Finite-time stabilization for a class of stochastic nonlinear systems via output feedback

This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.     

Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions

This paper addresses the problem of output feedback stabilization for a class of time-delay nonholonomic systems. One distinct characteristic or difficulty of this paper is that time-delay exists in polynomial nonlinear growing conditions. Based on input-state-scaling technique, homogeneous domination approach and Lyapunov–Krasovskii theorem, a new output feedback control law which guarantees all the system states converge to the origin is designed. Examples are provided to demonstrate the validness of the proposed approach.     

Further results on global state feedback stabilization of nonlinear high-order feedforward systems

In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved.     

Finite-time consensus of Markov jumping multi-agent systems with time-varying actuator faults and input saturation

This paper gives attention to the issue of finite-time leader-following consensus of nonlinear discrete-time multi-agent systems with Markov jump parameters. A robust fault-tolerant control protocol that takes the effect of time-varying actuator faults and actuator saturation into account is considered for the addressed system. The main purpose of the paper is to design a fault-tolerant controller such that the leader-following consensus of the addressed system is achieved over a prescribed finite-time interval. By using the Lyapunov functional approach, Abel’s lemma and some properties of Kronecker product, a sufficient condition for the existence of fault-tolerant state feedback controller for the addressed system is presented and an explicit parameterization of such a controller is obtained. Eventually, a numerical example along with its simulation results is exploited to reflect the applicability of the proposed design method, wherein the robust performance of controller is exhibited despite the presence of actuator saturation and time-varying actuator faults.     

Finite-time stability and stabilization for stochastic markov jump systems with mode-dependent time delays

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results.     

Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

Decentralized output feedback stabilization for switched stochastic high-order nonlinear systems with time-varying state/input delays

This paper investigates decentralized output feedback stabilization problem for a class of switched stochastic high-order systems with time-varying state/input delays. With the help of coordinate transformations, a scaling gain is incorporated into the observers and controllers for the nominal system. Based on the homogeneous domination approach and stochastic Lyapunov–Krasovskii stability theorem, it is shown that global asymptotic stability in probability of the closed-loop system can be implemented by tuning the scaling gain. Two examples are given to demonstrate the feasibility of the proposed control method.     

Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems

In this paper, the adaptive neural network output-feedback stabilization problem is investigated for a class of stochastic nonlinear strict-feedback systems. The nonlinear terms, which only depend on the system output, are assumed to be completely unknown, and only an NN is employed to compensate for all unknown upper bounding functions, so that the designed controller is more simple than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the closed-loop system can be proved to be asymptotically stable in probability. The simulation results demonstrate the effectiveness of the proposed control scheme.     

Finite-time decentralized adaptive neural constrained control for interconnected nonlinear time-delay systems with dynamics couplings among subsystems

The problem of finite-time decentralized neural adaptive constrained control is studied for large-scale nonlinear time-delay systems in the non-affine form. The main features of the considered system are that 1) unknown unmatched time-delay interactions are considered, 2) the couplings among the nested subsystems are involved in uncertain nonlinear systems, 3) based on finite-time stability approach, asymmetric saturation actuators and output constraints are studied in large-scale systems. First, the smooth asymmetric saturation nonlinearity and barrier Lyapunov functions are used to achieve the input and output constraints. Second, the appropriately designed 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. Note that, due to unknown time-delay interactions and the couplings among subsystems, the controller design is more meaningful and challenging. At last, based on finite-time stability theory and Lyapunov stability theory, a decentralized adaptive controller is proposed, which decreases the number of learning parameters. It is shown that the designed controller can ensure that all closed-loop signals are bounded and the tracking error converges to a small neighborhood of the origin. The simulation studies are presented to show the effectiveness of the proposed method.     

Global adaptive output feedback control for a class of nonlinear time-delay systems

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.     

Anti-windup adaptive PID control design for a class of uncertain chaotic systems with input saturation

In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers.     

一类线性离散时间系统的鲁棒故障检测

研究一类受白噪声影响的线性离散系统的鲁棒故障检测滤波问题。设计基于观测器的残差产生器。利用主元子空间算法。对观测器的参数矩阵进行设计。算例验证了提出方法的有效性。     

Nonlinear stabilization for a class of time delay systems via inverse optimality approach

This paper is devoted to obtain a stabilizing optimal nonlinear controller based on the well known Control Lyapunov-Krasovskii Functional (CLKF) approach, aimed to solve the inverse optimality problem for a class of nonlinear time delay systems. To determine sufficient conditions for the Bellman's equation solution of the system under consideration, the CLKF and the inverse optimality approach are considered in this paper. In comparison with previous results, this scheme allows us to obtain less conservative controllers, implying energy saving (in terms of average power consumption for a specific thermo-electrical process). Sufficient delay-independent criteria in terms of CLKF is obtained such that the closed-loop nonlinear time-delay system is guaranteed to be local Asymptotically Stable. To illustrate the effectiveness of the theoretical results, a comparative study with an industrial PID controller tuned by the Ziegler-Nichols methodology (Z-N) and a Robust-PID tuned by using the D-partition method is presented by online experimental tests for an atmospheric drying process with time delay in its dynamics.     

Robust stabilizing first-order controllers for a class of time delay systems

In this paper, stabilizing regions of a first-order controller for an all poles system with time delay are computed via parametric methods. First, the admissible ranges of one of the controller’s parameters are obtained. Then, for a fixed value of this parameter, stabilizing regions in the remaining two parameters are determined using the D-decomposition method. Phase and gain margin specifications are then included in the design. Finally, robust stabilizing first-order controllers are determined for uncertain plants with an interval type uncertainty in the coefficients. Examples are given to illustrate the effectiveness of the proposed method.