Search

In this paper, two novel algorithms to find the Nash equilibrium solution of the non‐zero‐sum games for continuous‐time input‐affine nonlinear systems are presented. Based on integral reinforcement learning method, the integral‐exploration‐coupled Hamilton‐Jacobi (HJ) equations are derived, which does not contain any information of the system dynamics. Then, based on neural networks approximation, two different adaptive tuning law of weights are given to estimate the approximate solution of the coupled HJ equations. Both two algorithms can estimate the value function and the policy without knowing or identifying the system dynamics. The closed‐loop system stability and the convergence of weights are guaranteed based on Lyapunov analysis. Finally, the simulation results of a two‐player non‐zero‐sum game demonstrate the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

The extended Kalman filter (EKF) is the most popular tool for state estimation of nonlinear stochastic systems. The conventional EKF can be refined via iterative re-linearization, leading to the so-called iterative EKF (IEKF). The performance of either EKF or IEKF will deteriorate in the presence of outliers. In this article, an outlier-resilient IEKF method is proposed using a more robust cost function, the correntropy, to replace the traditional mean squared error criterion. An iterative procedure is derived to maximize the correntropy criterion in a similar way to the Gauss–Newton optimization. Simulation results demonstrate the superiority of the proposed method as compared to the existing methods. [ABSTRACT FROM AUTHOR]

This article considers the global regulation problem for a class of non‐affine nonlinear uncertain systems. We will investigate the extended proportional‐derivative (EPD) controller together with its parameters design. The EPD controller is the natural extension of the classical PD control, which adjusts the input signal by using the regulation error together with its derivatives only. We will show that under some suitable conditions on nonlinearity and uncertainty of the systems, the regulation error of the closed‐loop system will converge to 0 exponentially, provided that the EPD controller parameters are chosen from an n‐dimensional unbounded set constructed in the article. In contrast to most of the existing literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms. We will also give an example where the regulation problem is solvable globally by the classical PD control, while the controlled system cannot be transformed into the nonlinear normal form globally. [ABSTRACT FROM AUTHOR]

This article proposes a robust particle filtering (PF) approach for a generic class of nonlinear systems with both additive time-varying uncertainty (ATVU) in the state transition equation and inaccurate process noise covariance matrices. To avoid sampling efficiency degradation of the PF approach caused by ATVU, we employ the disturbance observer-based PF (DOBPF) approach where the effect of ATVU is compensated in the particle generation stage. Different from the existing DOBPF method where disturbance estimation is achieved via the Kalman filter, the disturbance observer adopted in this article is in the form of variational Bayesian adaptive Kalman filter (VBAKF) which deals with the inaccurate process noise covariance matrices in both the dynamic models of the state and the ATVU. Compared with conventional PF approaches, the proposed method, named VBAKF-PF, exhibits enhanced robustness against both the ATVU in the state transition equation and the uncertainties of process noise covariance matrices. The simulation results demonstrate the superiority of VBAKF-PF over both the VBAKF and DOBPF methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive neural network (NN) control scheme is proposed for a class of nonlinear systems with unknown control direction. By introducing some differentiable functions and high-order Lyapunov functions, the obstacle caused by unknown control direction in NN control is successfully circumvented and all closed-loop signals are shown to be uniformly bounded up to infinite time. Meanwhile, by introducing an error transformation technique, it is rigorously proved that the argument of the unknown nonlinearities remains within a compact set which can be explicitly calculated a priori, making the NN approximation always valid. Moreover, with the aid of a bound estimation approach, we effectively compress the impact of approximation errors and external disturbances and steer the tracking error into a predefined small residual set. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper will review some fundamental results in the understanding of several basic problems concerning feedback and uncertainty. First, we will consider adaptive control of linear stochastic systems, in particular, the global stability and optimality of the well-known self-tuning regulators, designed by combining the least-squares estimator with the minimum variance controller. This natural and seemingly simple case had actually been a longstanding central problem in the area of adaptive control, and its solution offers valuable insights necessary for understanding more complex problems. Next, we will discuss the theoretical foundation of the classical proportional-integral-derivative (PID) control, to understand the rationale behind its widespread successful applications in control practice where almost all of the systems to be controlled are nonlinear with uncertainties, by presenting some theorems on the global stability and asymptotic optimality of the closed-loop systems, and by providing a concrete design method for the PID parameters. Finally, we will consider more fundamental problems on the maximum capability and limitations of the feedback mechanism in dealing with uncertain nonlinear systems, where the feedback mechanism is defined as the class of all possible feedback laws. Some extensions and perspectives will also be discussed in the paper. [ABSTRACT FROM AUTHOR]

As is well-known, the classical PID control plays a dominating role in various control loops of industrial processes. However, a theory that can explain the rationale why the linear PID can successfully deal with the ubiquitous uncertain nonlinear dynamical systems and a method that can provide explicit design formulae for the PID parameters are still lacking. This paper is a continuation of the authors recent endeavor towards establishing a theoretical foundation of PID for nonlinear uncertain systems. In contrary to most of the existing literature on linear or affine nonlinear systems, we will consider a class of non-affine nonlinear uncertain systems, and will show that a three dimensional parameter set can be constructed explicitly, such that whenever the PID parameters are chosen from this set, the closed-loop systems will be globally stable and the regulation error will converge to zero exponentially fast, under some suitable conditions on the system uncertainties. Moreover, we will also consider the simpler PI and PD control, and provide a necessary and sufficient condition for the choice of the PI parameters for a class of one dimensional non-affine uncertain systems, by applying the Markus–Yamabe theorem in differential equations. These theoretical results show explicitly that the ubiquitous PID control does indeed have strong robustness with respect to both the system nonlinear uncertainties and the selection of the controller parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive compensation control scheme is proposed for a class of nonlinear systems with unknown parameters and unknown actuator failures. The normal operation case and different failure cases of actuators are unified through a time-varying model. By introducing a smooth function, an integrable auxiliary signal, and a bound estimation approach, the effect of failures is successfully compensated for, and the total number of failures is not restricted to be finite. It is shown that all closed-loop signals are globally uniformly bounded, and the tracking error converges to zero asymptotically regardless of the possibly infinite number of actuator failures. An application to the longitudinal dynamic model of a twin otter aircraft is presented to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this paper is to understand and characterize the maximum capability of the feedback mechanism for a basic class of scalar discrete-time semiparametric minimum-phase control systems, where both parametric and nonparametric uncertainties are included. We will demonstrate that the necessary and sufficient condition to stabilize the class of systems is , where is the Lipschitz constant describing the “size” of the uncertainty of the nonparametric part. This critical value is the same as that first obtained in for a class of purely nonparametric systems, which shows that the capability of feedback is not influenced by the parameterized uncertainty in the systems, as long as the corresponding parametric nonlinear function has a linear growth rate. While the necessity proof is directly obtainable from , the main task of this paper is to prove the sufficiency part. [Copyright &y& Elsevier]

In this paper, a new anti-disturbance controller is presented for a class of non-linear systems with multiple disturbances. The first part of the disturbance is described by an exogenous model and the second part represents an uncertain variable bounded by a given function. A new non-linear disturbance observer is designed to estimate the composite disturbances. Then, a hierarchical control strategy consisting of disturbance-observer-based control and a robust adaptive controller is presented to achieve the anti-disturbance performance. A stability analysis for both the error estimation systems and the composite closed-loop system is provided. Finally, the approach is applied to a missile control system to show the efficiency of the approach. [ABSTRACT FROM PUBLISHER]

Abstract: It is fairly well known that there are fundamental differences between adaptive control of continuous-time and discrete-time nonlinear systems. In fact, even for the seemingly simple single-input single-output control system with a scalar unknown parameter and noise disturbance , and with a known function having possible nonlinear growth rate characterized by with , the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is . This was first found and proved by for the Gaussian white noise case, and then proved by for the bounded noise case. Subsequently, a number of other types of “critical values” and “impossibility theorems” on the maximum capability of adaptive feedback were also found, mainly for systems with known control parameter as in the above model. In this paper, we will study the above basic model again but with additional unknown control parameter , i.e.,  is replaced by in the above model. Interestingly, it turns out that the system is globally stabilizable if and only if . This is a new critical theorem for adaptive nonlinear stabilization, which has meaningful implications for the control of more general uncertain nonlinear systems. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the fault isolation (FI) problem for multivariate nonlinear non-Gaussian systems by using a novel filtering method. The generalized entropy optimization principle (GEOP) is established for non-Gaussian systems with multiple faults and disturbances, where the statistic information including entropy and mean of the residual variable is maximized in the presence of the target fault as well as all the nuisance faults and disturbances, and is minimized in the absence of the target fault but in the presence of the nuisance faults and disturbances. Different from the existing results where the output is measurable for feedback, the fault isolation filter is designed and driven by the joint output stochastic distributions rather than its deterministic value. The error dynamics is represented by a multivariate nonlinear non-Gaussian system, for which new recursive relationships are proposed to formulate the joint probability density functions (JPDFs) of the residual variable in terms of the JPDFs of the noises and the faults. Finally, a simulation example is given to demonstrate the effectiveness of the proposed multivariate FI algorithms. [Copyright &y& Elsevier]

A novel type of control scheme combining the disturbance-observer-based control (DOBC) with terminal sliding mode (TSM) control is proposed for a class of multiple-input-multiple-output (MIMO) continuous non-linear systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modelling perturbations. The other is supposed to have the bounded H2 norm. The disturbance observers based on regional pole placement and D-stability theory are presented, which can be constructed separately from the controller design. By integrating DOBC with TSM control laws, the disturbances can be rejected and attenuated, simultaneously, and the desired dynamic performances can be guaranteed for non-linear systems in finite time with known and unknown non-linear dynamics, respectively. Two simulation examples for a flight control system and a hard disk drive actuator are given respectively to demonstrate the effectiveness of the proposed control schemes compared with the previous schemes. [ABSTRACT FROM AUTHOR]

This article is concerned with robust particle filtering (PF) for nonlinear systems with state transition uncertainties. The uncertainty under consideration is characterized in part by an additive uncertainty term (AUT) in the state transition equation and in part by the parametric uncertainty in the probability distribution of process noises. To maintain the sampling efficiency of the PF algorithm in the presence of AUT, the disturbance observer (DO)-based PF approach is adopted, which consists of the DO for real-time AUT reconstruction and a modified PF with AUT-compensated sampling. Instead of using the traditional Kalman filter-based DO, a novel student’s $t$ DO is proposed to handle uncertain noise parameters and achieve robust disturbance estimation. The enhanced robustness of the proposed method, named student’s $t$ DO-based robust PF, has been demonstrated via numerical example. Furthermore, experimental tests on the skylight polarization-aided attitude and heading reference system show that the standard deviation of our method decreases by over 40% as compared with the conventional PF. [ABSTRACT FROM AUTHOR]

We show that the four-dimensional Martínez Alonso-Shabat equation is nonlinearly self-adjoint with differential substitution and the required differential substitution is just the admitted adjoint symmetry and vice versa. By means of computer algebra system, we obtain a number of local and nonlocal symmetries admitted by the equations under study. Then such symmetries are used to construct conservation laws of the equation under study and its reductions. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The classical control design based on linearised model is widely used in practice even to those inherently nonlinear systems. Although linear design techniques are relatively mature and enjoy the simple structure in implementations, they can be prone to misbehaviour and failure when the system state is far away from the operating point. To avoid the drawbacks and exploit the advantages of linear design methods while tackling the system nonlinearity, a hybrid control structure is developed in this paper. First, the model predictive control is used to impose states and inputs constraints on the linearised model, which makes the linearisation satisfy the small-perturbation requirement and reduces the bound of linearisation error. On the other hand, a combination of disturbance observer-based control andH∞control, called composite hierarchical anti-disturbance control, is constructed for the linear model to provide robustness against multiple disturbances. The constrained reference states and inputs generated by the outer-loop model predictive controller are asymptotically tracked by the inner-loop composite anti-disturbance controller. To demonstrate the performance of the proposed framework, a case study on quadrotor is conducted. [ABSTRACT FROM AUTHOR]

In this paper, a decentralized output-feedback adaptive backstepping control scheme is proposed for a class of interconnected nonlinear systems with unknown actuator failures. By introducing a kind of high-gain K -filters, a bound estimation approach and some smooth functions, the effect of actuator failures and interactions among subsystems is successfully compensated for and the actuators are allowed to change among the normal operation case and different failure cases infinitely many times. The proposed scheme is able to guarantee the global stability of the overall closed-loop system, regardless of the possibly infinite number of unknown actuator failures. An initialization technique is also introduced so that the L ∞ performance of tracking errors can be adjusted no matter if there exist unknown actuator failures. Simulation results performed on double inverted pendulums are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Disturbance-observer-based control (DOBC) and related methods have been researched and applied in various industrial sectors in the last four decades. This survey, at first time, gives a systematic and comprehensive tutorial and summary on the existing disturbance/uncertainty estimation and attenuation techniques, most notably, DOBC, active disturbance rejection control, disturbance accommodation control, and composite hierarchical antidisturbance control. In all of these methods, disturbance and uncertainty are, in general, lumped together, and an observation mechanism is employed to estimate the total disturbance. This paper first reviews a number of widely used linear and nonlinear disturbance/uncertainty estimation techniques and then discusses and compares various compensation techniques and the procedures of integrating disturbance/uncertainty compensation with a (predesigned) linear/nonlinear controller. It also provides concise tutorials of the main methods in this area with clear descriptions of their features. The application of this group of methods in various industrial sections is reviewed, with emphasis on the commercialization of some algorithms. The survey is ended with the discussion of future directions. [ABSTRACT FROM PUBLISHER]

In this article, a composite anti-disturbance control of disturbance rejection and attenuation for a class of nonlinear positive systems is proposed for the first time to achieve both positivity and stability. The disturbance observer-based control (DOBC) method is utilized to compensate for the effects of the modeled disturbances, while the $L_{1}$ control strategy is adopted to suppress the effects of the disturbances which are not compensable to satisfy the $L_{1}$ index performance. Besides, two analysis schemes of the closed-loop system are presented. The first scheme is commonly used and is easy for analysis, but it has some conservativeness. The second scheme is proposed novelly with less conservativeness, which releases the positivity constraint of disturbance estimation errors. The corresponding theorems and algorithms are proposed for necessary conditions and solutions. Finally, two examples are presented to illustrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlinear dynamical systems with zero dynamics, which is subject to both unknown nonparametric dynamics and external disturbances, and is required to track a given reference signal by using the output feedback. Our controller is designed based on both the extended state observer (ESO) and the projected gradient estimator. While the ESO is used to estimate the total uncertainties, the projected gradient algorithm is used to estimate the nonparametric uncertainties treated as “time-varying parameters”. This method overcomes the difficulties that the traditional active disturbance rejection control (ADRC) technique needs to have a “good” prior estimate for the uncertainties in the input channel. The closed-loop system is shown to be semi-globally stable, and at the same time, the tracking error can be made arbitrarily small. [ABSTRACT FROM AUTHOR]

This article presents a single‐hidden‐layer feedforward network (SLFN) aided fault‐tolerant control (FTC) scheme for a class of nonlinear systems subject to actuator faults. First, the upper bounds of the norms of the unknown functions, which cover information of actuator faults and amplitude saturation degrees, are deployed. The upper bounds are approximated by SLFNs with adaptive techniques. Subsequently, a sliding mode control approach is presented to allow for prompt corrective reactions, with explicit consideration of multivariable conditions and control input constraints. Finally, simulation results based on a nonlinear Boeing 747 aircraft model are presented to demonstrate the effectiveness of the proposed FTC scheme. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an anti-disturbance fault diagnosis scheme is proposed for non-Gaussian stochastic distribution systems (SDSs) with multiple disturbances. The available driven information for fault diagnosis is probability density functions (PDFs) of output rather than output value. Using B-spline expansion technique, the output PDFs can be approximated in terms of dynamic weights of B-spline neural network by which a nonlinear model can be established between input and weights. Therefore, the concerned problem is transformed into fault diagnosis problem of the weighting system presented by an uncertain nonlinear system with multiple disturbances and time-varying fault. Different from most of the existing results, the multiple disturbances are supposed to include unknown disturbance modeled by an exo-system and norm bounded uncertain disturbances. In the proposed approach, a disturbance observer is designed to estimate and compensate the modeled disturbance, and optimization technology is applied to attenuate the norm bounded disturbance. Finally, simulation results are given to show the efficiency of the proposed approach. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of robust fuzzy control for a class of uncertain nonlinear Markovian jump systems with time-varying delay. The class of systems under consideration is described by the Takagi–Sugeno fuzzy model. The goal of the paper is to design a mode-dependent fuzzy state-feedback controller such that the closed-loop system is stochastically stable with a prescribed performance of disturbance attenuation for all admissible parameter uncertainties. In order to obtain a less conservative control design, a new stochastic Lyapunov–Krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals. Then, by employing this functional, a delay decomposition approach to the design of robust fuzzy controllers is developed in terms of linear matrix inequalities. Finally, two examples are given to illustrate the merit and usability of the proposed design method. [Copyright &y& Elsevier]

Summary: The problem of semiglobal stabilization for nontriangular nonlinear systems with unknown control coefficients and uncertain output function is investigated in this paper. By virtue of homogeneous domination technique, a novel nonrecursive design approach is presented to construct the semiglobal controller. To that end, a new output‐driven reduce‐order observer is developed to estimate the unmeasurable states. Moreover, it has been shown that we can determine the maximal sector bound of output function, in which an output feedback controller can be designed to render the closed‐loop system semiglobally stable. The effectiveness of controller is demonstrated by a ship simulation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the resilient strategy design of the multi-tasking optimal control problem for a class of time-varying state-saturated systems. The system under investigation is subject to nonlinear disturbances and state saturations. In the context of noncooperative game, the resilient strategies are designed which can tolerate gain perturbations/variations resulting possibly from computational or implementation errors. First, an upper bound is derived on the individual cost function of each controller. Then, such an upper bound is minimized unilaterally via iteratively solving a convex optimization problem and, subsequently, the resilient control strategies are obtained in terms of the solutions to certain coupled backward Riccati-like recursions. Furthermore, the explicit expression for the derived upper bound is provided over the infinite horizon. Finally, a numerical example is exploited to demonstrate the validity of the proposed methodology. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the design problem of composite antidisturbance control for a class of nonlinear systems with multiple disturbances. First, a novel nonlinear disturbance observer‐based control scheme is constructed to estimate and compensate the disturbance modeled by the nonlinear exosystem. Then, by combining the dissipative control theory, a linear matrix inequality‐based design method of composite antidisturbance control is developed such that the augmented system is exponentially stable in the absence of unmodeled disturbances, and is dissipative in the presence of unmodeled disturbances. In this case, the original closed‐loop system is exponentially stable in the presence of modeled disturbances. Subsequently, two special cases of composite antidisturbance control are derived with H∞ performance and passivity, respectively. Finally, the proposed method is applied to control A4D aircraft to show its effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, an active disturbance rejection control (ADRC) method is investigated for the ranger neutral buoyancy vehicle (RNBV) via a delta operator approach. In order to eliminate unmodeled nonlinearities and exogenous disturbances for a neutral environment, a novel delta-domain ADRC method is put forward to achieve the tracking control performance of the RNBV. In the proposed ADRC method, an extended-state-observer (ESO) is designed in the delta domain to estimate the so-called total disturbance that reflects the aggregated impacts of the nonlinearities and disturbances. Then, by using the estimates provided by the ESO, a composite controller is developed such that the closed-loop system can be input-to-state stable. It is shown in practical experiments that the proposed delta-domain ADRC outperforms its discrete-domain counterpart in consideration of the finite-word-length effects. [ABSTRACT FROM AUTHOR]

This paper studies the problem of fuzzy normalization and stabilization for a class of rectangular descriptor systems in Takagi-Sugeno (T-S) fuzzy models. It delivers a feasible scheme for the design of proportional and derivative type dynamic compensator which ensures the closed-loop system normalized and admissible. The dynamic compensator parameters are computed by solving a set of quadratic matrix inequalities, and accordingly, an efficient algorithm is built to solve related matrix inequalities. Illustrative examples are given to show the effectiveness of the present results. [ABSTRACT FROM AUTHOR]