Non-triangular Form Research Articles

Towards Sustainable Transportation: Adaptive Trajectory Tracking Control Strategies of a Four-Wheel-Steering Autonomous Vehicle for Improved Stability and Efficacy

The objective of continuous increase in the evolution of autonomous and intelligent vehicles is to attain a trustworthy, economical, and safe transportation system. Four-wheel steering (4WS) vehicles are favored over traditional front-wheel steering (FWS) vehicles because they have excellent dynamic characteristics. This paper exhibits the trajectory tracking task of a two degree of freedom (2DOF) underactuated 4WS Autonomous Vehicle (AV). Because the system is underactuated, MIMO, and has a nontriangular form, the traditional adaptive backstepping control scheme cannot be utilized to control it. For the purpose of rectifying this issue, two-state feedback-based methods grounded on the hierarchical steps of the block backstepping controller are proposed and compared in this paper. In the first strategy, a modified block backstepping is applied for the entire dynamic system. Global stability of the overall system is manifested by Lyapunov theory and Barbalat’s Lemma. In the second strategy, a block backstepping controller has been applied after a reduction of the high-order model into various first-order subsystems, consisting of Lyapunov-based design and stability warranty. A trajectory tracking controller that can follow a double lane change path with high accuracy is designed, and then simulation experiments of the CarSim/Simulink connection are carried out against various vehicle longitudinal speeds and road surface roughness to demonstrate the effectiveness of the presented controllers. Furthermore, a PID driver model is introduced for comparison with the two proposed controllers. Simulation outcomes show that the proposed controllers can attain good response implementation and enhance the 4WS AV performance and stability. Indeed, enhancement of the stability and efficacy of 4WS autonomous vehicles would afford a sustainable transportation system by lessening fuel consumption and gas emissions.

A New Robust Adaptive Control Method for Complex Nontriangular Nonlinear Systems

The existing research studies on adaptive control frequently introduce many parameter estimations and lead to a complicated controller. This paper investigates the robust regulation issue for high-order system and plants to raise a new approach for adaptive control. Specifically, the considered system has odd system power, nontriangular form, and external disturbance. By introducing the transformations of a parameter estimation, the studied system is transformed into a new dynamic system. By employing fuzzy systems and some inequality skills, the appropriate bounds of nonlinear terms are established. Based on the adaptive method and homogeneous control, a recursive control design algorithm is provided to construct a new adaptive controller, which dominates those uncertain bounds and guarantees that the closed-loop system is semiglobally uniformly ultimately bounded (SUUB). The constructed controller employs only one adaptive law and has a much simpler form. Simulation examples verify the validness of the presented method.

Secure predictor-based neural dynamic surface control of nonlinear cyber–physical systems against sensor and actuator attacks

This paper addresses a secure predictor-based neural dynamic surface control (SPNDSC) issue for a cyber–physical system in a nontriangular form suffering from both sensor and actuator deception attacks. To avoid the algebraic loop problem, only partial states are employed as input vectors of neural networks (NNs) for approximating unknown dynamics, and compensation terms are further developed to offset approximation errors from NNs. With introduction of nonlinear gain functions and attack compensators, adverse effects of an intelligent adversary are alleviated effectively. Furthermore, we present stability analysis and prove the ultimate boundedness of all signals in the closed-loop system. The effectiveness of the proposed control strategy is illustrated by two examples.

Robust adaptive control for uncertain nonlinear systems with odd rational powers, unmodeled dynamics, and non-triangular structure

Numerous approaches have been reported for different control problems of low-order triangular nonlinear systems. Nevertheless, it shows that the dynamic models of some practical plants are high-order nonlinear systems with odd rational powers. Besides, these systems constantly possess a non-triangular form and suffer from the impact of unmodeled dynamics. The related studies of such systems are very few and more challenging. This work concentrates on adaptive control issue of high-order nonlinear system with odd rational powers, unmodeled dynamics, and non-triangular structure. Based on the small-gain theorem, and by employing the adaptive technique, adding a power integrator method, and neural network method, we successfully construct a new adaptive controller, which greatly decreases the use of parameter estimations in the adaptive control of the considered system. An example highlights that the strategy regulates the studied systems well and performs satisfied system responses.

Quantized Decentralized Adaptive Neural Network PI Tracking Control for Uncertain Interconnected Nonlinear Systems With Dynamic Uncertainties

In this paper, a decentralized adaptive neural network proportional-integral (PI) tracking control scheme is proposed for interconnected nonlinear systems with input quantization and dynamic uncertainties. This algorithm is underpinned by the use of the dynamic signal, graph theory, and function recombination to deal with the difficulties existing in the nontriangular form, unmodeled dynamics, and unknown interconnected terms. Recalling the backstepping method and neural network approximation technology, a new PI tracking controller characterized by simple structure and easy implementation is developed which ensures that all the closed-loop signals are uniformly ultimately bounded. The effectiveness of the obtained controller is exemplified via a numerical example and an application to an inverted pendulum.

Adaptive fuzzy control for nontriangular form systems with time‐varying full‐state constraints

SummaryThis article investigates an adaptive fuzzy tracking control problem for a class of nontriangular form systems with asymmetric time‐varying full state constraints. Unknown functions are approximated by the fuzzy logic systems. A domination approach is employed to tackle the nontriangular form structure. Time‐varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure full‐state constraints satisfaction. Based on the backstepping technique and time‐varying ABLFs, an adaptive controller is proposed and guarantees that all the signals in the closed‐loop system are ultimately bounded and the time‐varying full state constraints are met. Simulation examples are presented to further demonstrate the effectiveness of the proposed approach.

Fuzzy Adaptive Finite-Time Control Design for Nontriangular Stochastic Nonlinear Systems

This paper solves the stochastically finite-time control problem for uncertain stochastic nonlinear systems in nontriangular form. The considered controlled plants are different from the previous results of finite-time control systems, which are the multiple-input and multiple-output (MIMO) stochastic systems with the unknown functions consisting of all states, stochastic disturbance, and immeasurable states. Fuzzy logic systems and a state filter are used to model the uncertain systems and estimate the immeasurable states, respectively. Based on the finite-time theory and It $\hat{o}$ differential equation, a novel stochastically finite-time stability theorem is first raised. By combining the novel criterion and backstepping technique, an adaptive fuzzy stochastically finite-time control method is proposed. It is testified that all signals in the closed-loop signals are semiglobal finite-time stable in probability, and the tracking performances are well. Simulation example results further show the effectiveness of the proposed approach.

Observer-Based Adaptive Neural Control for Non-Triangular Form Systems With Input Saturation and Full State Constraints

This paper addresses the problem of adaptive output feedback control for a class of non-triangular time-varying delay system with input constraints and full-state constraints. A variable separation approach is adopted to overcome the design difficulty from the non-triangular structure. A novel Lyapunov function is introduced to compensate the time-delay terms. Unknown functions are approximated by the radial basis function neural networks. Only one parameter needs to be adjusted online, and a dynamic surface control technique is employed to reduce the computation burden. Combining the barrier Lyapunov function with a backstepping technique in the controller design procedure, the proposed controller guarantees that all the signals in the closed-loop system are uniformly ultimately bounded and the full-state constraints are met. The simulation results demonstrate the effectiveness of the proposed approach.

Controller design for a class of nontriangular nonlinear systems with input dependent growth rate

SummaryIn this paper, we consider the global control problem for a class of high‐order nonlinear systems in the nontriangular form. Compared with the existing results, the growth rate of the nonlinearities depends on the control input, which cannot be dominated by the traditional constant gain. Under the assumption that the nonlinear terms satisfy the homogeneous growth conditions, a dynamic state‐feedback controller is elaborately designed to stabilize the system based on the adding a power integrator technique and the domination methodology. Moreover, by choosing the dynamic gain appropriately, the assumptions on the nonlinearities can be further relaxed to the polynomial case. Numerical simulations are provided to show the effectiveness of the proposed control laws.

Finite-time stabilization of switched stochastic nonlinear systems with mixed odd and even powers

This paper investigates the finite-time stabilization of a class of switched stochastic nonlinear systems in p-normal form, where the power orders of the system are dependent upon the switching signal and the system structure is in non-triangular form. Compared with the existing results, some power orders of the system are allowed to be even. Under suitable assumptions, a state feedback control law with state-dependent switching is designed by using the convex combination method and the adding a power integrator technique. It is shown that the resulting closed-loop system is finite-time stable in probability. Simulation results of a continuously stirred tank reactor (CSTR) system are provided to show the effectiveness and applicability of the proposed method.

GLOBAL FINITE-TIME STABILIZATION FOR A CLASS OF HIGH-ORDER TIME-VARYING NON-LINEAR SYSTEMS WITH UNKNOWN CONTROL COEFFICIENTS

This paper investigates the problem of global finite-time stabilization by state feedback for a class of high-order time-varying non-linear systems in non-triangular form with unknown control coefficients.

Global stabilization of switched nonlinear systems in non-triangular form and its application

This paper investigates the problem of global stabilization of switched nonlinear systems in non-triangular form whose subsystems are not assumed to be asymptotically stabilizable. The use of multiple Lyapunov functions (MLFs) method permits removal of a common restriction in which the nonlinear structures in the non-switched nonlinear systems are restricted to a triangular structure when applying backstepping. Using the MLFs method and the adding a power integrator technique, we design state-feedback controllers for individual subsystems and construct a switching law to guarantee asymptotic stability of the closed-loop switched system. As an application of the proposed design method, the global stabilization problem of a continuously stirred tank reactor (CSTR) system and two inverted pendulums which cannot be handled by the existing methods is investigated.

Adaptive backstepping controller design for nonlinear uncertain systems using fuzzy neural systems

In this article, we propose an adaptive backstepping control scheme using fuzzy neural networks (FNNs), ABCFNN, for a class of nonlinear non-affine systems in non-triangular form. The nonlinear non-affine system contains the uncertainty, external disturbance or parameters variations. Two kinds of FNN systems are used to estimate the unknown system functions. According to the FNN estimations, the adaptive backstepping control (ABCFNN) signal can be generated by backstepping design procedure such that the system output follows the desired trajectory. To ensure robustness and performance, a proportional-integral-surface function and robust controller are designed to improve the control performance. Based on the Lyapunov stability theory, the stability of a closed-loop system is guaranteed and the adaptive laws of the FNN parameters are obtained. This approach is also valid for nonlinear affine system with uncertainty or disturbance. The uncertainty and disturbance terms are estimated by FNNs and treated by the ABCFNN scheme. Finally, the effectiveness of the proposed ABCFNN is demonstrated through the simulation of controlling a nonlinear non-affine system and the continuously stirred tank reactor plant to demonstrate the performances of our approach.

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.