Computational Optimal Control Software

From MISER to GEKKO

 

Video Demo
 

 

MISER Manual Example Problems:

 

                        Continuous Time

 

_    Problem 1

 

(pdf) and (html).

 

 

 

_    Problem 2

 

(pdf), and (html).

 

 

_    Problem 3

 

(pdf), and (html).

 

 

_    Problem 4

 

(pdf), and (html).

 

 

_    Problem 5

 

(pdf), and (html).

 

 

_    Problem 6

 

(pdf), and (html).

 

 

Discrete Time

 

 

_    Discrete-time Problem D1

 

(pdf), and (html).

 

 

_    Discrete-time Problem D2

 

(pdf), and (html).

 

 

_    Discrete-time Problem D3

 

(pdf), and (html).

 

 

Other interesting GEKKO exercise:

 

 

The Newton-Gregory problem of the impossibility of the 13^th kissing sphere (html).

 

 

Simple Pursuit on the boundary of the unit circle (as optimal control problem) (html).

 

 

Apollonius Pursuit (as optimal parameter selection problem) (html).

 

 

Simple Pursuit on the surface of unit sphere (as optimal control problem) (html).

 

 

If you are attempting to find the “closed-form solution” to the problem of Pursuit on the surface of unit sphere (as time optimal control problem), picture below may give you a hint.

Other simple but interesting related Python exercise:

 

Given, 3 non-intersecting non-touching circles with different radius, find and plot the 8 Apollonius Circles (html).

 

Given, 3 kissing circles, plot the Apollonius Gasket (html).

 

 

 

Reference:

1. Beal, L.D.R.; Hill, D.C.; Martin, R.A.; Hedengren, J.D. GEKKO Optimization Suite. Processes 2018, 6, 106.
2. Video Demo of MISER2 version 2.0 MATLAB version via PolyU vSCC MATLAB for my Capstone Project students (restricted access)

This page is prepared by

Dr. Heung Wing Joseph Lee