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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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5 results for “forward-shifts”

On the Exact Linearization and Control of Flat Discrete-time Systemsmath.OC

The paper tackles exact linearization and control of flat discrete-time systems.

problem Exact linearization and control of flat nonlinear discrete-time systems.

method Investigates conditions for choosing new inputs and feedbacks that may depend on forward-shifts of the new input.

result Easily verifiable conditions for choosing a feasible input and a new input that minimizes forward-shifts of the flat output.

flat systems discrete-time exact linearization control feedbacks

2022-01-01abs ↗pdf ↗

A Trajectory-Based Approach to Discrete-Time Flatnessmath.DG

Extended flatness approach for discrete-time systems considers forward and backward shifts.

problem Defining flatness for discrete-time systems with forward-shifts.

method Introducing backward-shifts to extend flatness definition.

result Extended flat systems maintain key properties like reachability and controllability.

discrete-time systems flatness forward-shifts backward-shifts trajectory-based approach

2020-12-15abs ↗pdf ↗

A Normal Form for Two-Input Flat Nonlinear Discrete-Time Systemsmath.DS

We find a normal form for two-input flat discrete-time systems.

problem No comparable normal form exists for flat continuous-time systems.

method State- and input transformations to achieve a triangular structure.

result A systematic parameterization of system variables by the flat output and its shifts.

flat systems discrete-time normal form triangular structure

2020-04-20abs ↗pdf ↗

Flatness of Discrete-time Systems, a simple Approachmath.DG

Discrete-time systems can be characterized by simple flat coordinates and their shifts.

problem Characterizing flatness of discrete-time systems.

method Developed a map from flat coordinates and their shifts to system state and input, fulfilling system equations identically.

result Derived necessary conditions for a system to be flat, without requiring differential geometry methods.

flatness discrete-time systems simple approach submersion shift systems

2023-03-09abs ↗pdf ↗

Differential-Geometric Decomposition of Flat Nonlinear Discrete-Time Systemsmath.OC

We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is available. The advantage of such a decomposition is that the complete system is flat …

2019-07-01abs ↗pdf ↗