Chaotification of unknown linear and nonlinear systems with applications

A new chaotification method (chaos anti-control) of dynamical systems, which have unknown parameters, is proposed in this paper. The method is based on tracking reference models, through a control law that chaotifies a class of non-linear systems, linear in the control and fully state feedback linearizable. Besides, adaptive laws for control parameters are derived that guarantee the stability of the resulting adaptive system and the convergence of the tracking error to zero. The proposed method has two possible approaches: indirect and direct. Finally, the proposed scheme is applied to secure communications, by means of encrypted information transmission and reception of a message in a chaotic system.     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive finite-time control for output regulation of nonlinear systems with completely unknown control directions

This article studies the finite-time output regulation problem for nonlinear strict-feedback systems with completely unknown control directions and unknown functions. First, according to the necessary conditions for the solvability of the output regulation problem, the output regulation problem of nonlinear strict-feedback systems and the external system is transformed into a stabilization problem of nonlinear systems. Second, an internal model with external signals is designed. Third, based on finite time, fuzzy control, output feedback control, and Nussbaum gain functions, the control law is designed so that all signals of the closed-loop system are the semi-global practically finite-time stable (SGPFS), and the tracking error converges to a small neighborhood of the origin in a finite-time. Finally, the proposed algorithm is applied to the finite-time tracking problem of Chua's oscillator system.     

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

In this paper, an adaptive neural output‐feedback control approach is considered for a class of uncertain multi‐input and multi‐output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K‐filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high‐frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time‐varying delays, so that the offered control approach is free of common assumptions on derivative of time‐varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed‐loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients

This paper is concerned with the global asymptotic regulation control problem for a class of nonlinear uncertain systems with unknown control coefficients. The allowed class of uncertainties include unmeasured input‐to‐state stable (ISS) and/or weaker integral ISS (iISS) inverse dynamics, parametric uncertainties, and uncertain nonlinearities. By using the Nussbaum‐type gain technique and changing the ISS/integral ISS inverse dynamics supply rates, we design a dynamic output feedback controller which could guarantee that the system states are asymptotically regulated to the origin from any initial conditions, and the other signals are bounded in closed‐loop systems. The numerical example of a simple pendulum with all unknown parameters and without velocity measurement illustrates our theoretical results. The simulation results demonstrate its efficacy. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive fault-tolerant tracking control for nonlinear systems with unknown control coefficient and input saturation

In this article, the tracking control problem is investigated for a class of nonlinear systems in the presence of unknown disturbance, input saturation, actuator fault, and unknown control coefficient. A novel disturbance observer-based adaptive fault-tolerant tracking control strategy is proposed with regard to nonlinear systems. Based on the Gaussian error function, the auxiliary dynamic system is designed to offset effects caused by the input saturation. Moreover, the Nussbaum-type function is employed to avert control singularity and deal with the unknown control coefficient. A theoretical analysis indicates that the boundedness of all signals in the closed-loop system can be guaranteed. Finally, two examples with one concerning the dynamic point-the-bit rotary steerable drilling tool system are given to confirm the validity of the method.     

Output feedback control of discrete-time nonlinear systems with unknown time-delay based on Takagi-Sugeno fuzzy models

In this paper, a new discrete-time fuzzy output feedback control method for nonlinear systems with unknown time-delay is proposed. The method follows on from the analysis and design method for a fuzzy controller and observer proposed by Ma et al. (IEEE T Fuzzy Syst (1998) 6(1):41–51), and the extension of this to nonlinear systems with known time-delay by Cao et al. (IEEE T Fuzzy Syst (2000) 8(2):200–211) For the case of unknown time-delay, we derive the sufficient condition for the asymptotic stability of the equilibrium point by applying Lyapunov-Krasovskii theorem and convert this condition into the famous LMI problem.     

An adaptive dynamic surface control of output constrained stochastic nonlinear systems with unknown control directions

This article is concerned about an adaptive dynamic surface control (DSC) of output constrained stochastic nonlinear systems with unknown control directions and unmodeled dynamics. Nonlinear mapping-based backstepping control design is presented for stochastic nonlinear systems with output constraint. The explosion of complexity exists in tradition backstepping method is avoided by using the DSC technique. The radial basis function neural networks are employed to deal with unknown nonlinear functions. Nussbaum gain technique is employed to handle the unknown control directions. And a dynamic signal is employed to dominate the unmodeled dynamics. The adaptive controller is designed can ensure that the tracking error converges on a small region of the origin. And all signals of the closed-loop systems are semiglobal uniformly ultimately bounded. Finally, the results of the simulation cases are provided to show the effectivity of the designed controller scheme.     

Adaptive output-feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

The prescribed-time output-feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict-feedback-like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state-dependent nonlinear functions throughout the system dynamics. We show that prescribed-time output-feedback stabilization (ie, both prescribed-time state estimation and prescribed-time regulation) is achieved through a novel output-feedback control design involving specially designed dynamics of an adaptation state variable and a high-gain scaling parameter in combination with a temporal transformation and a dual high-gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high-gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high-gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.     

Distributed cooperative neural control of a class of nonlinear multi-agent systems with unknown time-varying control coefficient

This article studies the leader–follower cooperative tracking problem of a class of multi-agent systems with unknown nonlinear dynamics. As the load of the following agent may be changing throughout the whole work process, we consider the control coefficient of the following agent to be time-varying and nonlinear instead of constant, which is more practical. All agents are connected by the directed communication graph with weighted topology. The followers can have unknown nonidentical nonlinear dynamics and external disturbances. The nonautonomous leader generates the reference trajectory for only part of the followers and others can only receive the information from their neighbors. To achieve the ultimate synchronization of all following agents to the leader, the novel cooperative adaptive control protocols are designed based on the neural approximation and adaptive updating mechanism. A novel singularity-avoided adaptive updating law is proposed to estimate the control coefficient and compensate for the unknown dynamics online. Lyapunov theory is used to prove the ultimate boundedness of the synchronization tracking error. The correctness and effectiveness of the presented control scheme are demonstrated by two simulations in SISO and MIMO cases, respectively.     

Robust output tracking of uncertain nonlinear time‐delay systems with unknown dead‐zone inputs via control schemes with a simple structure

The adaptive robust output tracking control problem is considered for a class of uncertain nonlinear time‐delay systems with completely unknown dead‐zone inputs. A new design method is proposed so that some adaptive robust output tracking control schemes with a rather simple structure can be constructed. It is not necessary to know the nonlinear upper bound functions of uncertain nonlinearities. In fact, the constructed output tracking control schemes are structurally linear in the state and have a self‐tuning control gain function that is updated by an adaptation law. In this paper, the dead‐zone input is nonsymmetric, and its information is assumed to be completely unknown. In addition, a numerical example is given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.     

Evaluation and design of actuator fault diagnosability for nonlinear affine uncertain systems with unknown indeterminate inputs

In this paper, the evaluation and design scheme of fault diagnosability are investigated by differential geometry theories for a class of nonlinear affine uncertain systems with unknown indeterminate inputs. Considering two coupling relationships of outputs with uncertainties and faults, the sufficient and necessary conditions of fault detectability and isolability are established. For the problem that uncertainties influence the system outputs and make the faults undetectable, a design scheme of fault diagnosability is proposed. For nonlinear affine uncertain systems, a relatively complete theoretical system of the evaluation and design of fault diagnosability comes into being. An illustrative example is given to demonstrate the effectiveness of the proposed evaluation and design scheme of fault diagnosability. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive output feedback control for a class of nonlinear systems with unknown virtual control coefficients signs

This paper presents a global output-feedback control scheme for a class of nonlinear systems that are transformed via a parameter-independent change of co-ordinates into a form in which there exist three kinds of unknown parameters: one is the unknown virtual control coefficients, one is the unknown parameters that multiply output nonlinearities and the other kind is the unknown parameters that multiply affine functions of the derivative of the measured output with coefficients that are smooth nonlinear functions of the measured output. We use two parameter-dependent changes of co-ordinates to transform the system considered into parametric output-feedback form. One transformation is used to eliminate the difficulty in dealing with unknown virtual control coefficients and the other transformation is used to remove the nonlinearities which are affine functions of the derivative of the measured output with coefficients that are smooth nonlinear functions of the measured output. Then the scheme presented by Ye (IEEE Trans. Automat. Control 2001; 46 :112–115) can be applied to the new system. Global results can be obtained for the overall closed-loop systems without any constraints on the nonlinear terms. Copyright © 2006 John Wiley & Sons, Ltd.     

Observer‐based adaptive neural control of uncertain MIMO nonlinear systems with unknown control direction

This paper investigates adaptive neural network output feedback control for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems with an unknown sign of control gain matrix. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. In order to deal with the unknown sign of control gain matrix, the Nussbaum‐type function is utilized. By using neural network, we approximated the unknown nonlinear functions and perfectly avoided the controller singularity problem. The stability of the closed‐loop system is analyzed by using Lyapunov method. Theoretical results are illustrated through a simulation example. Copyright © 2012 John Wiley & Sons, Ltd.     

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict‐feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.     

Adaptive variable universe of discourse fuzzy control for a class of nonlinear systems with unknown dead zones

In this paper, based on an adaptive nonbackstepping design algorithm, we proposed a novel variable universe of discourse fuzzy control (VUDFC) approach for a class of single‐input–single‐output strict‐feedback nonlinear systems with unknown dead‐zone inputs. Firstly, we convert the form of system into a normal form on the basis of some new state variables and coordinate transformation; at the same time, state‐feedback control is changed to output‐feedback control. Secondly, we design observers to estimate the new unmeasurable states. Then, different from considering the traditional backstepping‐based fuzzy control scheme, we introduce a direct VUDFC scheme, which is mainly based on changing of contraction‐expansion factors to modify the universe of discourse online, and fuzzy rules can automatically reproduce to develop the control performance; thus, the size of initial rule base is greatly reduced. This new algorithm can alleviate tracking error, improve the accuracy of the system, and strengthen robustness. Lastly, according to Lyapunov theorem analysis, we prove that all the signals in the closed‐loop system can be guaranteed to be stable, and the output can track the reference signal very well. Simulation results illustrated the effectiveness of the proposed VUDFC approach.     

Nonlinear control for uncertain nonlinear systems with unknown control directions using less or no parameter estimates

For the parametric strict‐feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed‐loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive finite-time tracking control for output-constrained nonlinear systems with non-strict-feedback structure

This article investigates the issue of adaptive finite-time tracking control for a category of output-constrained nonlinear systems in a non-strict-feedback form. First, by utilizing the structural characteristics of radial basis function neural networks (RBF NNs), a backstepping design method is extended from strict-feedback systems to a kind of more general systems, and NNs are employed to approximate unknown nonlinear functions. In addition, the system output is constrained to the specified region by applying the barrier Lyapunov function (BLF) technique. Furthermore, the finite-time stability of the system is proved by employing the Bhat and Bernstein theorem. As a result, an adaptive finite-time tracking control scheme for the output-constrained nonlinear systems with non-strict-feedback structure is proposed by applying RBF NNs, BLF, finite-time stability theory, and adaptive backstepping technique. It is demonstrated the finite-time stability of the system, the prescribed convergence of the system output and tracking error, the boundedness of adaptive parameters and state variables. Finally, a simulation example is implemented to illustrate the effectiveness of the presented neural control scheme.     

Adaptive control of feedforward nonlinear systems with uncertain time-varying parameters and an unknown time-varying delay in the input

In this paper, we consider a global regulation problem for a class of feedforward nonlinear systems. The key features of our considered system are identified by the presence of uncertain time-varying parameters associated with main diagonal states and input and an unknown time-varying delay in the input. Moreover, the growth rates of nonlinearity and the input-delay are only known to be finite. To solve our considered problem, we give a process to obtain a compact set that contains the allowed time-varying parameters. Then, we propose an adaptive controller which handles both unknown growth rate of nonlinearity and input-delay for system regulation. We carry out the rigorous system analysis and show the effectiveness of our proposed control scheme via an application example.     

Adaptive control of systems with unknown non-smooth non-linearities

In this paper we unify our recent results in adaptive control of systems with unknown non-smooth non-linearities such as dead-zone, backlash and hysteresis characteristics at the input or output of a linear dynamics. Our adaptive inverse approach employs an adaptive controller structure consisting of an adaptive inverse for cancelling the effect of an unknown non-linearity and a fixed (or adaptive) linear control law for a known (or unknown) linear dynamics. Despite the bilinear dependence on the unknown parameters, a linearly parametrized error system is constructed which enables us to design robust adaptive laws for updating the controller parameters to ensure closed loop signal boundedness and improve system tracking performance. © 1997 by John Wiley & Sons, Ltd.