Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.     

An Intelligent Robust Tracking Control for a Class of Electrically Driven Mobile Robots

This paper addresses the problem of designing robust tracking control for a class of uncertain wheeled mobile robots actuated by brushed direct current motors. This class of electrically‐driven mechanical systems consists of the robot kinematics, the robot dynamics, and the wheel actuator dynamics. Via the backstepping technique, an intelligent robust tracking control scheme that integrates a kinematic controller and an adaptive neural network‐based (or fuzzy‐based) controller is developed such that all of the states and signals of the closed‐loop system are bounded and the tracking error can be made as small as possible. Two adaptive approximation systems are constructed to learn the behaviors of unknown mechanical and electrical dynamics. The effects of both the approximation errors and the unmodeled time‐varying perturbations in the input and virtual‐input weighting matrices are counteracted by suitably tuning the control gains. Consequently, the robust control scheme developed here can be employed to handle a broader class of electrically‐driven wheeled mobile robots in the presence of high‐degree time‐varying uncertainties. Finally, a simulation example is given to demonstrate the effectiveness of the developed control scheme.     

Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

Based on proportional‐integral‐derivative (PID)/PD controls, we in the article investigate the tracking problem of a class of second‐order time‐varying switched nonlinear systems. To start with, for tracking a given point under arbitrary switching signals, we propose a sufficient condition about PID controller parameters, which can be implicitly described as semialgebraic sets. Successively, we consider the tracking problem under average dwell time (ADT)‐based switching signals and propose an alternative sufficient condition about PID controller parameters. Especially, for tracking an equilibrium point of the system without controls, we can further simply utilize the proportional‐derivative control and similarly construct corresponding semialgebraic conditions about proportional‐derivative controller parameters under arbitrary switching signals and ADT‐based switching signals. Finally, two examples are given to show the applicability of our theoretical results.     

A comparative study on a novel model‐based PID tuning and control mechanism for nonlinear systems

This work presents a novel predictive model‐based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM‐ and NN‐Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient‐ and steady‐state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises. Copyright © 2009 John Wiley & Sons, Ltd.     

Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

We study in this paper the problem of iterative feedback gains auto‐tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization‐based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model‐free multi‐parametric extremum seeking control to iteratively auto‐tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi‐parametric extremum seeking model‐free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction‐based Adaptive Robust Tracking Control of an Uncertain First‐Order Time‐Delay System

This paper considers the tracking problem of a delayed uncertain first‐order system which is simultaneously subject to (possibly large) known input delay, unknown but bounded time‐varying disturbance, and unknown plant parameter. The proposed predictor adaptive robust controller (PARC) involves prediction‐based projection type adaptation laws with model compensation and prediction‐based continuous robust feedback such that the closed loop system has global exponential convergence with an ultimate bound proportional to delay, disturbance bound, and switching gain. Further, if there are only delay and parameter uncertainties after some finite time, then semi‐global asymptotic tracking is guaranteed. The proposed design is shown to have significant closed loop performance improvement over the baseline controller.     

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

This paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.     

Integration of Derivative Control on SIPIC in Motor Speed Control

The proportional–integral–derivative (PID) controller is the most commonly used controller in control application due to its simplicity. However, the control output may exceed the plant input limit which eventually deteriorates the system performance. This is known as a windup phenomenon, which causes large overshoot, long settling time and instability in the control system. Various anti‐windup methods have been introduced to overcome the windup phenomenon such as the Steady‐State Integral Proportional‐Integral Controller (SIPIC). Due to the coupling of the proportional, integral and derivative tuning gains, it is difficult to tune for non‐overshoot and short settling time to coexist in a PID. With decoupling, a greater range of tuning gains can be applied to control the rising slope without disturbing the damping state. Currently, SIPIC with decoupling effect has only been studied for the proportional and integral tuning gains. This paper presents the effect of integrating derivative control on SIPIC in motor speed control. SIPIC+D shows better speed control on a direct current motor under no‐load and loading conditions compared with other existing anti‐windup added with derivative control.     

A Design Of Multiloop Predictive Self‐Tuning Pid Controllers

In this paper, a new design scheme of multiloop predictive self‐tuning PID controllers is proposed for multivariable systems. The proposed scheme firstly uses a static pre‐compensator as an approximately decoupling device, in order to roughly reduced the interaction terms of the controlled object. The static matrix pre‐compensator is adjusted by an on‐line estimator. Furthermore, by regarding the approximately decoupled system as a series of single‐input single‐output subsystems, a single‐input single‐output PID controller is designed for each subsystem. The PID parameters are calculated on‐line based on the relationship between the PID control and the generalized predictive control laws. The proposed scheme is numerically evaluated on a simulation example.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

Adaptive Neural Dynamic Surface Control For Nonlinear Pure‐Feedback Systems With Multiple Time‐Varying Delays: A Lyapunov‐Razumikhin Method

This paper focuses on the problem of adaptive neural control for a class of uncertain nonlinear pure‐feedback systems with multiple unknown time‐varying delays. The considered problem is challenging due to the non‐affine pure‐feedback form and the unknown system functions with multiple unknown time‐varying delays. Based on a novel combination of mean value theorem, Razumikhin functional method, dynamic surface control (DSC) technique and neural network (NN) parameterization, a new adaptive neural controller which contains only one parameter is developed for such systems. Moreover, The DSC technique can overcome the problem of ‘explosion of complexity’ in the traditional backstepping design procedure. All closed‐loop signals are shown to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the proposed design.     

Output feedback regulation of a class of high‐order feedforward nonlinear systems with unknown time‐varying delay in the input under measurement sensitivity

An output feedback regulation problem is considered for a class of high‐order feedforward nonlinear systems with delay in the input under measurement sensitivity. The key features are that the considered systems have uncertain high‐order feedforward nonlinearity and unknown time‐varying delay in the input. Then, the controller is supposed to be engaged where the output feedback information is distorted by measurement sensitivity. Our proposed controller has two gains—fixed and adaptive gains. The fixed gain is first designed to compensate for measurement sensitivity, and the adaptive gain is next utilized to dominate both unknown input delay and uncertain high‐order feedforward nonlinearity. Simulation examples are given to highlight the advantage of our control scheme.     

Static anti‐windup design for a class of Markovian jump systems with partial information on transition rates

This paper investigates the problem of static anti‐windup design for uncertain continuous‐time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time‐varying and norm‐bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output‐feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti‐windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed‐loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.     

A complete parameterization of clf‐based input‐to‐state stabilizing control laws

Sontag's formula proves constructively that the existence of a control Lyapunov function implies asymptotic stabilizability. A similar result can be obtained for systems subject to unknown disturbances via input‐to‐state stabilizing control Lyapunov functions (ISS‐clfs) and the input‐to‐state analogue of Sontag's formula. The present paper provides a generalization of the ISS version of Sontag's formula by completely parameterizing all continuous ISS control laws that can be generated by a known ISS‐clf. When a simple inner‐product constraint is satisfied, this parameterization also conveniently describes a large family of ISS controls that solve the inverse‐optimal gain assignment problem, and it is proved that these controls possess Kalman‐type gain margins. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive and Robust Stabilization of Feedforward Nonlinear Systems Driven by Symmetric and Non‐symmetric Dead‐zone Inputs

The stabilization of feedforward nonlinear systems subject to hard‐input nonlinearities is a challenging problem due to the presence of input uncertainties. This paper deals with adaptive control of a class of feedforward nonlinear systems driven by unknown dead‐zone inputs. The unknown dead‐zone input nonlinearity is assumed to be either symmetric or non‐symmetric. The control design is based on the combination of the invariant‐manifold stabilization technique with the classical adaptive and robust compensation methods. Simulation results showed that the presence of the dead‐zone inputs in the system dynamics can be handled even for arbitrary large dead‐zone parameters.     

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

Adaptive Control Scheme for Large‐Scale Interconnected Systems Described by Hammerstein Models

This paper proposes an adaptive algorithm for the online control of discrete‐time large‐scale nonlinear systems, which reduces the noise effects acting on the system output (regulation problem) and allows the system output to keep track of a time‐varying trajectory (tracking problem). We consider a large‐scale nonlinear system that can be decomposed into single‐input single‐output (SISO) interconnected nonlinear subsystems with known structure variables (orders, delays) and unknown time‐varying parameters. Each interconnected subsystem is described by block‐oriented models, specifically a discrete‐time Hammerstein model. Parameter adaptation is performed using a recursive parametric estimation algorithm based on the adjustable model method and the least squares techniques. Simulation results of an interconnected petroleum process are provided to demonstrate the effectiveness of the developed control scheme.     

A distributed leader‐following tracking controller using delayed control input information from neighbors

In this paper, we propose a simple, continuous, and distributed controller for the second‐order multiagent system to achieve leader‐following trajectory tracking, by exploiting the control input information of neighbors (CIIN) and using proportional‐derivative (PD) control in terms of local neighborhood synchronization error. A constant time delay is introduced in the CIIN as a design parameter to avoid the algebraic loop issue arising from the control input coupling. We develop an easily testable condition on the PD gains to ensure that the resulting neutral‐type error system is input‐to‐state stable for an arbitrary bounded delay, and prove that when the leader's acceleration is a Lipschitz continuous function with respect to time, the ultimate bound of tracking errors is strictly increasing with respect to the introduced time delay. Moreover, we analyze the robustness of the controller with respect to model uncertainties and show its potential advantages over two existing controllers in balancing the steady‐state tracking precision, the communication cost, and the continuity of controller signal. Finally, extensive simulations are conducted to show the effect of the delay on system stability, to verify the condition on PD gains, to confirm the robustness of the controller, and to demonstrate the detailed advantages.