Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.     

Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control

In this paper, we discussed the robust finite-time stability of conic type nonlinear systems with time varying delays. Some novel conditions are derived to design a linear quadratic regulator (LQR) based sliding mode control (SMC) by proposing an integral switching surface. The sufficient conditions are derived for the considered nonlinear system using Lyapunov–Krasovskii stability theory and linear matrix inequality (LMI) approach. The proposed conditions can be solved using some standard numerical packages. Finally, a practical example is provided to validate the advantages and effectiveness of the proposed results.     

Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems

This paper precedes chaos control of fractional-order chaotic systems in presence of uncertainty and external disturbances. Based on some basic properties on fractional calculus and the stability theorems, we present a hybrid adaptive intelligent backstepping-sliding mode controller (FAIBSMC) for the finite-time control of such systems. The FAIBSMC is proposed based on the concept of active control technique. The asymptotic stability of the controller is shown based on Lyapunov theorem and the finite time reaching to the sliding surfaces is also proved. Illustrative and comparative examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.     

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.     

Adaptive fault-tolerant control for continuous-time Markovian jump systems with signal quantization

This paper investigates the adaptive fault-tolerant control problem for a class of continuous-time Markovian jump systems with digital communication constraints, parameter uncertainty, disturbance and actuator faults. In this study, the exact information for actuator fault, disturbance and the unparametrisable time-varying stuck fault are totally unknown. The dynamical uniform quantizer is utilized to perform the design work and the mismatched initializations at the coder and decoder sides are also considered. In this paper, a novel quantized adaptive fault-tolerant control design method is proposed to eliminate the effects of actuator fault, parameter uncertainty and disturbance. Moreover, it can be proved that the solutions of the overall closed-loop system are uniformly bounded, which is asymptotically stable almost surely. Finally, numerical examples are provided to verify the effectiveness of the new methodology.     

Sampled-data control for continuous-time Markovian jump linear systems via a fragmented-delay state and its state-space model

This paper considers a stability analysis problem for continuous-time Markovian jump linear systems under aperiodic samplings which are represented as Markovian jump linear systems with input delay. For the systems, this paper constructs a Lyapunov functional by utilizing a fragmented-delay state, which is defined between the last sampling instant and the present time, and a new state space model of the fragmented state. Based on the Lyapunov functional, a stability criterion is derived in terms of linear matrix inequalities by using reciprocally convex approach and integral inequality. Here, the reciprocally convex approach and integral inequality are associated not only with the current state, the delayed state, and the maximum-admissible delay state, but also with the fragmented-delay state. The simulation result shows the effectiveness of the proposed stability criterion.     

Finite-time sliding mode attitude control for rigid spacecraft without angular velocity measurement

The continuous finite-time nonsingular terminal sliding mode (NTSM) attitude tracking control for rigid spacecraft is investigated. Firstly, a finite-time attitude controller combined with a new adaptive update law is designed. Different from existing controllers, the proposed controller is inherently continuous and the chattering is effectively reduced. Then, an adaptive model-free finite-time state observer (AMFFTSO) and an angular velocity calculation algorithm (AVCA) are developed to estimate the unknown angular velocity. The unique feature of the proposed method is that the finite-time estimation of angular velocity is achieved and no prior knowledge of quaternion derivative upper bound is needed. Next, based on the estimated angular velocity, a finite-time attitude controller with only attitude measurement is developed. Finally, some simulations are presented and the effectiveness of the proposed control scheme is illustrated.     

Finite-time control for periodic systems with Markov jump sensor nonlinearities and random input gains

Finite-time control for periodic systems with sensor nonlinearities and random input gains is addressed in this work. The variation of sensor nonlinearities is modeled by a Markov chain, and a stochastic variable is used to describe the influence of the actuator. A mode- and sensor nonlinearity-dependent non-fragile controller is designed to improve the performance and the non-fragility of the controller. The finite-time boundedness of the closed-loop system is ensured by a sufficient condition, the corresponding controller is then designed. Finally, the effectiveness of the developed results is illustrated by a numerical example.     

Sparsely distributed sliding mode control for interconnected systems

This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems’ information as well as its own local information. As the local controllers/observers have access to some other sub-systems’ states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.     

State feedback control for stochastic Markovian jump delay systems based on LaSalle-type theorem

This paper investigates the problem of stochastic stability and stabilization of stochastic Markovian jump delay systems (SMJDSs) based on LaSalle theorem. The time delays are assumed to be time-varying and numerous stochastic disturbances are considered. Attention is focused on the design of the mode-dependent state feedback controller for SMJDSs based on LaSalle theorem such that the closed-loop SMJDSs are almost surely asymptotically stable. The sufficient conditions for the solvability of the state feedback control problem are obtained in terms of linear matrix inequalities (LMIs). When the LMIs are feasible, the desired state feedback controller is also given. Two numerical examples including the vertical take-off and landing (VTOL) helicopter system are employed to demonstrate the effectiveness and usefulness of the method proposed in this paper     

Event-triggered passive control for Markovian jump discrete-time systems with incomplete transition probability and unreliable channels

This paper investigates the passivity of Markovian jump discrete-time systems (MJDTSs) with channel fading via event-triggered state feedback control. First, the concerned MJDTSs contain infinitely distributed delays and switching rules with partially known transition probability (TP) information. Next, the fading channel, as an unreliable channel, is introduced into MJDTSs to better reflect the engineering practice in networked environment. Due to the present of channel fading, a series of random variables satisfying some certain probability density functions (PDFs) will be obstacles in the process of proof. Then, an event-triggered controller is designed for MJDTSs with channel fading and incomplete transition probability (ITP) for the first time. Thanks to this event-triggered mechanism, the state feedback control could greatly reduce energy consumption during transmission. Subsequently, under the above controller, we obtain some novel sufficient criteria in the form of linear matrix inequalities (LMIs) to ensure the passivity of closed-loop system. Finally, some simulation results are provided to demonstrate the feasibility and effectiveness of the proposed theoretical method.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Necessary and sufficient criteria for asynchronous stabilization of Markovian jump systems

This paper is concerned with asynchronous stabilization for a class of discrete-time Markovian jump systems. The mode of designed controller is considered to be not perfectly synchronous with the activated mode of the Markovian jump system. In order to achieve the asymptotic stability with asynchronous controller, a conditional probability is introduced to describe the asynchronism of system and controller modes, which is dependent on the active system mode. Besides, due to the difficulty in acquiring all the mode transition probabilities in practice, the transition probabilities of the Markovian jump system and the controllers are supposed to be partially unknown. A necessary and sufficient condition is developed to guarantee the stochastic stability of the resultant closed-loop system and further extended to asynchronous stabilization with partially known transition probabilities. Finally, the effectiveness and advantages of the proposed methods are demonstrated by two illustrative examples.     

Reliable control for event-triggered singular Markov jump systems with partly unknown transition probabilities and actuator faults

In this paper, the problem of reliable controller design for event-triggered singular Markov jump systems with partly known transition probabilities, nonlinear perturbations and actuator faults is studied. To mitigate the burden of data transmissions over network, two event-triggered schemes with different triggering conditions are introduced. The switch law between the two event-triggered schemes is governed by a random variable with Bernoulli distribution. Taking nonlinear perturbations and actuator faults into account, the resulting closed-loop system is converted into a time-delay singular Markov jump system with partly known transition probabilities. Sufficient conditions of stochastically admissible for the resulting closed-loop system are obtained in terms of a group of linear matrix inequalities. The co-design of desirable reliable controller and weighting matrices of event-triggered schemes is presented. Finally, two numerical examples are given to show the effectiveness of the developed results.     

Event-triggered sliding mode control of uncertain switched systems under denial-of-service attacks

This study is concerned with the event-triggered sliding mode control problem for a class of cyber-physical switched systems, in which the Denial-of-Service (DoS) attacks may randomly occur according to the Bernoulli distribution. A key issue is how to design the output feedback sliding mode control (SMC) law for guaranteeing the dynamical performance of the closed-loop system under DoS attacks. To this end, an event-triggered mechanism is firstly introduced to reduce the communication load, under which the measurement signal is transmitted only when a certain triggering condition is satisfied. An usable output signal for the controller is constructed to compensate the effect of unmeasured states and DoS attacks. And then, a dynamic output feedback sliding mode controller is designed by means of the attack probability and the compensated output signals. Both the reachability and the mean-square exponential stability of sliding mode dynamics are investigated and the corresponding sufficient conditions are obtained. Finally, some numerical simulation results are provided.     

Stability of Markov jump systems with quadratic terms and its application to RLC circuits

The paper presents results for the second moment stability of continuous-time Markov jump systems with quadratic terms, aiming for engineering applications. Quadratic terms stem from physical constraints in applications, as in electronic circuits based on resistor (R), inductor (L), and capacitor (C). In the paper, an RLC circuit supplied a load driven by jumps produced by a Markov chain—the RLC circuit used sensors that measured the quadratic of electrical currents and voltages. Our result was then used to design a stabilizing controller for the RLC circuit with measurements based on that quadratic terms. The experimental data confirm the usefulness of our approach.     

Sliding mode output-feedback control of discrete-time Markov jump systems using singular system method

The issue of adaptive sliding mode controller design via output knowledge is studied for discrete-time Markov jump systems in this paper by means of using singular system scheme. To force the system state onto the sliding motion, an appropriate switching surface depended on the system output is established. Meanwhile, the reachability of the sliding manifold is guaranteed by synthesizing the robust sliding mode controller and adaptive sliding mode controller for the accessible and inaccessible upper bounds of sliding patch, respectively. By using Lyapunov functional technique, sufficient criteria to guarantee the sliding motion to be stochastically admissible are proposed. Then the reachability conditions of the predesigned switching surface are developed. Finally, simulation results are provided to illustrate the effectiveness of the proposed approach.     

Robust sliding mode control for stochastic singular Markovian jump systems with unmatched one-sided Lipschitz nonlinearities

This paper investigates sliding mode control of stochastic singular Markovian jump systems with nonlinearity. The unmatched nonlinearity satisfies one-sided Lipschitz condition and quadratically inner-boundedness. In term of a new technical variable transformation, sufficient conditions are developed for nonlinear stochastic singular Markovian jump systems constrained on sliding manifold to guarantee stochastic admissibility and uniqueness of solution based on implicit function theorem. The sliding mode control law by which the trajectories of system can be compelled to the predefined sliding surface in finite time no matter what initial state value is, is synthesized. The derivative singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily.The technical treatment of the nonlinear matrix term avoids the classification discussion of sliding mode controller design. Convex optimization problems subject to linear matrix inequalities are formulated to optimize the desired indexes of interest. Finally, the effectiveness of the proposed approach is illustrated by a numerical example and a practical example.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.