Uncertain Nonlinear Time-varying Systems Research Articles

On extended state based Kalman filter for nonlinear time-varying uncertain systems with measurement bias

This paper addresses the state estimation for a class of nonlinear time-varying stochastic systems with both uncertain dynamics and unknown measurement bias. A novel extended state based Kalman filter (ESKF) algorithm is developed to estimate the original state, the uncertain dynamics and the measurement bias. It is shown that the estimation error of the proposed algorithm is bounded in the mean square sense. Also, the estimation of the measurement bias asymptotically converges to its true value, such that the influence of measurement bias is eliminated. Furthermore, the asymptotic optimality of the estimation result is proved while the uncertain dynamics approaches to a constant vector. Finally, a simulation study for harmonic oscillator system model is provided to illustrate the effectiveness of proposed method.

Robust Three Stage Central Difference Kalman Filter for Helicopter Unmanned Aerial Vehicle Actuators Fault Estimation

This paper proposes state and fault estimations for uncertain time-varying nonlinear stochastic systems with unknown inputs. we suppose, the information about the fault and unknown inputs is not perfectly known. For this purpose, in this manuscript, we developed a robust three-stage central difference Kalman filter (RThSCDKF). We used RThSCDKF for model-based fault detection and identification (FDI) in nonlinear hover mode of helicopter unmanned aerial vehicle (HUAV) in the presence of external disturbance. In this system, actuator faults are affected by each other. The proposed method estimates and decouples actuator faults in the presence of external disturbances. This model can detect stuck and floating faults that are important to detect. At the end, this method is compared with the three-stage extended Kalman filter (ThSEKF). Simulation results show the effectiveness of the proposed robust method for detection and isolation of various actuator faults and also this shows more accuracy with respect to ThSEKF.

Finite-Time Tracking Control for Nonstrict-Feedback State-Delayed Nonlinear Systems with Full-State Constraints and Unmodeled Dynamics

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.

Completely distributed neuro-learning consensus with position constraints and partially unknown control directions

In this paper, we propose a new neural network-based iterative learning leader-less consensus control algorithm for the second-order uncertain time-varying nonlinear multi-agent systems, where the position of each agent is constrained in an open interval which can be pre-selected and the control direction can be non-identical and partially unknown. With the help of a novel barrier composite energy function and multiple piece-wise Nussbaum functions, the designed completely distributed learning protocols can make the positions and velocities of the agents achieve the exact consensus on a finite time interval as the iteration number increases to infinity. Meanwhile, the position trajectories of the agents at each iteration do not exceed the constraints bounds. Besides, to testify the feasibility and utility of the presented algorithm, two simulation examples are given in the end.

Robust deterministic least-squares filtering for uncertain time-varying nonlinear systems with unknown inputs

The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches.

Joint state and fault estimation for time-varying nonlinear systems with randomly occurring faults and sensor saturations

This paper is concerned with the joint state and fault estimation problem for a class of uncertain time-varying nonlinear stochastic systems with randomly occurring faults and sensor saturations. A random variable obeying the Bernoulli distribution is used to characterize the phenomenon of the randomly occurring faults and the signum function is employed to describe the sensor saturation due to physical limits on the measurement output. The aim of this paper is to design a locally optimal time-varying estimator to simultaneously estimate both the system states and the fault signals such that, at each sampling instant, the covariance of the estimation error has an upper bound that is minimized by properly designing the estimator gain. The explicit form of the estimator gain is characterized in terms of the solutions to two difference equations. It is shown that the developed estimation algorithm is of a recursive form that is suitable for online computations. In addition, the performance analysis of the proposed estimation algorithm is conducted and a sufficient condition is given to verify the exponential boundedness of the estimation error in the mean square sense. Finally, an illustrative example is provided to show the usefulness of the developed estimation scheme.

On extended state based Kalman filter design for a class of nonlinear time-varying uncertain systems

This paper considers the filtering problem for a class of multi-input multi-output systems with nonlinear time-varying uncertain dynamics, random process andmeasurement noise. An extended state based Kalman filter, with the idea of timely estimating the unknown dynamics, is proposed for better robustness and higher estimation precision. The stability of the proposed filter is rigorously proved for nonlinear time-varying uncertain system with weaker stability condition than the extended Kalman filter, i.e., the initial estimation error, the uncertain dynamics and the noises are only required to be bounded rather than small enough. Moreover, quantitative precision of the proposed filter is theoretically evaluated. The proposed algorithm is proved to be the asymptotic unbiased minimum variance filter for constant uncertainty. The simulation results of some benchmark examples demonstrate the feasibility and effectiveness of the method.

Suboptimal variable structure control of uncertain nonlinear slowly varying systems

ABSTRACTIn this paper, a new robust suboptimal controller is designed to stabilize a class of uncertain nonlinear time-varying systems with slowly varying parameters. In the design procedure of the proposed controller, first a suboptimal control law is designed for the nominal system based on considering a given cost function and an appropriate Slowly Varying Control Lyapunov Function (SVCLF). After that, a robustifying term is added to the nominal controller in order to vanish the effects of model uncertainties and/or external disturbances in a finite time. For this purpose, a special sliding surface, which is a combination of terminal and integral sliding surfaces, is used. This surface has the advantages of both of terminal and integral surfaces. Due to the structure of this surface, the actual trajectories track the desired one in the finite time. The other innovation of the proposed approach is accessing a chattering-free Controller. Finally, in order to confirm the applicability of the proposed controller and verify the theoretical results, it is applied on a practical benchmark system (a time-varying inertia pendulum). Computer simulations show the efficiency of the proposed controller.

State feedback stabilization of a class of uncertain nonlinear systems on non-uniform time domains

This paper deals with the stabilization problem for a class of uncertain nonlinear systems on non-uniform time domains. Some sufficient conditions are derived to design a state feedback controller for a class of uncertain nonlinear time-varying systems under vanishing perturbations. Using some Gronwall’s integral inequalities, the uniform exponential stability of the closed-loop systems on arbitrary time scales, is guaranteed. Then, based on the Lyapunov theory, new sufficient conditions are proposed to derive the controller which ensures the practical stability of the closed-loop time-invariant nonlinear uncertain system under non-vanishing perturbations. Some examples illustrate these results.

Design of an adaptive chattering avoidance global sliding mode tracker for uncertain non-linear time-varying systems

In this paper, a novel adaptive global sliding mode control technique is suggested for the tracking control of uncertain and non-linear time-varying systems. The proposed scheme composed of a global sliding mode control structure to eliminate reaching mode and an adaptive tracker to construct the auxiliary control term for eliminating the impacts of unwanted perturbations. Using the Lyapunov direct method, the tracking control of the non-linear system is guaranteed. Moreover, superior position tracking performance is obtained, the control effort is considerably decreased and the chattering phenomenon is removed. Furthermore, using adaptation laws, information about the upper bounds of the system perturbations is not required. To indicate the effectiveness of the suggested scheme, three simulation examples are presented. Simulation results demonstrate the superiority and capability of the offered control law to improve the transient performance of a closed-loop system using online adaptive parameters.

Global output-feedback stabilization for a class of uncertain time-varying nonlinear systems

This paper investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. Detailedly, based on a time-varying observer and transformation, an output-feedback controller is designed by skillfully combining adaptive technique, time-varying technique and well-known backstepping method. It is shown that, with the appropriate choice of the design parameters/functions, all the signals of the closed-loop system are bounded, and furthermore, the original system states globally converge to zero. It is worth mentioning that, the heavy nonlinearities are compensated by an updating law, while the serious unknowns and time-variations are compensated by a time-varying function. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant.

Finite-Horizon Approximate Optimal Guaranteed Cost Control of Uncertain Nonlinear Systems With Application to Mars Entry Guidance.

This paper studies the finite-horizon optimal guaranteed cost control (GCC) problem for a class of time-varying uncertain nonlinear systems. The aim of this problem is to find a robust state feedback controller such that the closed-loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost. A neural network (NN) based approximate optimal GCC design is developed. Initially, by modifying the cost function to account for the nonlinear perturbation of system, the optimal GCC problem is transformed into a finite-horizon optimal control problem of the nominal system. Subsequently, with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties, the solution to the optimal GCC problem is given in terms of a parametrized Hamilton-Jacobi-Bellman (PHJB) equation. Then, a NN method is developed to solve offline the PHJB equation approximately and thus obtain the nearly optimal GCC policy. Furthermore, the convergence of approximate PHJB equation and the robust admissibility of nearly optimal GCC policy are also analyzed. Finally, by applying the proposed design method to the entry guidance problem of the Mars lander, the achieved simulation results show the effectiveness of the proposed controller.

H∞fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

In this paper, the finite-horizon H∞ fault estimation problem is investigated for a class of uncertain nonlinear time-varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoulli-distributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite-horizon fault estimator to achieve the specified H∞ performance. The time-varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities. Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach. Copyright © 2014 John Wiley & Sons, Ltd.

H∞ fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

Summary In this paper, the finite-horizon H∞ fault estimation problem is investigated for a class of uncertain nonlinear time-varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoulli-distributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite-horizon fault estimator to achieve the specified H∞ performance. The time-varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities. Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach. Copyright © 2014 John Wiley & Sons, Ltd.

Global Finite-Time Stabilization via Time-Varying Feedback for Uncertain Nonlinear Systems

This paper focuses on the global finite-time stabilization via time-varying state-feedback for a class of uncertain time-varying nonlinear systems. The problem is rather difficult to solve, mainly due to the presence of more serious unknowns and time-variations and higher nonlinearities in the systems under investigation, particularly those in the control coefficients of the systems. To solve the problem, by skillfully combining time-varying methods and finite-time control theory in the existing literature, a novel time-varying (nonadaptive) design scheme is successfully proposed to finite-time stabilizing controllers. The remarkable feature of the design scheme is the selection of time-varying design functions which can capture the unknowns and time-variations in the systems as time increases. It is shown that if the design parameters and design functions in the designed controller are suitably chosen, then all the signals (i.e., the system states and control input) of the closed-loop system are globally bounded, and furthermore, the system states will reach zero in finite-time and remain zero thereafter. When only unknowns are limited in a known constant interval, a state-feedback controller can be designed to establish the finite-time stability for the resulting closed-loop system. When both unknowns and time-variations are limited in a known constant interval, the global uniform finite-time stability can be established.

Estimation of Regions of Attraction for Time-Varying Uncertain Nonlinear Systems Modeled by a Particular Class of Linear Differential Inclusion

This paper proposes the use of a particular class of linear differential inclusion (LDI) for the estimation of regions of attraction of asymptotically stable equilibrium points of nonlinear dynamical systems with time-varying parametric uncertainties bounded by a polytope. In this paper, we provide a systematic procedure based on the mean value theorem in conjunction to a linear matrix inequality based approximation technique to obtain the description of the uncertain nonlinear system via the proposed LDI form, which can be written equivalently as a particular class of a time-varying linear system. Through this suitable system representation in the form of this time-varying linear system, a numerical algorithm based on convex optimization is proposed to determine these regions of stability. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Practical stabilization of a class of uncertain time-varying nonlinear delay systems

In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.

Semiglobal ISpS Disturbance Attenuation With Output Tracking via Direct Adaptive Design

Direct adaptive partial state feedback control is presented to achieve semiglobally input-to-state practically stable (ISpS) disturbance attenuation with output tracking for a class of uncertain time-varying nonlinear systems in which the unmeasured dynamics do not possess a constant disturbance attenuation level (CDAL). Identifying a necessary condition for the existence of a CDAL, direct adaptive neural networks (NNs) control is developed, where the universal approximation property of NNs and the domination design are employed together to overcome the difficulties due to the lack of state information, unknown system nonlinearities, and unknown state-dependent disturbance attenuation gain. The proposed method is coherent in the sense that it is applicable to the case in which a CDAL exists.

Small Gain Theorem with Restrictions for Uncertain Time-varying Nonlinear Systems

This paper gives three versions of the small gain theorem with restrictions for uncertain time-varying nonlinear systems. The result can be viewed as an extension of the small gain theorem with restrictions for time-invariant nonlinear systems or the small gain theorem without restrictions for time-varying nonlinear systems. The result can be applied to study the stabilization problem or the output regulation problem of uncertain nonlinear systems.

Intelligent Robust Control for Uncertain Nonlinear Time-Varying Systems and Its Application to Robotic Systems

This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.