Strict-feedback Nonlinear Systems Research Articles

Event-Triggered Backstepping Control of Fractional-Order Chaotic Systems with Dead Zone Via Disturbance Observer

This paper comes up with an adaptive event-triggered tracking control scheme for a kind of fractional-order strict feedback nonlinear systems with actuator dead-zone inputs and uncertain external disturbances. The presented strategy can overcome the defect in standard backstepping control scheme which leads to the “explosion of complexity” problem of virtual signals, and strengthen the transmission efficiency by an event-triggered scheme. An error compensation mechanism is presented for promoting the tracking accuracy and reducing the effect filter error. The designed controller guarantees that the tracking error converges into a small neighborhood near the origin, and all closed-loop signals are bounded. Moreover, Zeno behavior will be avoided. The numerical simulation is given to verify the accuracy and effectiveness of the designed technique.

Predefined-time adaptive fuzzy control for nonlinear output constraint systems with unknown backlash-like hysteresis via command filtering

In this article, the predefined-time adaptive fuzzy control problem for strict-feedback nonlinear systems with asymmetric time-varying output constraint and unknown backlash-like input hysteresis is considered. An innovative predefined-time adaptive control method, in which utilises unified barrier function (UBF) to deal with the output constraint problem and adopts a differential equation to represent the unknown backlash-like hysteresis, is presented by combining a novel command filter with backstepping technology. Fuzzy logic systems (FLSs) are employed to estimate the unknown nonlinearities. Moreover, by designing appropriate parameters, the constructed control strategy ensures that all signals are predefined-time bound and the tracking error stays in a small neighbourhood adjacent zero. Ultimately, two simulation examples are given to prove the effectiveness of the presented control algorithm.

Adaptive predefined-time consensus for nonlinear multi-agent systems with input delay and performance constraints

This paper investigates the predefined-time tracking consensus issue for a class of non strict-feedback nonlinear multi-agent systems (MASs) under input delay and error performance constraints by adaptive backstepping control strategy. Firstly, the impact of input delay is eliminated by Pade approximation. With the help of an intermediate state variable, the considered MASs with input delay are revised as the independent-delay systems. Secondly, under constrained distributed error and corrected nth virtual error, the ln-type barrier Lyapunov function (BLF) is adopted to solve the error performance constrains and reduce the complexity of differentiation. Meanwhile, an adaptive predefined-time controller is designed to realize the tracking purpose by backstepping method and radial basis function neural networks (RBFNNs) approximation. Finally, a numerical simulation example and a practical application are presented to test the effectiveness for the proposed control strategy.

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Adaptive finite time command filtered backstepping control scheme of uncertain strict-feedback nonlinear systems

This paper proposes an adaptive finite time command filtered backstepping control scheme for single‐input and single‐output (SISO) uncertain strict-feedback nonlinear systems. The problem of the explosion of complexity existing in the adaptive backstepping control design and the singularity problem are solved by using the proposed adaptive finite time control method. In addition, the compensating signals are introduced to deal with the effect of the known filtering errors caused by the command filters. By using the finite time Lyapunov stability theory, the proposed adaptive finite time control strategy guarantees that all the signals in the closed-loop system are practical finite time stable, and the tracking errors converge to an arbitrarily small neighbourhood of the origin in finite time. Simulation and experimental results of the DC-DC buck converter are given to illustrate the effectiveness of the proposed adaptive finite time control scheme.

Deep neural networks-prescribed performance optimal control for stochastic nonlinear strict-feedback systems

This article explores the application of deep neural networks (DNNs) for optimized backstepping control design in a category of stochastic nonlinear strict-feedback systems with unknown dynamics, focusing on prescribed performance. DNNs, distinguished by their ability to handle high-complexity functions and enhance function approximation, are employed to estimate unknown nonlinear functions. The weight updating strategy for each layer of DNNs is determined through a Lyapunov function analysis. Tomitigate potential issues such as the tracking error exploding at uncertain moments, prescribed performance control (PPC) is introduced to constrain the tracking error within a predetermined range. Subsequently, a novel optimal tracking control scheme, integrating the backstepping method and Hamilton–Jacobi–Bellman (HJB) equation, is presented. The results indicate that all signals in the closed-loop system are bounded in probability, and the tracking error is maintained within a set of predefined arbitrarily small residuals. Simulation outcomes affirm the efficacy of the proposed control scheme.

Observer-based self-triggered adaptive neural network control for nonlinear systems with prescribed time

This paper is concerned with the adaptive neural networks (NNs) prescribed-time control problem for a class of strict-feedback nonlinear systems subject to unmeasured states via the self-triggered control (STC). By developing a new state observer with prescribed-time function, an adaptive NNs self-triggered controller is designed to solve the problem of prescribed-time performance (PTP). Due to the initiative of the STC, it has excellent practical significance in terms of contracting computing resources and network communication resources. With the proposed new strategy, the PTP of the closed-loop system can be guaranteed, and all the signals within the closed-loop system are bounded. Finally, the practicability and effectiveness of the above prescribed-time STC algorithm are verified via some physical simulations.

Adaptive Fuzzy Tracking Control With Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems.

For strict-feedback systems with mismatched uncertainties, adaptive fuzzy control techniques are developed to provide global prescribed performance with prescribed-time convergence. First, a class of prescribed-time prescribed performance functions are designed to quantify the performance constraints of the tracking error. Additionally, a novel error transformation function is provided to eliminate the initial value limitations and resolve the singularity issue in previous research. To ensure the convergence of the tracking error into a prescribed bounded region within a prescribed time and satisfactory transient performance, controllers with or without approximating structures are established. Notably, the settling time and initial condition of the prescribed performance function are completely independent of the initial tracking error and system parameters, thereby improving upon existing results. Furthermore, the disadvantage of the semi-global boundedness of tracking error induced by dynamic surface control can be eliminated through the use of a novel Lyapunov-like energy function. Finally, the effectiveness of the proposed strategies is validated through numerical simulations performed on practical examples.

Distributed adaptive tracking consensus control for a class of heterogeneous nonlinear multi-agent systems

The proposed approach differs from existing works in that it models the constraints of each follower as a nonlinear strict feedback system, rather than relying on a desired reference trajectory for accessible subsystems. To address the limitations caused by uncertain terms in systems, radial basis functions neural networks are utilized to compensate for these unknown nonlinear terms. This leads to a novel distributed adaptive consensus tracking control protocol for high-order nonlinear heterogeneous multi-agent systems, based on the backstepping technique. By introducing a non-zero parameter in the traditional radial basis functions neural network, a new universal approximation is constructed, which overcomes the limitation of the approximation’s finite domain. Additionally, the approximation precision can be adjusted online using provided laws, and the dimension explosion of virtual and real control gains can be avoided through the use of the designed control approach. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Adaptive consensus control and attack detection of nonlinear multiagent systems under false data injection attacks and unknown control directions

This paper investigates the consensus control problem for strict-feedback nonlinear multiagent systems (MASs) under false data injection attacks (FDIAs) and unknown control directions. Different from the existing results, an attack detection mechanism that only uses the information of adjacent agents is designed to judge the occurrence times of the FDIAs, and the negative effects of FDIAs are eliminated by proposing a switching topologies strategy. By introducing the multiple Nussbaum functions, the multiple unknown control directions are addressed, while the effects of these functions enhance each other rather than offset each other. It is shown that the consensus performance and the boundedness of all the signals in the closed-loop systems can be ensured. Finally, the validity of the proposed control scheme is verified through a simulation example.

Barrier-function based adaptive trajectory tracking control for high-order nonlinear systems with collision avoidance

This paper considers the problem of trajectory tracking and collision avoidance for a class of high-order nonlinear strict feedback systems with unknown nonlinearities. The main issue is how to ensure collision avoidance and tracking performance simultaneously in the presence of unknown nonlinear functions. To address the issue, an integral-multiplicative barrier Lyapunov function (BLF) is integrated into the backstepping procedure to remove the dynamic mismatching issue of the existing SUM-type BLF. It has been proven that the proposed adaptive approach ensures both collision avoidance and tracking performance of high-order nonlinear systems in multi-obstacle environments, and all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation results confirm the effectiveness of the proposed method.

Composite learning prescribed performance control of strict-feedback nonlinear systems with mismatched parametric uncertainties

A composite learning prescribed performance control (CLPPC) approach is presented for strict-feedback nonlinear systems with mismatched parametric uncertainties. A finite-time performance function based on polynomial is introduced to predefined a restriction region with respect to the tracking error. By introducing an error transformation function, the tracking error restriction problem of the original system is transformed into the stability problem of an equivalent transformation system. To guarantee the convergence of unknown parameters, online recording data and instantaneous are used to generate a prediction error, which is used together with filtered tracking errors to update parameter estimations under an interval excitation condition. All signals are proven to be ultimately uniformly stable under the proposed CLPPC strategy. Furthermore, the tracking error is limited within the predefined region after the predefined time. Simulation results verify the effectiveness of the proposed approach.

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems.

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Dynamic Event-Based Adaptive Fixed-Time Control for Uncertain Strict-Feedback Nonlinear Systems With State Constraints.

In this article, the event-triggered fixed-time tracking control is investigated for uncertain strict-feedback nonlinear systems involving state constraints. By employing the universal transformed function (UTF) and coordinate transformation techniques into backstepping design procedure, the proposed control scheme ensures that all states are constrained within the time-varying asymmetric boundaries, and meanwhile, the undesired feasibility condition existing in other constrained controllers can be removed elegantly. Different from the existing static event-triggered mechanism, a dynamic event-triggered mechanism (DETM) is devised via constructing a novel dynamic function, so that the communication burden from the controller to actuator is further alleviated. Furthermore, with the aid of adaptive neural network (NN) technique and generalized first-order filter, together with Lyapunov theory, it is proved that the states of closed-loop system converge to small regions around zero with fixed-time convergence rate. The simulation results confirm the benefits of developed scheme.

Event-triggered impulsive tracking control for uncertain strict-feedback nonlinear systems via the neural-network-based backstepping technique

This paper studies the problem of event-triggered impulsive tracking control (ETITC) for uncertain strict-feedback nonlinear systems (USFNSs). In contrast to existing impulsive control schemes, this paper incorporates the neural-network (NN)-based backstepping technique into impulsive control design, such that stronger nonlinearities and uncertainties are allowed to be included in the concerned systems. The proposed state-feedback ETITC scheme guarantees that all the signals of the closed-loop system are bounded and the tracking error ultimately converges to an adjustable bounded region, while also avoiding the Zeno behavior. In addition, by constructing a NN-based observer, this paper further develops an output-feedback ETITC scheme to extend its investigation to the scenario where full states are not available for impulsive control design. Finally, an illustrative example involving a chemical reactor system is presented to demonstrate the effectiveness of our control schemes.

Hierarchical Robust Generalized Nash Equilibrium Seeking of High-Order Uncertain Nonlinear Systems.

This article investigates the distributed generalized Nash equilibrium (GNE) seeking problem of noncooperative games (NGs) for high-order strict-feedback nonlinear multiagent systems (MASs). In particular, the feasible action set of each agent is not only subject to local set and inequality constraints but also coupled through an equality constraint with other agents. This constraint structure is more general and covers most of the constraints in the GNE seeking literature. To accomplish the concerned GNE seeking objective, we propose a novel hierarchical GNE seeking approach in this article to decouple the distributed GNE seeking algorithm design into two layers. First, we construct a distributed primary-dual GNE estimator to generate virtual reference signals that converge to the GNE. Then, with the output of the estimator as the reference signal, we develop an adaptive tracking controller to solve the resultant tracking problems under output constraints. To overcome the negative effects of the disturbances, novel compensating terms associated with smooth functions and positive integrable time-varying functions are incorporated in the controller design, which thereby realizes the exact GNE seeking in the presence of nonvanishing mismatched disturbances. At last, an example is given to support the theoretical analysis of the proposed algorithms.

Dynamic event-triggered adaptive control for state-constrained strict-feedback nonlinear systems with guaranteed feasibility conditions

Dynamic event-triggered adaptive control for state-constrained strict-feedback nonlinear systems with guaranteed feasibility conditions

Lifelong reinforcement learning tracking control of nonlinear strict-feedback systems using multilayer neural networks with constraints

This paper presents a novel safe integral reinforcement learning (IRL)-based optimal trajectory tracking scheme for nonlinear systems with uncertain dynamics that is subject to constraints. We leverage multilayer neural networks (MNNs) for actor-critic MNNs along with an NN identifier in the backstepping process for minimizing a discounted value function. A time-varying barrier Lyapunov function (TVBLF) is utilized for handling constraints and to provide safety assurances. Online weight update laws for the actor and critic MNNs are derived that are driven by Bellman error and control input error. We introduce an online lifelong learning (LL) method in the critic NN, utilizing the Bellman error in MNNs to address catastrophic forgetting. The method’s effectiveness is demonstrated through simulations on mobile robot multitask tracking. The paper concludes with a stability analysis of the closed-loop system.

Global regulation for uncertain feedforward nonlinear systems based on event-triggered impulsive control: a time-varying gain scaling approach

This paper addresses the problem of global regulation for uncertain feedforward nonlinear systems using event-triggered impulsive control. By constructing a state transformation with a time-varying scaling gain, both the state-feedback and output-feedback event-triggered impulsive control strategies are established. It is proven that the proposed impulsive controllers ensure the global regulation of the concerned systems while avoiding the Zeno behaviour. Furthermore, the derived results of this work are generalised to a broader class of uncertain feedforward nonlinear systems incorporating time-varying nonlinearities, as well as to a class of uncertain strict-feedback nonlinear systems. It is noteworthy that this paper is the first attempt to design an impulsive regulating controller for feedforward nonlinear systems. Finally, a simulation example is presented to verify the effectiveness of our theoretical results.

A signal smoothness-based approach to prescribed performance control of strict-feedback nonlinear systems with quantization

This paper investigates the prescribed performance control problems of strict-feedback nonlinear systems with state quantization, input quantization, unknown disturbances and unknown nonlinear functions. Since the quantized states are discontinuous, the differentiability of the stabilizing functions in the backstepping technique cannot be guaranteed. To this end, a smooth approximation of the quantized states is first obtained by introducing a class of functions. Based on this smooth approximation, a quantized control scheme is presented such that all the closed-loop signals are bounded with the prescribed performance bounds. It is shown that the unknown nonlinearities and the unknown disturbances are not estimated and the derivatives of the stabilizing functions are eliminated. Lastly, two examples are provided to illustrate the effectiveness of the presented method.