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 |