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This note studies the robust output feedback stabilization problem of multi-input multi-output invertible nonlinear systems with output-dependent multipliers. An "ideal" state feedback is first designed under certain mild assumptions. Then,…

Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…

By computing a feedback control via the linear quadratic regulator (LQR) approach and simulating a non-linear non-autonomous closed-loop system using this feedback, we combine two numerically challenging tasks. For the first task, the…

We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad…

This study proposes a feedback linearisation based on the back-stepping method with simple implementation and unique design process to design a non-linear controller with a goal of improving both steady-state and transient stability. The…

We revisit the long standing problem of the geometric free variable approach to computing the generating function for disk amplitudes in the matrix model formulation of the 3-state Potts model coupled to 2D discrete gravity. This method is…

This paper studies coefficient-level, structure-preserving output-feedback stabilization of linear port-Hamiltonian (pH) descriptor systems. Existing stabilization conditions generally require explicit pH representations, which may be…

Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output…

The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…

This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…

In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…

The non-linearity and non-convexity of power flow models and the phase coupling challenge the analysis and optimization of unbalanced distribution networks. To tackle the challenges, this paper proposes an online feedback-based linearized…

The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV…

We study systems of combinatorial Dyson-Schwinger equations with an arbitrary number $N$ of coupling constants. The considered Hopf algebra of Feynman graphs is $\mathbb{N}^N$-graded, and we wonder if the graded subalgebra generated by the…

Analytical solutions to nonlinear differential equations -- where they exist at all -- can often be very difficult to find. For example, Duffing's equation for a system with cubic stiffness requires the use of elliptic functions in the…

Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given…

This paper develops methods for analyzing periodic orbits of states of linear feedback shift registers with periodic coefficients and estimating their lengths. These shift registers are among the simplest nonlinear feedback shift registers…

This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…

The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…

In this work, we derive dynamic output-feedback controllers that render the closed-loop system externally positive. We begin by expressing the class of discrete-time, linear, time-invariant systems and the class of dynamic controllers in…