Robust Adaptive Neural Tracking Control for a Class of Perturbed Uncertain Nonlinear Systems With State Constraints

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, robust adaptive neural tracking control is developed for a class of uncertain SISO nonlinear systems in a Brunovsky form with unknown nonlinear dead-zone and unknown control gain & its sign. The design is based on the principle of sliding mode control and the use of Nussbaum-type function in solving the problem of the completely unknown function control gain. A novel description of general nonlinear dead-zone, which makes the control system design possible, is introduced by using the mean value theorem. The approach removes the condition of the equal slope with defined region for the dead-zone. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation for the upper bound of the optimal approximation error and the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded

ABSTRACTThis article investigates the tracking control problem for a class of uncertain nonlinear systems with time‐varying asymmetric state constraints of arbitrary time period. State constraints of arbitrary time period refer to the system states that are constrained during arbitrary finite time and are free for the other time (i.e., unconstrained), it is more common. This article addresses this issue for the first time. A novel shifting function is defined which moves any states or tracking errors out of the constraint area to the desired positions. Then, a barrier Lyapunov function is designed for the tracking error after shifting transformation, which ensures the satisfaction of state constraints. Dynamic surface control is used to avoid the high‐order derivation of functions which solves the complexity problem caused by item explosion in backstepping design. Lastly, a simulation illustration is given to verify the effectiveness and outstanding features of the proposed method. It demonstrates that state constraints of arbitrary time period are satisfied, all signals in the closed‐loop system are ultimately bounded, and the tracking error converges to an adjustable neighborhood of origin.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

Some systems suffer from not only input saturation but also input rate saturation due to special need or actuator limitation. This paper investigates the regulation control of a class of uncertain nonlinear systems with input rate saturation. By transformation, the rate saturation of input can be converted to the state and input constraints of certain linear systems. An LMI based method can then be introduced and improved to solve the transformed problem. The optimized state-feedback controller is robust to parametric uncertainties. It can guarantee the exponential stability of the original system without external disturbances, and can make the state trajectories exponentially converge to a defined region with external disturbances. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

In this paper, an infinite horizon optimal robust guaranteed cost control scheme of a class of continuous-time uncertain nonlinear systems is established based on adaptive dynamic programming. The main idea lies in that the optimal robust guaranteed cost control problem can be transformed into an optimal control problem. Actually, the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to help solving the modified Hamilton-Jacobi-Bellman equation corresponding to the nominal system. Then, an additional stabilizing term is introduced to reinforce the updating process of the weight vector and reduce the requirement of an initial stabilizing control. An example is provided to illustrate the effectiveness of the present control approach.

The problem of memoryless robust stabilization is discussed for a class of nonlinear uncertain systems with time-varying delay. The time-varying delay is assumed to unknown but known bound. The uncertainties are dependent on the delay states and have known bounds. No matching and Lipschitz's boundedness conditions are required. The continuous state feedback controller is proposed based on the Lyapunov direct methods such that the trajectories of the closed-loop nonlinear uncertain time-delay systems are uniformly and ultimately bounded on a compact set of which the diameter can be made arbitrarily large by choosing design parameters. The authors show that several previous results can be considered as a special cases. The effectiveness of the proposed approaches are demonstrated by the simulation results.

This paper addresses the tracking control problem for a class of uncertain nonlinear systems with full state deferred constraints. The constraints considered occur after a period of system operation rather than from the beginning. An attempt has been made to use a shifting function to realize the purpose of deferred constraint. Moreover, the difficulty of asymmetric constraint on states comes from the design on barrier function. Due to this, an unified barrier function is proposed to prevent system states from violating the constraint range, indirectly. Meanwhile, it effectively removes the restriction condition used in existing results that the upper and lower bound signs of constraint functions are the same. Consequently, the goals of tracking a reference signal and state constraints are achieved through the control scheme designed. Theoretical analysis and simulations are presented to demonstrate the efficacy of the proposed control strategy.

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

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

In this paper, a high-gain nonlinear observer based fault detection and diagnosis (FDD) approach is proposed for a general class of nonlinear uncertain systems with measured output probability density functions (PDFs). The objective of the presented FDD algorithm is to use the measured output probability density functions (PDFs) and the input of the system to construct a exponential observer-based residual generator such that the fault can be detected and diagnosed. The main result is given in a constructive manner by developing a novel nonlinear observer, without resort to any linearization. By a coordinates transformation, the design of the proposed observer does not necessitate the resolution of kind of linear matrix inequalities (LMIs) and its expression is explicitly given. The exponential convergence of the errors in the presence of parameters uncertainties is proved to guarantee the fastness of the proposed fault diagnosis scheme. Furthermore, the bound of the estimation errors in the presence the faults is minimized by appropriately choosing the parameters of the presented observer. Finally a simulation example is given to illustrate the efficiency of the proposed fault detection and diagnosis method.

A new robust tracking control approach is proposed for strict-feedback nonlinear systems with state and input constraints. The constraints are tackled by extending the control input as an extended state and introducing an integral barrier Lyapunov function (IBLF) to each step in a backstepping procedure. This extends current research on barrier Lyapunov functions(BLFs)-based control for nonlinear systems with state constraints to IBLF-based control for strict-feedback nonlinear systems with state and input constraints. Since the IBLF allows the original constraints to be mixed with the error terms, the use of IBLF decreases conservatism in barrier Lyapunov functions-based control. In the backstepping procedure, neural networks (NNs) with projection modifications are applied to estimate system uncertainties, due to their ability in guaranteeing estimators in a given bounded area. To facilitate the use of the once-differentiable NNs estimators in the backstepping procedure, the virtual controllers are passed through command filters. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the proposed control.

A new scheme of adaptive fuzzy sliding mode control for a class of uncertain nonlinear systems is presented, which is by incorporating adaptive model tracking control with fuzzy sliding mode control. It cannot only provide the instantaneous response characteristics of tracking error, make system have good control property and strong robustness against parameter variations and external disturbance, but also eliminate the chattering of conventional sliding mode control. The simulation results show the correctness of this scheme.

ABSTRACTThis paper is concerned with the global practical tracking via adaptive output feedback for a class of uncertain nonlinear systems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinearities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high gain is the multiplication of two dynamic gains: one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical example demonstrates the effectiveness of the proposed method.