Least squares based iterative identification algorithms for input nonlinear controlled autoregressive systems based on the auxiliary model

For the difficulty that the information vector in the identification model contains the unknown variables, we substitute these unknown variables with the outputs of the auxiliary model and then develop an auxiliary model based recursive least squares algorithm, an auxiliary model based least squares iterative (AM-LSI) algorithm, and derive an equivalent matrix decomposition based AM-LSI algorithm for input nonlinear controlled autoregressive systems based on the auxiliary model. The simulation results show that the proposed algorithms can estimate the parameters of a class of input nonlinear systems.     

Optimal input design for hydrodynamic derivatives estimation of nonlinear dynamic model of AUV

Input design has a dominant role in developing the dynamic model of an autonomous underwater vehicle (AUV) through system identification. Optimal input design is the process of generating informative inputs that can be used to provide a good-quality dynamic model of AUV. In this paper, amplitude-modulated pseudo-random binary signal (APRBS) inputs are optimally designed in order to estimate the hydrodynamic derivatives of an AUV’s nonlinear dynamic model. The input controls are designed so as to minimize uncertainty in estimating hydrodynamic derivatives. The employed approach can design multiple inputs and apply constraints on an AUV system’s inputs and outputs. The genetic algorithm is utilized to solve the constraint optimization problem. The presented algorithm is used for designing the input signals of Hydrolab300 AUV, and the estimation obtained by these inputs is compared with that of zigzag maneuver. According to the results, the designed APRBS inputs improve the uncertainties that exist in estimating hydrodynamic derivatives better than zigzag inputs.     

A dynamic model for a Timoshenko beam in an elastic-plastic state

Summary In this paper, equations which describe the propagation of elastic-plastic waves of combined stress resultants in a Timoshenko beam under symmetrical bending and tension or compression are derived. It is assumed that the beam material exhibits a weak work-hardening and strain-rate independent behaviour. The normality rule is postulate for the plastic strain rates of an infinitesimal volume element. The wave propagation is described by a hyperbolic system of differential equations, the state variables of which are the stress resultants and the strain rates of an infinitesimal beam element. It is shown that the actual distribution of shear stress in the plastic range need not be taken into account by means of a plastic shear correction factor.

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Ein dynamisches Modell für einen Timoshenko-Balken im elastisch-plastischen Zustand

Übersicht Diese Arbeit stellt ein Modell vor, das die Ausbreitung von elastischen und plastischen Wellen kombinierter Schnittgrößen in dynamisch hochbeanspruchten Balken unter gerader Biegung und Normalkraft beschreibt. Das Werkstoff-verhalten wird als schwach verfestigend und zeitunabhängig angenommen. Die Normalitätsregel wird für die plastischen Verzerrungsgeschwindigkeiten eines Volumenelements postuliert. Die Ausbreitung der Wellen wird durch ein hyperbolisches System von Differentialgleichungen beschrieben, dessen Zustandsvariablen die Schnittgrößen und die Formänderungs-geschwindigkeiten eines Balkenelements sind. Schließlich wird gezeigt, daß die Einführung eines plastischen Schubkorrekturfaktors nicht erforderlich ist.

     

Recursive least squares parameter estimation algorithm for dual-rate sampled-data nonlinear systems

This paper focuses on the identification problem of Hammerstein systems with dual-rate sampling. Using the key-term separation principle, we derive a regression identification model with different input updating and output sampling rates. To solve the identification problem of the dual-rate Hammerstein systems with the unmeasurable variables in the information vector, an auxiliary model-based recursive least squares algorithm is presented by replacing the unmeasurable variables with their corresponding recursive estimates. Convergence properties of the algorithm are analyzed. Simulation results show that the proposed algorithm can estimate the parameters of a class of nonlinear systems.     

Particle filtering for nonlinear dynamic state systems with unknown noise statistics

In this paper, we provide a tutorial for the applications of cost-reference particle filter (CRPF) to problems in signal processing disciplines. CRPF works in particle filtering (PF) framework although it may not be viewed as a Bayesian approach because the estimation is not based on the expected posterior function. CRPF has an interesting feature, i.e., the information of the noise statistics is not needed in its applications as opposed to the cases of the Kalman filter and standard PF approaches that work in dynamic state systems. Therefore, it is highly effective when the noise information is not available; nevertheless, it may not show optimal performance in general. In this paper, we introduce and disseminate this useful approach that is not known to many researchers even in related fields, and show how to effectively apply to problems which we provide as examples.     

An adaptive quenching algorithm for a nonlinear single-degree-of-freedom system

An indirect adaptive quenching algorithm for a nonlinear single-degree-of-freedom system with unknown constant system parameters is presented. The system is subject to external or parametric sinusoidal disturbances and the resulting control signal is also sinusoidal. The quenching algorithm provides a reduction in the control effort required compared to direct disturbance cancellation. The disturbance sinusoid and the unknown parameters are incorporated into the system model and an extended Kalman filter (EKF) with modified update equations is used to estimate the system state and parameters. The estimates are then used to form the quenching signal. The adaptive quenching algorithm is found to work well inside a quenching region defined by the separatrices and suggests the use of a hybrid control law. The algorithm was verified by implementing it on an analog computer.     

A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems

This paper proposes a method to generate several independent periodic attractors, in continuous-time nonchaotic systems (with an equilibrium point or a limit cycle), based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on a precise zone of a precise curve that depends on the parameters of the system. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced. Throughout this study, the proposed methodology is illustrated with several examples.     

Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model

This paper presents a gradient-based iterative identification algorithm and an auxiliary-model-based multi-innovation generalized extended stochastic gradient algorithm for input nonlinear systems with autoregressive moving average (ARMA) noises, i.e., the input nonlinear Box–Jenkins (IN–BJ) systems. The estimation errors given by the gradient-based iterative algorithm are smaller than the generalized extended stochastic gradient algorithm under same data lengths. A simulation example is provided.     

Estimation of Lyapunov exponents from a time series for n-dimensional state space using nonlinear mapping

It has been demonstrated that when estimating Lyapunov exponents using a time series, nonlinear mapping used for characterizing the evolution of the neighbors leads to more accurate negative exponents and is more robust to noise in the times series. However, the number of unknown elements of the matrices associated with nonlinear mapping increases significantly with the embedding dimensions of the state space where the dynamics is reconstructed. Such unknown coefficients are solved from a set of linear algebraic equations based on the least square-root fit method. Derivation of such linear equations and computer programming are tedious and error prone especially for the systems with high embedding dimensions. In this work, we develop a general form of the linear algebraic equations and the corresponding computer program in terms of arbitrary embedding dimensions. A stable robotic system with all negative Lyapunov exponents and the Lorenz system with positive, zero, and negative exponents are used to demonstrate the efficacy of the proposed method. The work can contribute significantly to estimating Lyapunov exponents for systems with large embedding dimensions.     

Mem-models and state event location algorithm for a prototypical aerospace system

Nonlinear Dynamics - This paper presents a suite of dynamic models enhanced by mem-models. A prototypical pogo stick model might mimic a space hopper or a segmented telescope mirror actuator, while...     

An improved precise integration method for nonlinear dynamic system

In the present paper, based on the precise integration method established in linear dynamic system, an improved precise integration method is presented for nonlinear dynamic system. Firstly, the nonlinear dynamic system is converted into an augmented Lie type dynamic system. Then the precise integration method is improved for solving the above augmented equation and preserving its group structure in the meantime. Finally, two numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.     

基于双速度模式的多级惯性系动基座粗对准算法

由于传统载体系速度(V b)辅助惯性系对准算法(IA)中的近似忽略项,不可避免的存在模型误差问题将会影响捷联惯性导航系统对准精度,且会随载体速度增大而更加明显.对传统多级IA算法进行改进,提出基于双速度模式的惯性系初始对准算法来解决其模型误差问题且不牺牲其对准精度的稳定性,同时利用回溯计算来逐步提高对准精度,保证对准快...     

A low-complexity tracker design for uncertain nonholonomic wheeled mobile robots with time-varying input delay at nonlinear dynamic level

A low-complexity design problem of tracking scheme for uncertain nonholonomic mobile robots is investigated in the presence of unknown time-varying input delay. It is assumed that nonlinearities and parameters of robots and their bounds are unknown. Based on a nonlinear error transformation, a tracking control scheme ensuring preassigned bounds of overshoot, convergence rate, and steady-state values of a tracking error is firstly presented in the absence of input delay, without using any adaptive and function approximation mechanism to estimate unknown nonlinearities and model parameters and computing repeated time derivatives of certain signals. Then, we develop a low-complexity tracking scheme to deal with unknown time-varying input delay of mobile robots where some auxiliary signals and design conditions are derived for the design and stability analysis of the proposed tracking scheme. The boundedness of all signals in the closed-loop system and the guarantee of tracking performance with preassigned bounds are established through Lyapunov stability analysis. The validity of the proposed theoretical result is shown by a simulation example.