Parameter Convergence Analysis Research Articles

Third-degree B-spline collocation method for singularly perturbed time delay parabolic problem with two parameters

This study deals with a fitted third-degree B-spline collocation method for two parametric singularly perturbed parabolic problems with a time lag. The proposed method comprises the Cranck-Nicolson method for time discretization and the third-degree B-spline method spatial variable discretization. Rigorous numerical experimentations were carried out on some test examples. The obtained numerical results depict that the proposed scheme is more accurate than some methods existing in the literature. Parameter convergence analysis of the scheme is carried out and shows the present scheme is (ε−μ)−uniform convergent with the order of convergence ((Δt)2 + ℓ2).

An improved Hammerstein system identification method using Stein Variational Inference and sampling technology

This paper considers the identification of the Hammerstein system with immeasurable process noise. The complexity of the Hammerstein system makes it difficult to obtain accurate mathematical expressions of the parameters, or even impossible to obtain accurate mathematical expressions at all. In this contribution, we cast the Hammerstein system parameter identification problem as a posterior parameter estimation problem and take a sampling and Stein variational inference viewpoint to solve it. Improved Stein variational gradient descent(ISVGD)algorithm is proposed in posterior parameter calculation. Compared with other methods, not only the prior distribution of parameters but also the proposal distribution of parameters is considered. In other words, The posterior information is enriched and the parameter identification accuracy is improved. At the same time, ISVGD and reversible jump markov chain monte carlo (RJMCMC) algorithms are used (called ISVGD-RJMCMC algorithm) in the structure detection problem. In the algorithm, the correct basis function number k can be found in the parameter estimation. It tends to be accurate but is slow to converge. Three simulation examples were given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches were analyzed, including parameter estimation accuracy and error, system order estimation and parameter convergence analysis.

Transient Improvement of Model-Reference Adaptive Control and Parameter Convergence Rate Analysis

The parameter convergence analysis of a modified model-reference adaptive control (M-MRAC) algorithm is presented. The plants considered are continuous with relative degree one. It is verified that the M-MRAC scheme approaches the MRAC scheme when a control design gain increases. Moreover, before this gain reaches high values, the M-MRAC improves the update parameters’ convergence. This analysis is performed by noting a clear connection between the M-MRAC and the conventional MRAC by adding a control output injection term. The methodology developed allows for estimating the parameter convergence rate, and simulation results illustrate the improvement in the transient behavior and the parameter convergence attained with the analyzed adaptive schemes.

Dynamic response of an axisymmetric transversely isotropic medium with its modulus varying with depth subjected to LWD load

ABSTRACT In this paper, the dynamic response of an axisymmetric transversely isotropic medium with its modulus varying with depth subjected to the lightweight deflectometer (LWD) load is calculated by an analytical solution method. In this model, the analytical solutions are expressed as power series, and both cases of vertical modulus, increasing and decreasing with depth, are considered. This study can be divided into three key steps. Firstly, the ordinary differential equations are obtained via the Hankel–Laplace transform, and the general solutions of dynamic response are obtained according to the Frobenius method. Secondly, combined with the boundary conditions, the dynamic responses of the subgrade in the time domain are calculated. The accuracy and reliability of this dynamic model are proved by parameter convergence analysis, finite element method and comparison validation. Lastly, the effect of thickness, non-uniform distribution of modulus and transverse isotropy subjected to LWD load are analysed and discussed. The calculation methods and the corresponding results are meaningful for the design and non-destructive monitoring of the subgrade.

Adaptive Cooperative Tracking and Parameter Estimation of an Uncertain Leader over General Directed Graphs

This paper studies the cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, where the symmetry of Laplacian matrix does not hold. This is due to two newly developed Lyapunov equations, which solely depend on communication network topologies. Interestingly, using these Lyapunov equations, many results of multi-agent systems over undirected graphs can be extended to general directed graphs. Finally, this paper also advances the knowledge base of adaptive control systems by providing a main tool in the analysis of parameter convergence for adaptive observers.

Adaptive Parameter Estimation With Convergence Analysis for the Prandtl–Ishlinskii Hysteresis Operator

Abstract Hysteresis is a nonlinear characteristic ubiquitously exhibited by smart material sensors and actuators, such as piezoelectric actuators and shape memory alloys. The Prandtl–Ishlinskii (PI) operator is widely used to describe hysteresis of smart material systems due to its simple structure and the existence of analytical inverse. A PI operator consists of a weighted superposition of play (backlash) operators. While adaptive estimation of the weights for PI operators has been reported in the literature, rigorous analysis of parameter convergence is lacking. In this article, we establish persistent excitation and thus parameter convergence for adaptive weight estimation under a rather modest condition on the input to the PI operator. The analysis is further supported via simulation, where a recursive least square (RLS) method is adopted for parameter estimation.

Adaptive leaderless consensus of agents in jointly connected networks

In this paper, the leaderless consensus problem of multi-agent systems with jointly connected topologies and nonlinear dynamics is considered, in which the nonlinear dynamics are assumed to be non-identical and unknown. The unknown nonlinear dynamics existing in the systems are assumed to be linearly parameterized, and an adaptive design method for leaderless multi-agent systems is presented. By just using the relative position information between each agent and its neighbors, a distributed adaptive consensus control algorithm for the considered systems is proposed, in which the network graphs are jointly connected. Both the global uniform asymptotical stability and the global uniform asymptotical parameter convergence analysis of the adaptive control algorithm are carried out by using adaptive control theory, Lyapunov theory and algebraic graph theory. Finally, an example is given to illustrate the validity of our theoretical results.

Adaptive Group Consensus of Multi-Agent Networks via Pinning Control

This paper studies the group consensus problem in networks of multi-agent systems, in which the nonlinear dynamics of all agents are unknown and nonidentical. We assume that the unknown dynamics are linearly parameterized. Adaptive control method is adopted in the algorithm design. A novel algorithm is proposed for the multi-agent systems to reach group consensus via pinning control strategies, which only rely on the relative position information between neighboring agents. The stability and parameter convergence analysis are done based on Lyapunov theory, Barbalat's lemma, adaptive control theory and algebraic graph theory. Finally, a simulation example is given to validate our theoretical results.

Adaptive Coordination Control of Multi-Agent Systems with Switching Topologies and Unknown Nonlinear Dynamics

In this paper, we study the leader-following adaptive consensus problem for multi-agent systems with unknown nonlinear dynamics. The topologies of the networks are switching. A novel adaptive consensus algorithm is proposed by using linear parameterizations of unknown nonlinear dynamics of all agents. By stability analysis and parameter convergence analysis of the proposed algorithm, adaptive consensus can be realized based on neighboring graphs. The stability analysis is based on algebraic graph theory and Lyapunov theory, the PE condition plays a key role in parameter convergence analysis. Example is given to validate the theoretical results.

Identification of nonlinear flight dynamics: theory and practice

This article presents an innovative time-domain nonlinear mapping-based identification method. The method reported is applied to identify the unknown parameters of multivariable dynamic systems which are mapped by nonlinear differential equations. A systematic identification method is introduced, and a novel algorithm is developed using nonlinear error maps. An analysis of parameter convergence is provided and the regions of convergence can be found using the second method of Lyapunov. Innovative nonquadratic Lyapunov functions are designed and used. Analytical and numerical studies are performed to illustrate and validate the identification concept. The unsteady flight of a high-alpha aircraft in the longitudinal axis is chosen as a nonlinear case study. The unknown parameters are identified. Simulation results show that the model dynamics match the experimental data. The reported example demonstrates that the time-domain nonlinear mapping-based identification method ensures robustness and reduces major shortcomings in stability, convergence, and computational efficiency compared with other algorithms available.

Nonlinearities enhance parameter convergence in strict feedback systems

Following the development of a parameter convergence analysis procedure for output-feedback nonlinear systems (1995, 1998), the authors shift their attention to strict feedback nonlinear systems in this paper. They develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real matrix. Moreover, the authors show that this convergence is exponential. Finally, they prove that even if the rows of this constant matrix are not linearly independent, partial parameter convergence is still achieved, in the sense that the parameter error vector converges asymptotically to the left nullspace of this matrix.