This paper investigates the adaptive robust control problem based on reinforcement learning for an affine nonlinear system with unknown time-varying uncertainty. Inspired by ability to estimate uncertainty of neural network, a novel policy iteration algorithm is proposed which alternates between value evaluation, estimation, and update steps until law obtained. Especially during step approximat...

We revisit the concept of observation error for nonlinear observers of nonlinear systems. In order to obtain a coordinate free notion of such an error we define it using fiber bundles over the system manifold. The new notion ties in nicely with Brockett’s and Willems’ classical description of nonlinear systems as bundles as well as with the related description of observers as bundles due to van...

The goal of this paper is to establish the precise connection between the centro-affine invariants of plane curves and the feedback invariants of nonlinear scalar control systems in the plane. We will also show how the centro-affine structure provides a shortcut to the structure equations for feedback equivalence one obtains by applying Cartan’s equivalence method.

We study the recently introduced notion of output-input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. The subject of this paper is developing the theory of output-input stability in the multi-input, multi-output setting. We show that output-input stability can be viewed as a combination of two system properties, one related to d...

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem real-world industrial applications. Koopman operator theory allows one to analyze through the lens of linear bilinear systems. The key idea these methods lies in transformation coordinates system into observables, which are that allow representation original (control system) as highe...

The performance of global affine and nonlinear transformations for speaker adaptation in a hidden Markov model (HMM) speech recognition system are compared in this paper. The nonlinear transformation was obtained with a multilayer perceptron network (MLP) which was trained during the adaptation process to transform the mean vectors of the HMMs such that the output probabilities of the HMMs for ...

Active noise control (ANC) systems employing the conventional fast affine projection (FAP) algorithms may lead to low ANC performance when the non-unity step size is chosen. To solve the problem, an LDL T fast affine projection algorithm was proposed recently for the linear ANC. In this paper, the LDL T -FAP algorithm is further utilized, along with a third-order Volterra filter, for nonlinear ...

This paper considers the problem of the stabilization of affine nonlinear control systems. First, we assume that the systems under investigation are of the generalized Byrnes–Isidori normal form. A new way to approximate the center manifold is proposed, which can reduce the error degree of the center manifold approximation. A new matrix product, called the semi-tensor product, is introduced to ...

In this paper we introduce affine invariants based on a multiscale framework combined with nonlinear comparison operations. The resulting descriptors are histograms, which are computed from a set of comparison results using binary coding. The new constructions are analogous to other multiscale affine invariants, but the use of highly nonlinear operations yields clear advantages in discriminabil...

This article discusses essentially nonlinear systems. Following the approach of applying pseudolinear inequalitiesdeveloped in a number works, new estimates for variation Lyapunov functions along solutionsof considered systems equations are obtained. Based on these estimates, we obtain sufficient conditionsfor equiboundedness solutions second-order and conditions stability anessentially system ...