Quantized feedback adaptive command filtered backstepping control for a class of uncertain nonlinear strict-feedback systems

In this article, an event-triggered robust adaptive dynamic programming (ETRADP) algorithm is developed to solve a class of multiplayer Stackelberg-Nash games (MSNGs) for uncertain nonlinear continuous-time systems. Considering the different roles of players in the MSNG, the hierarchical decision-making process is described as the designed value functions for the leader and all followers, which assist to transform the robust control problem of the uncertain nonlinear system into an optimal regulation problem of the nominal system. Then, an online policy iteration algorithm is formulated to solve the derived coupled Hamilton-Jacobi equation. Meanwhile, an event-triggered mechanism is designed to alleviate computational and communication burdens. Moreover, critic neural networks (NNs) are constructed to obtain the event-triggered approximate optimal control polices for all players, which constitute the Stackelberg-Nash equilibrium of the MSNG. By using Lyapunov's direct method, the stability of the closed-loop uncertain nonlinear system is guaranteed under the ETRADP-based control scheme in the sense of uniform ultimate boundedness. Finally, a numerical simulation is provided to demonstrate the effectiveness of the present ETRADP-based control scheme.

Cascade control for a class of uncertain nonlinear systems: a backstepping approach

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In this paper, by incorporating this dynamic structure control technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of explosion of complexity inherent in the existing method. Taking the neural network as a model of the system, control signals are directly obtained by minimizing the cumulative differences between a setpoint and output of the model. The applicability in nonlinear system is demonstrated by simulation experiments.

International audience

Differential games, partial-state stabilization, and model reference adaptive control

This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

This paper proposes a robust adaptive fuzzy control scheme for the uncertain nonlinear time-delay systems preceded by an unknown dead-zone. It is well known that time-delay and dead-zone characteristics are frequently encountered in various engineering systems. The dead-zone phenomena may occur in various components of control systems including sensors, amplifiers and actuators, especially in pneumatic valves, in electric servo motors and in hydraulic components. On the other hand, the time-delay phenomena are quite commonly found in chemical process, hydraulic systems and pneumatic systems. In most practice motion systems, the dead-zone characteristics are usually poorly known and may vary with time. Therefore, by using a description of a dead-zone and exploring the properties of this dead-zone model intuitively and mathematically, a robust adaptive fuzzy control method is presented without constructing the dead-zone inverse. According to some adaptive laws, the unknown nonlinear functions of the plant are approximated by the fuzzy logic system. Based on Lyapunov stability theorem, the proposed robust adaptive fuzzy control scheme can guarantee the robust stability of the whole closed-loop nonlinear time-delay system with an unknown dead-zone in the actuator and obtain good tracking performance as well. Finally, an example and simulation results are provided to show the efficiency of the proposed control method.

Adaptive fault compensation control for nonlinear uncertain fractional-order systems: Static and dynamic event generator approaches

An analytic model predictive control method is proposed to deal with a class of bounded uncertain nonlinear systems. Firstly, it can be redefined as the nominal system with uncertain model form, and the optimal control law with uncertainties is obtained. Derivation shows that the obtained control law is bounded and the analytic model predictive control that eliminates uncertainties is then able to acquire utilizing the boundary value. Apply Routh-Hurwitz criterion theory to prove the stability of the closed-loop system, therefore, provide the selection conditions of controller parameter. The analytic model of the original system predictive control in the process of solving the uncertainty problem is then converted into a deterministic problem. The controller can be realized without extra compensation of uncertainties in the process of controlling nonlinear systems. Finally, the article is able to introduce the design of analytic model predictive control which were achieved by application in the ship rudder roll stabilization controller design. The simulation results show that, under two different sea conditions, the proposed method has good robustness and control effects, comparing to the model that does not consider the uncertain predictive control and generalized predictive control of the analytic model. And it is proved that the control method has important theoretical significance and engineering application values.

In this paper the problem of prescribed tracking performance for a class of nonlinear systems in the presence of uncertain dynamics and state quantization is addressed. The proposed controller is capable of not only establishing stability for the closed-loop system but also guaranteeing predefined performance bounds on the transient and steady-state error performance. The control design procedure incorporates only quantized measurements, is model-free and of low-complexity, with respect to the specifications of the quantizer employed for the output measurement. For the quantization, static uniform-hysteretic quantizers are implemented, to simplify further the control solution, and guarantee the well-posedness of the closed-loop and the chattering-free quantization performance. Simulation studies clarify all design aspects and illustrate its effectiveness.

On Switched Controller Design for Robust Control of Uncertain Polynomial Nonlinear Systems Using Sum of Squares

This paper establishes an exponential H ∞ stabilisation method for uncertain nonlinear system with time-varying delay and external disturbance via non-fragile memory-based saturated controller. Based on the construction of an augmented Lyapunov–Krasovskii functional (LKF) and distributed-delay polytopic method, some delay-dependent and delay-derivation-dependent criteria to ensure the exponential H ∞ stabilisation of the nonlinear system are derived in terms of linear matrix inequalities (LMIs). Then, the optimisation problems with reduced conservatism concerning the admissible initial condition set are specifically formulated. Subsequently, simulation results are presented to demonstrate the validity and practicality of the suggested method.

This paper has proposed a novel class of the stable discrete-time multilayer perceptron (MLP) neural observer for a class of discrete-time multiple-input multiple-output uncertain nonlinear systems. It is trained online and is used to estimate the states of the system especially when there is no prior knowledge about the dynamics of the system and can be applied as a basis for designing an intelligent control. The weight updating for the MLP is the developed backpropagation algorithm. Online training, convergence of the observer error to neighborhood of origin, robustness against uncertainties and disturbance, low computational expense and fast convergence rate are the main qualities of the suggested method. Lyapunov’s direct method is used to guarantee the stability of the proposed system. To demonstrate the performance of the discrete-time MLP observer, two discrete-time nonlinear dynamic systems are simulated in MATLAB/Simulink. Simulation results confirm the proficiency of the system even at different operating conditions and the presence of disturbance and measurement noise.