Adaptive tracking control for a class of stochastic nonlinearly parameterized systems with time-varying input delay using fuzzy logic systems

A robust controller is developed for uncertain, second-order nonlinear\nsystems subject to simultaneous unknown, time-varying state delays and known,\ntime-varying input delays in addition to additive, sufficiently smooth\ndisturbances. An integral term composed of previous control values facilitates\na delay-free open-loop error system and the development of the feedback control\nstructure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals\nguarantees uniformly ultimately bounded tracking under the assumption that the\ndelays are bounded and slowly varying.\n

In this paper, the problems of exponential stability and control design for switched systems with time-varying delay are investigated. Under a class of switching signals counting with average dwell time, a new less conservative stability condition is proposed for the systems. To facilitate controller design for the switched systems with time-varying input delay, a new state transformation method is developed, with which the non-linear term in matrix inequality is removed. The method is also applicable to the existing stability conditions for controller design, while the existing methods may be not able to obtain computational control procedures from the stability conditions. In this paper, the computational algorithms are established for the stability analysis and control synthesis. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed techniques.

In this paper, a novel online tube model predictive control (Tube-MPC) method is proposed for flexible hypersonic vehicle with time-varying input delay. The polytopic linear parameter varying (LPV) model with time-varying input delay is established and further transformed into a polytopic LPV delay-free model by input delay model transformation (IDMT). Since the flexible states cannot be measured accurately due to vehicle body deformation, the polytopic Luenberger observer is developed. To reduce control conservatism, substitute observations are used to replace the actually observed states such that the new reduced control error invariant set (CEI) is generated. On the basis, the Tube-MPC controller is designed, where the offline robust feedback control law and the online nominal control law are devised via linear matrix inequality (LMI) separately. For figuring out the invariant set of nominal control, an offline-online synthesized method is proposed by combining interpolation-based offline computation (IOFC) with substitute observation-based online computation (SOOC). In IOFC, the sequences of observation error invariant set (OEI) and CEI are computed offline iteratively and further interpolated so as to reduce online computation burden. The online judgement and update mechanism is proposed in SOOC. When the observed states enter the expanded invariant set constructed by the interpolated OEI and CEI, the substitute observation-based control error invariant set (SOCEI) will be calculated online and accordingly the nominal control law can also be updated. The simulation results verify the proposed control method’s effectiveness for flexible hypersonic vehicle with time-varying input delay.

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

This paper investigates the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with time-varying input delay. The drift and diffusion terms satisfy the linear growth condition and are dependent on unmeasurable states and the delayed input. First, we use a change of coordinates to introduce a scaling gain into the system. Then, based on the high-gain observer technique, a delay-free output feedback controller with the scaling gain is developed. Based on the Lyapunov–Krasovskii method and the idea of feedback domination, it is shown that the closed-loop system can be rendered globally asymptotically stable in probability via appropriately choosing the scaling gain. Finally, two examples are presented to illustrate the effectiveness of the proposed scheme.

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

In this paper, a dynamic decoupling approach is proposed to improve the robust Takagi-Sugeno (T-S) fuzzy model-based control to cope with system uncertainty, input actuator nonlinearity, and input time delay. First, the basic dynamic decoupling concept is introduced by involving virtual input dynamics, such that the system uncertainty and control input are decoupled in each fuzzy rule. This leads to simplified linear matrix inequality (LMI) conditions. Next, the dynamic decoupling approach is extended to controlling uncertain systems with input actuator nonlinearity (e.g., saturation, quantization, dead-zone, etc.) or time-varying input delay. Due to the decoupling between uncertainty, actuator nonlinearity, and input delay, more relaxed stability conditions are obtained for the asymptotic stability and H ∞ control performance. Furthermore, the limit on the initial condition is removed when considering input saturation. Larger and faster time-varying state and input delays are allowed under fewer LMIs. Finally, to show the advantages of the developed control method, numerical simulations are carried out on an inverted pendulum (subject to either the saturation, quantization, or delay input), a delay mass-spring-damper system, and a delay truck-trailer system.

Motorized functional electrical stimulation (FES) cycling has been demonstrated to have numerous health benefits for individuals suffering from neurological disorders. FES-cycling is usually designed to track the desired trajectories in real time. However, there are input delays between the exertion of the stimulation and the corresponding muscle contraction that potentially destabilize the system and undermine training efforts. Meanwhile, muscle fatigue gives rise to a time-varying input delay and decreased force. Moreover, switching between FES and motor control can be chattering and destabilizing owing to the high frequency. This article constructs Lyapunov-Krasovskii functionals to analyze the stability and robustness of the nonlinear cycling system with time-varying input delay. A new average dwell time condition is then provided to ensure the input-to-state stability of the considered systems. Finally, numerical simulations are illustrated to verify the effectiveness of the developed controller.

This paper is concerned with the problem of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control of nonlinear stochastic systems with time-varying interval delay. Firstly, a novel kind of fuzzy model, stochastic fuzzy hyperbolic model (SFHM), is proposed to represent a class of nonlinear stochastic systems with time-varying interval delay. The SFHM is a overall nonlinear stochastic model, which is much fitter for the nonlinear multivariable plant whose expert knowledge is difficult to find. The identification of SFHM is more convenient than that of stochastic T-S fuzzy model. Specifically, it also can be seen as a neural network model and we can learn the model parameters by the learning method of neural network. Secondly, delay-range-dependent and delay-derivative-range-dependent criteria on stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance are developed for the SFHM by using new Lyapunov-Krasovskii functionals and improved free-weighting matrix technique for the SFHM case. Finally, simulation results show the validity of the proposed method.

This manuscript considers the finite time adaptive neural tracking control problem for a class of the nonstrict-feedback stochastic nonlinear systems with Bouc-Wen hysteresis input. During the design process, a Bouc-Wen model is first adopted to obtain the input hysteresis phenomenon. By fusion with the backstepping technique and the neural network approximation capability, the unknown nonlinearities are coped with, a constructive finite time adaptive neural network control strategy is proposed. Furthermore, the finite-time mean square stability of stochastic nonlinear systems is proved, and at last the effectiveness of the proposed control strategy is validated by the simulations.

This paper investigates the fusion of unknown dead-zone nonlinearity with adaptive fuzzy control techniques in face of nonlinear time-delayed systems. Control design achieved by using the backstepping recursive method and Fuzzy logic systems in Mamdani type is used to approximate the unknown nonlinear functions, and Lyapunov-Krasovskii functionals are used to compensate the effect of delay term. Based on Lyapunov stability theory and Theorem 1, the proposed adaptive fuzzy controller guarantees that all the closed-loop signals are semi-globally uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the Validity of the theoretical results.

Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay

A delay decomposition approach to [formula omitted] filter design for stochastic systems with time-varying delay

Adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with non-lower triangular structure

Robust backstepping control of uncertain nonlinear systems with unknown time-varying input delay