Nonlinear Time-varying Uncertainties Research Articles

Safety‐guaranteed constraint‐oriented modelling and control for bidirectional vehicular platoons

The safety of a vehicular platoon is seriously threatened in the presence of actuator saturations, (possibly fast) time-varying non-linear uncertainties. Meanwhile, the string stability and the strong string stability cannot eliminate the potential safety hazard caused by large initial error conditions. This study focuses on safety-guaranteed distributed control of the vehicular platoon with a bidirectional communication topology and the constant time headway policy. The authors formulate bilateral inequality constraints on the spacing error between adjacent vehicles to represent the collision-avoidance and compact formation performance. A novel state transformation technique is proposed to convert the bounded spacing error space to an unconstrained state space. On the basis, Comprehensive equality constraints for the transformed states are established by integrating the information of proximal (preceding and following) vehicles. In addition, an anti-windup compensation method is utilised to handle actuator saturations. Then an adaptive constraint-following controller is designed to render the uniform boundedness and uniform ultimate boundedness performance of the transformed state. As a result, the string stability, the strong string stability, the collision-avoidance and compact formation are guaranteed despite the presence of actuator saturations and complex uncertainties. Numerical simulations are performed to validate the effectiveness of the proposed control scheme.

NESO-Based Path Following Control for Underactuated Hovercrafts with Unknown Nonlinear Uncertainties and a Safety Limit Constraint

In this brief, the path following control problem of underactuated hovercrafts subject to nonlinear time-varying uncertainties and a safety limit constraint (SLC) is addressed. A novel homogenous nonlinear extended state observer (NESO)-based safe motion controller for a path following control scenario of underactuated hovercrafts is proposed. First, a NESO is constructed to estimate and compensate the nonlinear time-varying uncertainties for the underactuated hovercraft. Then, a NESO-based backstepping sliding mode control (BSMC) law with a turning SLC is proposed to achieve the yaw control for underactuated hovercrafts, which improves both safety and maneuverability of the underactuated hovercraft during the path following control scenario. The nonlinear time-varying turning SLC is first directly taken into the control system design, which is achieved by introducing an auxiliary dynamic system to limit the virtual input control during the backstepping design process. A NESO-based backstepping surge control law is also designed to achieve the surge control for underactuated hovercrafts. Furthermore, all error signals of the proposed closed-loop control system are proven to be bounded. Finally, an application case is tested on an underactuated hovercraft to illustrate the effectiveness and superiority of the designed control scheme.

Permanent-Magnet SLM Drive System Using AMRRSPNNB Control System with DGWO

Because permanent-magnet synchronous linear motors (SLM) still exhibit nonlinear friction, ending effects and time-varying dynamic uncertainties, better control performances cannot be achieved by using common linear controllers. We propose a backstepping approach with three adaptive laws and a beating function to control the motion of permanent-magnet SLM drive systems that enhance the robustness of the system. In order to reduce greater vibration in situations with uncertainty actions in the aforementioned control systems, we propose an adaptive modified recurrent Rogers–Szego polynomials neural network backstepping (AMRRSPNNB) control system with three adaptive laws and reimbursed controller with decorated gray wolf optimization (DGWO), in order to handle external bunched force uncertainty, including nonlinear friction, ending effects and time-varying dynamic uncertainties, as well as to reimburse the minimal rebuild error of the reckoned law. In accordance with the Lyapunov stability, online parameter training method of the modified recurrent Rogers–Szego polynomials neural network (MRRSPNN) can be derived by utilizing an adaptive law. Furthermore, to help reduce error and better obtain learning fulfillment, the DGWO algorithm was used to change the two learning rates in the weights of the MRRSPNN. Finally, the usefulness of the proposed control system is validated by tested results.

Switched Concurrent Learning Adaptive Control of Switched Systems With Nonlinear Matched Uncertainties

This paper investigates the model reference adaptive control (MRAC) problem of switched systems with nonlinear matched uncertainties based on mode-dependent average dwell time method. A novel switched MRAC scheme is proposed, which simultaneously uses both current and recorded data from the switched system, to study the convergence of the state tracking error and the weight error without depending on the persistency of excitation. It is critical to establish the relationship among the nonlinear matched uncertainties, the switched concurrent learning(CL) algorithm, the average dwell time of each subsystem, and the convergence domains of the state tracking error and the weight error. First, we find a class of switching signals characterized by mode-dependent average dwell time conditions such that the switched reference model is bounded-input bounded-state stable. Second, in the case of time-invariant nonlinear uncertainties, we design a switched CL adaptive law that ensures that the tracking error converges to zero, and the adaptive weights exponentially converge to their ideal values. Subsequently, in the case of nonlinear time-varying uncertainties, we estimate the convergence rates of the state tracking error and the weight error of each subsystem outside a ball, and thus obtain sufficient conditions that ensure the convergence of the trajectories of the state tracking error and the weight error to a ball centered at the origin with a given radius. Finally, the proposed approach is applied to an electro-hydraulic system, and its effectiveness is demonstrated.

Admixed recurrent Gegenbauer polynomials neural network with mended particle swarm optimization control system for synchronous reluctance motor driving continuously variable transmission system

To cut down influence of nonlinear time-varying uncertainty action in a synchronous reluctance motor driving continuously variable transmission system, an admixed recurrent Gegenbauer polynomials neural network with mended particle swarm optimization control system is posed for improving control performance. The admixed recurrent Gegenbauer polynomials neural network with mended particle swarm optimization control system involves an observer control, a recurrent Gegenbauer polynomial neural network control and a remunerated control. The weights of recurrent Gegenbauer polynomials neural network controller are regulated by using the adaptive law and the gradient descent technology. The remunerated control with a reckoned law is derived and computed by means of the Lyapunov stability theorem so as to pledge stability of the control system. Likewise, to speedup convergence of weights in the recurrent Gegenbauer polynomial neural network, the mended particle swarm optimization algorithm is used for regulating two kinds of learning rates. At last, three kinds of experimental results are demonstrated to confirm the usefulness of the put forward control system with comparative studies.

L1 adaptive control for general partial differential equation (PDE) systems

ABSTRACTThis paper addresses the L1 adaptive control problem for general Partial Differential Equation (PDE) systems. Since direct computation and analysis on PDE systems are difficult and time-consuming, it is preferred to transform the PDE systems into Ordinary Differential Equation (ODE) systems. In this paper, a polynomial interpolation approximation method is utilized to formulate the infinite dimensional PDE as a high-order ODE first. To further reduce its dimension, an eigenvalue-based technique is employed to derive a system of low-order ODEs, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE system is augmented with nonlinear time-varying uncertainties. On the basis of the reduced-order ODE system, a dynamic state predictor consisting of a linear system plus adaptive estimated parameters is developed. An adaptive law will update uncertainty estimates such that the estimation error between predicted state and real state is driven to zero at each time-step. And a control law is designed for uncertainty handling and good tracking delivery. Simulation results demonstrate the effectiveness of the proposed modeling and control framework.

Trajectory tracking of quadrotor flying manipulators using [formula omitted] adaptive control

This paper concerns with tracking control of an unmanned quadrotor vehicle equipped with a multi-link robotic manipulator. We present an analytic model of the system that formulates unknown interactions between the aerial platform and the manipulator in the form of nonlinear time-varying uncertainties. Based on the proposed model, a novel trajectory tracking scheme is synthesized by combining two inner feedback linearization loops to stabilize the nominal quadrotor and manipulator dynamics and a master L1 adaptive loop to systematically compensate for uncertainties and realize the desired closed-loop behavior. We show that this scheme leverages predictable transient and steady state performance in the presence of coupling effects and given a specified reference trajectory. Simulation studies have shown the effectiveness of the proposed aerial manipulator control method.

Tracking Design of an Omni-Direction Autonomous Ground Vehicle by Hierarchical Enhancement Using Fuzzy Second-Order Variable Structure Control

Owing to the hierarchical architecture of the derived model of the omni-direction autonomous ground vehicle (OD-AGV), the virtual desired trajectory (VDT) is first designed by the first switching surface, which is set as the linear dynamic pose error of the OD-AGV. In sequence, the trajectory tracking control (TTC) is designed by the second switching surface, which is the linear dynamic tracking error of the VDT. To deal with nonlinear time-varying uncertainties including system disturbance and different ground conditions, enhanced fuzzy second-order variable structure control (EF2VSC) is designed into both VDT and TTC. Finally, the experiments for tracking the circular trajectories with different curvatures, traveling velocities, and poses of the OD-AGV are presented to validate the effectiveness and robustness of the proposed hierarchical enhancement using fuzzy second-order variable structure control (HEF2VSC).

Active control for non-autonomous diaphragm-type pneumatic isolation system by using an augmented adaptive sliding-mode controller

An augmented adaptive sliding-mode controller is proposed in this paper for a diaphragm-type pneumatic vibration isolation (PVI) system containing nonlinear characteristics and time-varying uncertainties with unknown bounds. To capture and deal with the time-varying uncertainties, a controller design based primarily on the functional approximation (FA) technique complemented with an adaptive fuzzy sliding-mode control (AFSMC) is adopted. The resultant hybrid design is denoted as FA+AFSMC to differentiate itself from other attempting solutions. Lyapunov stability theory is utilized not only to stabilize the closed-loop system but also to formulate updating laws for weighting coefficients of the FA and tuning parameters of the AFSMC. This developed scheme has online learning ability when it faces the system’s nonlinear and time-varying behaviors. Experimental explorations which incorporates both pressure and velocity measurements as feedback signals reveals that the proposed FA+AFSMC scheme outperforms other attempting solutions, such as passive isolation and pure AFSMC scheme, by a significant margin.

Observer-based reset law design for uncertain systems by using model predictive strategy

In reset control systems, the reset law determines reset values at reset times. This paper considers the observer-based reset law design for uncertain systems with both nonlinear uncertainties and time-varying parameter uncertainties. A model predictive strategy is proposed to design the reset law by minimizing a quadratic performance index. The optimization problem is transformed into a linear matrix inequalities (LMIs) formulation, and the reset law is solved by using an LMI technique. The proposed approach is applied to a typical continuous stirred-tank reactor system to show the effectiveness of the obtained results.

Adaptive Neural Network Control for a Class of MIMO Uncertain Pure-Feedback Nonlinear Systems

In this paper, robust adaptive neural network control is investigated for a class of multi-input-multi-output (MIMO) pure-feedback nonlinear system with unknown nonlinearities. The unknown nonlinearities could be come from unmodeled dynamics, modeling errors, or nonlinear time-varying uncertainties. Based on the backstepping design technique and the universal approximation property of the neural network (NN), robust adaptive control is synthesized by employing a single NN to approximate the lumped uncertain nonlinearities. The proposed control can eliminate the circularity problem completely, and guarantees semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop and convergence of the tracking error to an arbitrarily small residual set.

Flocking for multi-agent systems with unknown nonlinear time-varying uncertainties under a fixed undirected graph

This paper presents a flocking algorithm for networked multi-agent systems with unknown, nonlinear, time-varying uncertainties by integrating cooperative control and adaptive control methods. An ideal multi-agent system without uncertainties is introduced first. The cooperative control law, based on an artificial potential function, is designed to make the ideal multi-agent system achieve flocking under a fixed and connected undirected graph. Information of ideal states, instead of real states, is exchanged among agents through a communication network. The presence of uncertainties will lead to the degeneration of the performance or even destabilize the entire multi-agent system. The adaptive control law is therefore introduced to handle unknown, nonlinear, time-varying uncertainties. By integrating the cooperative control law with the adaptive control law, the real multi-agent system stays close to the ideal multi-agent system which achieves flocking asymptotically under a connected graph. Simulation results of two-dimensional flocking with uncertainties are provided to demonstrate the presented flocking algorithm.

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

Adaptive Control for Systems with Output Constraints Using an Online Optimization Method

In this paper, a new controller framework incorporating an L1 adaptive control and an online optimization scheme is presented. This framework provides a method for maintaining output constraints in the presence of non-linear time-varying matched uncertainties by predicting future output trajectories within a finite time horizon. The stability conditions of the system are derived, and the prediction error is characterized. The online optimization is formulated into a linear program problem for which many efficient algorithms exist. Simulation results demonstrate the effectiveness of the controller framework.

Robust optimal attitude control of a laboratory helicopter without angular velocity feedback

SUMMARYIn this paper, the robust, optimal, output control problem is dealt with for a 3-degree-of-freedom laboratory helicopter. The control goal is to achieve the practical tracking of the desired elevation and pitch angles without the angular velocity feedback. A nominal linear time-invariant system is introduced and the real system is considered as the nominal one with uncertainties, including parameter perturbations, nonlinear time-varying uncertainties, and external disturbances. An observer is first used to estimate angular velocity. Then a nominal controller based on the optimal control method is designed for the nominal system to achieve the desired tracking properties. Lastly, a robust output compensator is added to restrain the effects of uncertainties in the real system. It is shown that asymptotic tracking properties and robust stability can be achieved. Experimental results on the laboratory helicopter are shown to verify the effectiveness of the proposed control method.

Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.

Semiglobal robust backstepping output tracking for strict-feedback form systems with nonlinear uncertainty

Output tracking controller design problem is dealt with for a class of nonlinear systems in strict-feedback form in the presence of time-varying nonlinear uncertainties and unmodeled dynamics with multi-operation points. A new method based on signal compensation is proposed to design a robust controller, which consists of a nominal controller and a robust compensator. It is shown that semiglobal robust tracking property can be achieved. A new feature of our results is that the controller is a linear and time-invariant one and “explosion of complexity” problem is avoided.

Robust H ∞ preview control of an active suspension system with norm-bounded uncertainties

A robust H∞ preview control is investigated for an active suspension system with look-ahead sensors. The uncertain system is described by a state-space model with linear nominal parts and additional nonlinear time-varying norm-bounded uncertainties. Proof of robust stability and a feedback-type robust H∞ preview controller are derived by augmenting the dynamics of the original system and previewed road input. As, however, the augmented previewed road input gives the system a much larger dimension than the original system, much more computation time is required for solving of Riccati equations. To resolve this problem, a decomposed robust H∞ preview controller is proposed. Robust stability and performance variations for system uncertainties are shown using a numerical example of a quarter-car model.

Robust Tracking Controller Backstepping Design for SISO Uncertain Nonlinear System

Controller design problem is dealt with for a class of plants with time-varying nonlinear uncertainties and unmodeled dynamics. A new method based on signal compensation is proposed to design a robust controller. A controller designed by this method consists of a nominal controller and a robust compensator. It is shown that robust tracking property and robust tracking transient performance can be achieved simultaneously. A salient feature of our results, shown in the present paper, is that the controller is linear and time-invariant one and we can tell the users how to tune on-line the parameters of the controller with the proposed robust and transient performance.