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We propose an extension of the input-output feedback linearization for a class of multivariate systems that are not input-output linearizable in a classical manner. The key observation is that the usual input-output linearization problem…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a…
The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions. In the specific setting…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for…
A differential system $[A] : \; Y'=AY$, with $A\in \mathrm{Mat}(n, \bar{k})$ is said to be in reduced form if $A\in \mathfrak{g}(\bar{k})$ where $\mathfrak{g}$ is the Lie algebra of the differential Galois group $G$ of $[A]$. In this…
This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned…
This paper presents the control and stabilization of the rotary inverted pendulum based on a general controller scheme. The proposed scheme has its foundation in classical control theory, and the importance of an integrator in disturbance…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…
We consider a nonlinear control system modeled as an ordinary differential equation subject to disturbance, with a state feedback controller parameterized as a feedforward neural network. We propose a framework for training controllers with…
Triangular numbers that are multiple of other triangular numbers are investigated. It is known that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers which are triangular numbers. If the…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…
A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
This paper proposes a new extended-state observer-based framework for adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an extended-state observer with an internal…