T-S fuzzy tracking control of nonlinear constrained time-delay systems using a reference-management approach

A new control design approach is proposed for a class of nonlinear systems expressed by Takagi–Sugeno (T-S) fuzzy model, considering several objectives including robustness against input time-varying delay, input constraint satisfaction, and reference tracking. The proposed controller is designed on the basis of an augmented model, Lyapunov–Krasovskii functional, linear matrix inequality (LMI) tools, and parallel distributed compensation (PDC) approach. Proof of the input-to-state stability (ISS) criterion is provided for the error dynamics. Input constraint satisfaction is performed using a reference-management algorithm based on the linearized closed-loop system from the reference input to the constrained variables. In order to illustrate the effectiveness of the proposed control approach, simulations are performed on three practical examples, including a flexible-joint robot and a continuous stirred tank reactor (CSTR).     

Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.     

Robust unified dissipativity vibration control design for offshore steel jacket platform in ocean environments under self-excited nonlinear wave force

This paper addresses the challenge of delayed proportional integral control (DPIC) of an offshore steel jacket platform (OSJP) subjected to a self-excited nonlinear wave force and structural uncertainty using the unified criteria. By introducing discrete and distributed state delays in the control input, a DPIC was established to stabilize the OSJPs. The goal of this study is to design a proper controller that will stabilize the dynamic of an OSJP while subjected to structural uncertainty and nonlinear wave force. The OSJP is investigated as a nonlinear dynamics with mixed state delays, allowing us to study its robust asymptotic stability using the Lyapunov-Krasovskii function (LKF) in the context of the extended dissipativity performance index. A novel closed-loop system-based stability criterion is derived as a result of using tighter integral inequalities to estimate the upper bounds of the delay and influential control gains can be achieved if a set of linear matrix inequalities (LMIs) is checked by simulation results, that the proposed control scheme can significantly improve the control’s performance. Finally, it was demonstrated that the proposed control approach is more effective and multi-dynamic performances have been illustrated through the comparisons to previously published results in the literature.     

Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H_∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H_∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H_∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.     

Decentralized adaptive neural control for interconnected stochastic nonlinear delay-time systems with asymmetric saturation actuators and output constraints

This paper investigates the problem of decentralized adaptive backstepping control for a class of large-scale stochastic nonlinear time-delay systems with asymmetric saturation actuators and output constraints. Firstly, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are designed to ensure that the output parameters are restricted. Secondly, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. At last, based on Lyapunov stability theory, a decentralized adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters. It is shown that the designed controller can ensure that all the closed-loop signals are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are provided to show the effectiveness of the proposed method.     

Observer-based adaptive dynamic surface control of time-delayed non-strict systems with input nonlinearities

This paper proposes an adaptive dynamic surface controller for uncertain time-delay non-strict nonlinear systems with unknown control direction and unknown dead zone. To this end, the problem of uncertainty in nonlinear terms of the overall system is managed such that the estimation of these terms is obtained by applying a fuzzy logic, which is established based on an adaptive approach. A particular observer is then designed to approximate the immeasurable states. Furthermore, to overcome the delay issue in the system, the Lyapunov Krasovskii functional is used to achieve design conditions for dynamic surface control. Moreover, the breach of the output in the system is addressed by employing a Barrier Lyapunov Function. Then, with the aim of the designed controller, the stability of the closed-loop system is ensured such that all states are limited, and the errors are semi-globally uniformly ultimately bounded (SGUUB). Finally, as an illustration of the effectiveness of the proposed controller, a practical simulation is provided.     

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.     

Network-based PI control for output tracking of continuous-time systems with time-varying sampling and network-induced delays

For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.     

Output feedback control with performance recovery analysis for a class of time-delay nonlinear systems

A class of nonlinear systems is considered in this paper which contains multiple time-varying delays and additional disturbances. Motivated by a robust model-free state-feedback controller, an observer-based output-feedback controller is designed to achieve uniformly ultimately bounded tracking. A high-gain-like observer is designed to estimate the unmeasurable current states utilizing the delayed output, and the estimated states are further used to facilitate the development of the output-feedback controller. The control input is saturated to avoid the side effects resulting from the high-gain-like observer’s peaking phenomenon. Under some sufficient conditions, it is proved that the saturation of the controller will no longer take place after a specific time, and both the estimation error and the tracking error will be uniformly ultimately bounded. In the stability analysis, Lyapunov–Krasovskii functionals are implemented to alleviate the difficulties resulting from the delays. Relationships among the delays, the desired trajectories, and the maximal tolerable error are identified. Behaviors of the closed-loop system under different observation and control gains are also analyzed. A two-link revolute robotic arm is taken as an example to conduct a series of simulations, and the results show that the output-feedback controller can recover the performance of the corresponding state-feedback controller.     

Decentralized adaptive output-feedback control of interconnected nonlinear time-delay systems using minimal neural networks

This paper presents a minimal-neural-networks-based design approach for the decentralized output-feedback tracking of uncertain interconnected strict-feedback nonlinear systems with unknown time-varying delayed interactions unmatched in control inputs. Compared with existing approximation-based decentralized output-feedback designs using multiple neural networks for each subsystem in lower triangular form, the main contribution of this paper is to provide a new recursive backstepping strategy for a local memoryless output-feedback controller design using only one neural network for each subsystem regardless of the order of subsystems, unmeasurable states, and unknown unmatched and delayed nonlinear interactions. In the proposed strategy, error surfaces are designed using unmeasurable states instead of measurable states and virtual controllers are regarded as intermediate signals for designing a local control law at the last step. Using Lyapunov stability theorem and the performance function technique, it is shown that all signals of the total controlled closed-loop system are bounded and the transient and steady-state performance bounds of local tracking errors can be preselected by adjusting design parameters independent of delayed interactions.     

Finite-time stabilization of continuous-time switched positive delayed systems

This paper deals with the problems of finite-time stability and stabilization for continuous-time switched positive linear time-delay systems under mode-dependent average dwell time switching signals. First, finite-time stability conditions are established by constructing an multiple piecewise copositive Lyapunov–Krasovskii functional. Then, finite-time stabilization is achieved by designing a state-feedback controller in the form of linear programming. This numerical construction approach proposed for controller cancels the restriction of the multiple piecewise copositive Lyapunov–Krasovskii functional on controllers, which can decrease the conservatism. Finally, two numerical examples are given to show the advantages of our methods.     

Event-based dynamic output-feedback controller design for networked control systems with sensor and actuator saturations

This paper is concerned with the problem of event-triggered dynamic output-feedback H_∞ control for networked control system with sensor and actuator saturations. The event-triggered scheme combined with sensor saturation is first introduced to judge whether the newly sampled signal should be transmitted to the dynamic output-feedback controller or not. Under this scheme, the concurrent closed-loop system is first modeled as a control system with an interval time-varying delay and nonlinear items. Through constructing the Lyapunov–Krasovskii functional and employing linear matrix inequality approach, sufficient conditions for H_∞ asymptotical stability are derived for the networked control system; furthermore, under the above stability condition, a dynamic output-feedback controller and the corresponding event-triggered parameters are co-designed through linear matrix inequality approach. Lastly, a numerical example is employed to prove the practical utility of this method.     

Resilient sampled-data control design for singular networked systems with random missing data

This paper proposes an active resilient control strategy for singular networked control systems with external disturbances and missing data scenario based on sampled-data scheme. To characterize the missing data scenario, a stochastic variable satisfying Bernoulli distributed white sequence is introduced. Based on this scenario, in this paper, two different models are proposed. For both the models, by using Lyapunov–Krasovskii functional approach, which fully uses the available information about the actual sampling pattern, some sufficient conditions in terms of linear matrix inequalities (LMIs) are separately obtained to guarantee that the resulting closed-loop system is admissible and strictly dissipative with a prescribed performance index. In particular, Jensen’s and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results. Then, if the obtained LMIs are feasible, the corresponding parameters of the designed resilient sampled-data controller are determined. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed control design technique.     

Adaptive output-feedback control for nonlinear time-delay systems in pure-feedback form

The main contribution of this paper is to develop an adaptive output-feedback control approach for a class of uncertain nonlinear systems with unknown time-varying delays in the pure-feedback form. Both the non-affine nonlinear functions and the unknown time-varying delayed functions related to all state variables are considered. These conditions make the controller design difficult and challenging because the output-feedback controller should be designed using only the output information. In order to overcome these conditions, we design an observer-based adaptive dynamic surface controller where the time-delay effects are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique using neural networks. A first-order filter is added to the control input to avoid the algebraic loop problem caused by the non-affine structure. It is proved that all the signals in the closed-loop system are semi-globally uniformly bounded and the tracking error converges to an adjustable neighborhood of the origin.     

Linear output-feedback-based semi-global stabilization for switched nonlinear time-delay systems

This paper focuses on the problem of semi-global output-feedback stabilization for a class of switched nonlinear time-delay systems in strict-feedback form. A switched state observer is first constructed, then switched linear output-feedback controllers for individual subsystems are designed. By skillfully constructing multiple Lyapunov–Krasovskii functionals and successfully solving several troublesome obstacles, such as time-varying delay and switching signals and nonlinearity in the design procedure, the switched linear output-feedback controllers designed can render the resulting closed-loop switched system semi-globally stabilizable under a class of switching signals with average dwell time. Furthermore, under some milder conditions on nonlinearities, the semi-global output-feedback stabilization problem for switched nonlinear time-delay systems is also studied. Simulation studies on two examples, which include a continuous stirred tank reactor, are carried out to demonstrate the effectiveness of the proposed approach.     

Stabilization for time-delay nonlinear systems with unknown time-varying control coefficients

A control scheme based on dynamic gains is proposed for the time-varying nonlinear time-delay systems with unknown control coefficients. A class of Nussbaum functions are introduced to deal with the problem of unknown control directions. Dynamic gains technique and Lyapunov–Krasovskii functional are developed to handle the time delays in nonlinear system. It is shown that the system state is regulated to origin asymptotically, and the boundedness of all closed-loop signals is guaranteed. Simulation results are provided to demonstrate the effectiveness of the proposed methodology.     

A new robust fault-tolerant controller for self-repairing flight control system

A new robust fault-tolerant controller scheme integrating a main controller and a compensator for the self-repairing flight control system is discussed. The main controller is designed for high performance of the original faultless system. The compensating controller can be seen as a standalone loop added to the system to compensate the effects of fault guaranteeing the stability of the system. A design method is proposed using nonlinear dynamic inverse control as the main controller and nonlinear extended state observer-based compensator. System robustness is greatly improved by using the new configuration controller. The stability of the whole closed-loop system is analyzed. Feasibility and validity of the new controller is demonstrated with an aircraft simulation example.     

Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control

This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.     

Output feedback control for a class of high-order nonholonomic systems with complicated nonlinearity and time-varying delay

This paper considers the output feedback control problem for high-order nonholonomic time-delay system. Remarkably, the studied system allows the polynomial time-delay growing conditions. Moreover, the applicable power ranges of nonlinear drift and diffusion terms are further relaxed to be a interval rather than a fix point. By choosing a new Lyapunov–Krasovskii (L–K) functional, and by modifying the adding a power integrator method, a delay-independent output feedback controller is designed such that the system is globally asymptotically stable. A simulation example is given to show the validity of the proposed theory.     

Robust integral backstepping control for sensorless IPM synchronous motor controller

In this paper, a sensorless speed control for interior permanent magnet synchronous motors (IPMSM) is designed by combining a robust backstepping controller with integral actions and an adaptive interconnected observer. The IPMSM control design generally requires rotor position measurement. Then, to eliminate this sensor, an adaptive interconnected observer is designed to estimate the rotor position and the speed. Moreover, a robust nonlinear control based on the backstepping algorithm is designed where an integral action is introduced in order to improve the robust properties of the controller. The stability of the closed-loop system with the observer–controller scheme is analyzed and sufficient conditions are given to prove the practical stability. Simulation results are shown to illustrate the performance of the proposed scheme under parametric uncertainties and low speed. Furthermore, the proposed integral backstepping control is compared with the classical backstepping controller.