HCS Toolbox for MATLAB

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User Manual for Version 0.2

Introduction

Get Started

Installation

Mathematical Backgrounds

Homogeneous Euclidean Space $\mathbb{R}^n_{\mathbf{d}}$

Homogeneous Norm $\|\cdot\|_{\mathbf{ d } }$

Addition $\tilde +$ in Homogeneous Space

Multiplication $\tilde \cdot$ in Homogeneous Space

Homogeneous Inner Product $\langle \cdot,\cdot\rangle_{\mathbf{ d } }$

Homogeneous Homeomorphism $\Phi$

Inverse Homogeneous Homeomorphism $\Phi^{-1}$

Homogeneous Geometric Objects

Homogeneous Curve

Homogeneous Sphere

Homogeneous Projection

Homogeneous Cone

Control Design

Homogeneous Proportional Control (HPC)

Fixed-time HPC

Homogeneous Sliding Mode Control (HSMC)

Homogeneous Proportional-Integral Control (HPIC)

Fixed-time HPIC

HSMC with integral action

Upgrading Linear Proportional Controller (LPC) to HPC

Upgrading Linear Proportional-Integral Controller (LPIC) to HPIC

Observer Design

Homogeneous Observer (HO)

Fixed-time HO

Upgrading Linear Observer (LO) to HO

Examples

Demo of compuation of homogeneous norm

Demo of compuation of homogeneous projection

Demo of homogeneous algebra

Plot of homogeneous curve

Plot of homogeneous sphere

Plot of homogeneous cone

Demo HPC

Demo Fixed-time HPC

Demo HSMC

Demo HPIC

Demo Fixed-time HPIC

Demo HSMC with integral action

Demo Upgrading LPC to HPC

Demo Upgrading LPIC to HPIC

Demo HO

Demo Fixed-time HO

Demo Upgrading LO to HO