategy and ensures higher order switching-type sliding motion, which is a novel concept in the field of discrete time plants. The controller synthesis process is simplified by performing a specific system state transformation. It is demonstrated that the width of the layer to which the representative point of the system is driven decreases as the relative degree of the sliding variable gets bigger. It has further been proven that achieving a narrower quasi-sliding mode band width is reflected in reduced state error. Finally, the reaching phase elimination for variables with arbitrary relative degree is considered. This is obtained by implementing a time-varying sliding surface in a finite number of initial time instants. Uniform ultimate boundedness of all state variables is guaranteed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of passivity-based asynchronous sliding mode control for a class of uncertain singular Markovian jump systems with time delay and nonlinear perturbations. The asynchronous control strategy is employed due to the nonsynchronization between the controller and the system modes. Considering the singularity of the system, a novel integral-type sliding surface is constructed, and then the asynchronous sliding controller is synthesized to ensure that the sliding mode dynamics satisfy the reaching condition. Sufficient conditions are presented such that the corresponding sliding mode dynamics are admissible and robustly passive. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Power management of mobile digital systems-on-chip necessitates large voltage regulation performances. DC/DC converters used to supply digital cores are facing stringent constraints with respect to load transients, reference tracking and accuracy. The fast transient response offered by sliding-mode control is well suited to DC/DC converters with fast varying load. Fixed switching-frequency is also mandatory for EMI and noise related issues. Fixed-switching frequency sliding-mode control has been experimented as a multi-loop system. There is a necessity to investigate the stability when multi-loops interact and the parameter set for each loop is quite large. The paper details a methodology for the stability analysis of a frequency-controlled sliding-mode DC/DC converter. The proposed stability analysis takes the possible cross-interactions into account and can be used to optimise the DC/DC controller without the limitations of a non-interaction criterion. As a verification a DC/DC converter is implemented in CMOS 130 nm. Experimental results agree with the analysis main recommendations. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive sliding mode control system using a double loop recurrent neural network (DLRNN) structure is proposed for a class of nonlinear dynamic systems. A new three-layer RNN is proposed to approximate unknown dynamics with two different kinds of feedback loops where the firing weights and output signal calculated in the last step are stored and used as the feedback signals in each feedback loop. Since the new structure has combined the advantages of internal feedback NN and external feedback NN, it can acquire the internal state information while the output signal is also captured, thus the new designed DLRNN can achieve better approximation performance compared with the regular NNs without feedback loops or the regular RNNs with a single feedback loop. The new proposed DLRNN structure is employed in an equivalent controller to approximate the unknown nonlinear system dynamics, and the parameters of the DLRNN are updated online by adaptive laws to get favorable approximation performance. To investigate the effectiveness of the proposed controller, the designed adaptive sliding mode controller with the DLRNN is applied to a $z$ -axis microelectromechanical system gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed methodology can achieve good tracking property, and the comparisons of the approximation performance between radial basis function NN, RNN, and DLRNN show that the DLRNN can accurately estimate the unknown dynamics with a fast speed while the internal states of DLRNN are more stable. [ABSTRACT FROM AUTHOR]

In this paper, a new robust fault-tolerant compensation control method for uncertain linear systems over networks is proposed, where only quantized signals are assumed to be available. This approach is based on the integral sliding mode (ISM) method where two kinds of integral sliding surfaces are constructed. One is the continuous-state-dependent surface with the aim of sliding mode stability analysis and the other is the quantization-state-dependent surface, which is used for ISM controller design. A scheme that combines the adaptive ISM controller and quantization parameter adjustment strategy is then proposed. Through utilizing \mathcal H_\infty control analytical technique, once the system is in the sliding mode, the nature of performing disturbance attenuation and fault tolerance from the initial time can be found without requiring any fault information. Finally, the effectiveness of our proposed ISM control fault-tolerant schemes against quantization errors is demonstrated in the simulation. [ABSTRACT FROM PUBLISHER]

An investigation has been made into the sliding mode control (SMC) problem for singular stochastic Markov systems (SSMSs) in this paper. By using replacement of matrix variables, a new mean square admissibility criterion of SSMSs is proposed first. Based on this admissibility criterion, the desired state-feedback controller is designed to guarantee the closed-loop system to be mean-square admissible. Then, the obtained results given in the form of strict linear matrix inequalities are applied to solve SMC problem of SSMSs. In order to illustrate the workability and applicability of the theoretic results developed, numerical examples are provided. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust passivity-based sliding mode control (SMC) for uncertain singular systems with semi-Markov switching and actuator failures. The attention is focused on designing a common sliding surface to weaken the jumping effect and developing a sliding mode controller to accommodate to actuator faults for passification of the singular semi-Markovian jump system. Based on linear matrix inequality technique, sufficient conditions are derived to ensure the closed-loop system to be stochastically admissible and robustly passive. Then the finite-time reachability of the sliding surface is guaranteed by the proposed SMC law. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

In existing work of sliding mode observers (SMOs) for descriptor systems, a necessary condition is that the system must be infinitely observable. This paper presents a scheme that circumvents that condition, by reformulating the system as a reduced-order system where certain structures in the system matrix are manipulated and certain states are treated as unknown inputs. Following that, an SMO is implemented on the reduced-order system where state and fault estimation can be achieved. Necessary and sufficient conditions of this scheme are also presented. Finally, a simulation example shows the effectiveness of the proposed scheme. [ABSTRACT FROM PUBLISHER]