Uncertain Strict-feedback Systems Research Articles

Prescribed performance under input saturation for uncertain strict-feedback systems: A switching control approach

We consider the problem of achieving prescribed performance metrics on the output tracking error, for uncertain strict-feedback systems, while satisfying inelastic control input constraints in the form of magnitude saturation. Inspired by the prescribed performance control (PPC) methodology, we propose a switching control strategy comprised of two operational units: a traditional PPC and a Safety Controller. The former enforces the output error to evolve strictly inside a user-defined performance envelope that incorporates all the desired performance characteristics. However, in the presence of input saturation this envelope can be easily violated, leading to PPC instability. On the other hand, the Safety Controller enables the safe escaping, thus avoiding the appearance of this internal instability phenomenon. We prove that the closed-loop system solution is complete and non-zeno. Furthermore, we show that the tracking error evolves inside a modified performance envelope, guaranteeing a prescribed minimum convergence rate and a controlled maximum steady-state error. Simulation studies clarify and verify the theoretical findings.

Neuroadptive Practical Prescribed Time Tracking Control of Fully Quantized Uncertain Strict Feedback Systems

Neuroadptive Practical Prescribed Time Tracking Control of Fully Quantized Uncertain Strict Feedback Systems

Event-triggered adaptive control for nonlinear systems using time-receding horizons without initial dependence

This paper investigates the full-state constraint event-triggered adaptive control for a class of uncertain strict-feedback systems. The lack of information on the coupling dynamics of virtual variables in backstepping increases the complexity of feedback design. Given this, the requirements of shaping system performance constraints, eliminating initial dependence, and reducing data transfer costs together give rise to an interesting and challenging problem. Constructing the time-receding horizon (TRH) and stitching it with the quadratic Lyapunov function (QLF) is the key to constrained tracking. Specifying TRHs as a set of smooth bounds with fixed-time convergence and forcing the system to stabilize within the constrained region before the prescribed settling time provide a sufficient condition for practical finite-time stability (PFS). For relaxing the initial dependence, a tuning function is designed to match the performance constraints under arbitrary system initial conditions. A dual-channel event-triggered mechanism (ETM) is developed to automatically adjust the controller and estimator data flow updates with less transmission burden. By combining a specific inequality with backstepping, uncertainties are overcome without the “complexity explosion” in recursion steps. Finally, simulations demonstrate the effectiveness of the proposed method.

Dynamic Event-Triggered Control for a Class of Uncertain Strict-Feedback Systems via an Improved Adaptive Neural Networks Backstepping Approach

Dynamic Event-Triggered Control for a Class of Uncertain Strict-Feedback Systems via an Improved Adaptive Neural Networks Backstepping Approach

Adaptive neural optimized control for uncertain strict-feedback systems with unknown control directions and pre-set performance

In this paper, we develop an adaptive neural strategy based on optimized backstepping (OB) technology for strict-feedback systems with unknown control directions and pre-set performance. First, the OB technique is used to construct each optimized virtual controller and optimized actual controller in backstepping, so as to achieve global optimization. Second, the problem of unknown control directions is overcome by using a Nussbaum-type function. Next, a time-varying switching function and the quartic barrier Lyapunov function are introduced to solve the control problem of the pre-set time and accuracy. The proposed control strategy makes the tracking error of the system converge to the pre-set accuracy within the pre-set time. At the same time, all of the signals of the closed-loop system are bounded. Finally, two set simulations verify the effectiveness of the proposed control strategy.

Adaptive Optimized Fuzzy Control of Uncertain Strict-Feedback Systems with Preset Tracking Accuracy

Adaptive Optimized Fuzzy Control of Uncertain Strict-Feedback Systems with Preset Tracking Accuracy

Practical prescribed-time tracking control for uncertain strict-feedback systems with guaranteed performance under unknown control directions

In this paper, we consider the practical prescribed-time performance guaranteed tracking control problem for a class of uncertain strict-feedback systems subject to unknown control direction. Due to the existence of unknown nonlinearities and uncertainties, it is challenging to design a controller that can ensure the stability of closed-loop system within a predetermined finite time while maintaining the specified transient performance. The underlying problem becomes further complex as the control directions are unknown. To deal with the above problems, a special translation function as well as Nussbaum type function are introduced in the prescribed performance control (PPC) framework. Finally, a PPC as well as preset finite time tracking control scheme is designed, and its effectiveness is confirmed by both theoretical analysis and numerical simulation.

An adaptive hybrid control strategy for a class of nonlinear systems

This study provides an adaptive fuzzy control scheme for the class of nonlinear uncertain strict-feedback systems with external disturbances. The backstepping and synergetic control theories are used to develop a robust control approach for this class of systems. The unknown behaviors of the system are estimated through fuzzy systems. The stability is analyzed using the Lyapunov method, which shows that the proposed control method ensures that all the signals of the closed-loop system are bounded, and the tracking error converges approximately to zero. Two simulation examples are given to demonstrate the efficiency of the developed control approach.

Resilient anti-disturbance dynamic surface control of uncertain strict-feedback systems subject to partial loss of actuator effectiveness

This paper is concerned with the tracking control of a class of uncertain strict-feedback systems subject to partial loss of actuator effectiveness, in addition to uncertain model dynamics and unknown disturbances. A resilient anti-disturbance dynamic surface control method is proposed to achieve stable tracking regardless of partial actuator faults. First, data-driven adaptive extended state observers are designed based on memory-based identifiers, such that the uncertain model dynamics, external disturbances and the unknown input gains due to actuator faults can be estimated. Next, a resilient anti-disturbance dynamic surface controller is developed based on recovered information from the data-driven adaptive extended state observers. After that, it is proven that the cascade system formed by the observer and controller is input-to-state stable. Finally, comparative studies are performed to validate the efficacy of the resilient anti-disturbance dynamic surface control method for nonlinear strict-feedback systems subject to partial loss of actuator effectiveness.

Featured Cover

The cover image is based on the Research Article Adaptive dynamic surface asymptotic tracking control of uncertain strict-feedback systems with guaranteed transient performance and accurate parameter estimation by Wenrui Shi et al., https://doi.org/10.1002/rnc.6170.

Adaptive Fuzzy Control With Global Stability Guarantees for Unknown Strict-Feedback Systems Using Novel Integral Barrier Lyapunov Functions

In this article, the adaptive fuzzy tracking control problem for a class of uncertain strict-feedback systems with unknown nonlinearities is investigated with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">particular emphasis on global stability</i> . The proposed control scheme is designed by integrating the barrier Lyapunov functions (BLFs) with the techniques of fuzzy approximation and backstepping. The novel integral BLFs (iBLFs) are introduced to overcome the design difficulties induced by the virtual control coefficients and determine <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> the compact set for guaranteeing the validity of fuzzy approximation. Compared with existing approximation-based control results, the developed controller not only guarantees global stability without requiring prior information of system nonlinearities and assumptions on the time derivatives of virtual control coefficients, but also prevents the “explosion of complexity” issue without attaching additional filters. The simulation results further confirm the effectiveness of the theoretical findings.

Sliding mode differentiator-based event-triggered control for state-constrained nonlinear systems with unknown virtual control coefficients

In this paper, a novel event-triggered (ET) adaptive neural tracking control scheme is proposed for uncertain strict-feedback systems subject to asymmetric time-varying full-state constraints, unknown virtual control coefficients and external disturbances. The lower-order time-varying asymmetric barrier Lyapunov function (TVABLF) is constructed to ensure that state constraints are not transgressed. Then, a simple backstepping-based control procedure is developed to remove the existing restrictions on a high power of piecewise TVABLF and high-order differentiability of virtual laws. In particular, a novel adaptive updating law is constructed to co-design the controller and the ET scheme by the combination of the Nussbaum gain technique, thereby solving the ET controller design difficulty resulting from unknown control coefficients. The proposed scheme can guarantee all states within the time-varying constrained areas, achieve the satisfactory tracking ability and save the communication resource. Finally, the effectiveness of the proposed scheme is testified by numerical and practical examples.

Adaptive pre-assigned finite-time control of uncertain nonlinear systems with unknown control gains

This paper mainly studies an adaptive finite-time control problem for a kind of uncertain strict feedback systems with unknown control gains. First, the original strict-feedback system is transformed into a pure-feedback system. And then, we propose a modified adaptive finite-time design idea on the basis of the property of pre-assigned finite-time function (PFTF) and Nussbaum gain. The designed controller can make sure that all states converge to an arbitrarily region in finite-time and signals in the closed-loop system are finite-time bounded. Moreover, the presented controller is smooth and the settling time does not rely on the initial values and design parameters. Finally, the simulation study is made to illustrate the innovativeness for the proposed scheme.

Tracking control of state constrained fractional order nonlinear systems

This article investigates adaptive output-feedback control problems for full-state constrained fractional order uncertain strict-feedback systems with unmeasured states and input saturation. By considering the structure of the systems, a fractional order observer is framed to estimate unmeasurable states. By using the backstepping procedure and barrier Lyapunov function, the adaptive controller with adaptation laws are proposed in each step. With the Lyapunov stability theory for fractional order systems, it proves all the states remain in their constraint bounds and the error system converges to a bounded set containing the origin. In the end, Two examples are presented to show the effectiveness of the designed control scheme.

Composite Learning Prescribed Performance Control of Nonlinear Systems

This paper investigates a composite learning prescribed performance control (PPC) scheme for uncertain strict-feedback system. Firstly, a prescribed performance boundary (PPB) condition is developed for the tracking error, and the original system is transformed into an equivalent one by using a transformation function. In order to ensure that the tracking error satisfies the PPB, a sufficient condition is given. Then, a control scheme of PPC combined with neural network (NN) and backstepping technique is proposed. However, the unknown functions cannot be guaranteed to estimate accurately by this method. To solve this problem, predictive errors are defined by applying online recorded date and instantaneous date. Furthermore, novel composite learning laws are proposed to update NN weights based on a partial persistent excitation (PE) condition. Subsequently, the stability of the closed-loop system is guaranteed and all signals are kept bounded by using composite learning PPC method. Finally, simulation results verify the effectiveness of the proposed methods.

Finite-Time Robust Intelligent Control of Strict-Feedback Nonlinear Systems With Flight Dynamics Application.

The tracking control is investigated for a class of uncertain strict-feedback systems with robust design and learning systems. Using the switching mechanism, the states will be driven back by the robust design when they run out of the region of adaptive control. The adaptive design is working to achieve precise adaptation and higher tracking precision in the neural working domain, while the finite-time robust design is developed to make the system stable outside. To achieve good tracking performance, the novel prediction error-based adaptive law is constructed by considering the estimation performance. Furthermore, the output constraint is achieved by imbedding the barrier Lyapunov function-based design. The finite-time convergence and the uniformly ultimate boundedness of the system signal can be guaranteed. Simulation studies show that the proposed approach presents robustness and adaptation to system uncertainty.

Prescribed Performance Neural Control of Strict-Feedback Systems via Disturbance Observers

This paper provides a disturbance observer-based prescribed performance control method for uncertain strict-feedback systems. To guarantee that the tracking error meets a design prescribed performance boundary (PPB) condition, an improved prescribed performance function is introduced. And radial basis function neural networks (RBFNNs) are used to approximate nonlinear functions, while second-order filters are employed to eliminate the “explosion-complexity” problem inherent in the existing method. Meanwhile, disturbance observers are constructed to estimate the compounded disturbance which includes time-varying disturbances and network construction errors. The stability of the whole closed-loop system is guaranteed via Lyapunov theory. Finally, comparative simulation results confirm that the proposed control method can achieve better tracking performance.

A New Nussbaum-Type Function and its Application in the Control of Uncertain Strict-Feedback Systems

In this study, an adaptive fuzzy output tracking control scheme is proposed for uncertain strict-feedback systems with unknown control directions. Nussbaum-type functions are designed, with which the effects of multiple unknown control directions can be handled. Compared with the existing Nussbaum-type functions dealing with the same problem, the proposed Nussbaum-type functions have smaller amplitudes that are more conducive to the design of the controller. Fuzzy functions are used to estimate the unknown terms by combining adaptive laws with backstepping procedure. Adaptive fuzzy controller is constructed to guarantee that the output tracking error system is asymptotically stable and all states in the closed-loop system are bounded. Finally, numerical simulation studies are presented to illustrate the effectiveness of the proposed criteria.

Global Predefined Time and Accuracy Adaptive Neural Network Control for Uncertain Strict-Feedback Systems With Output Constraint and Dead Zone

This article proposes a global adaptive neural network tracking control method for uncertain strict-feedback nonlinear system with output constraint and dead zone to achieve predefined-time convergence of the tracking error to predefined accuracy. First, an integral-type Barrier Lyapunov function (BLF) is constructed to handle output constraint. Next, radial basis function neural network (RBFNN) control and robust control are used to tackle unknown nonlinear function. The continuous switching function is designed to switch RBFNN control to robust control when the arguments of the unknown function exceed the active region of neural network. Utilizing the property of radial basis function, we derive the upper bound of the term containing the unknown nonlinear function and design adaptive laws to determine the derived upper bound and robust control gain. Then, the predefined time virtual control inputs are obtained and their derivatives are estimated by finite time differentiator. Finally, we use the dead zone inverse technique to obtain the actual control input. Stability analysis shows the presented control scheme achieves global convergence of the errors to predefined accuracy within predefined time. The simulation results verify the effectiveness of the presented control scheme.

Adaptive Prescribed Performance Output Regulation of Nonlinear Systems with Nonlinear Exosystems

The paper studies the prescribed performance output regulation problem for a class of nonlinear uncertain strict-feedback systems which are driven by nonlinear exosystems. Fuzzy logic systems (FLSs) are used to approximate the unknown functions. A fuzzy adaptive observer is designed to estimate the system state. A fuzzy internal model is designed to reject disturbance. Simultaneously, a parameter-type Lyapunov function and L function are designed to ensure the prescribed performance of the system. As illustrated by example, the proposed prescribed performance fuzzy adaptive output feedback control scheme is shown to guarantee semi-globally uniformly ultimately bounded, and the dynamic performance and steady-state performance of the tracking error are dependent on the prescribed performance functions.