Scaling of Optimal Control Models in MATLAB

TOMLAB /PROPT Manual
Contents
1 PROPT Guide Overview
2 Introduction to PROPT
3 Modeling optimal control problems
4 Multi-phase optimal control
5 Scaling of optimal control problems
6 Setting solver and options
7 Solving optimal control problems
8 | | OPTIMAL CONTROL EXAMPLES | |
9 Acrobot
10 A Linear Problem with Bang Bang Control
11 Batch Fermentor
12 Batch Production
13 Batch Reactor Problem
14 The Brachistochrone Problem
15 The Brachistochrone Problem (DAE formulation)
16 Bridge Crane System
17 Bryson-Denham Problem
18 Bryson-Denham Problem (Detailed)
19 Bryson-Denham Problem (Short version)
20 Bryson-Denham Two Phase Problem
21 Bryson Maxrange
22 Catalyst Mixing
23 Catalytic Cracking of Gas Oil
24 Flow in a Channel
25 Coloumb Friction 1
26 Coloumb Friction 2
27 Continuous State Constraint Problem
28 Curve Area Maximization
29 Denbigh’s System of Reactions
30 Dielectrophoresis Particle Control
31 Disturbance Control
32 Drug Displacement Problem
33 Optimal Drug Scheduling for Cancer Chemotherapy
34 Euler Buckling Problem
35 MK2 5-Link robot
36 Flight Path Tracking
37 Food Sterilization
38 Free Floating Robot
39 Fuller Phenomenon
40 Genetic 1
41 Genetic 2
42 Global Dynamic System
43 Goddard Rocket, Maximum Ascent
44 Goddard Rocket, Maximum Ascent, Final time free, Singular solution
45 Goddard Rocket, Maximum Ascent, Final time fixed, Singular solution
46 Greenhouse Climate Control
47 Grusins Metric
48 Hang Glider Control
49 Hanging Chain
50 High Dimensional Control
51 Hyper Sensitive Optimal Control
52 Initial Value Problem
53 Isometrization of alpha pinene
54 Isoperimetric Constraint Problem
55 Jumbo Crane Container Control
56 Lee-Ramirez Bioreactor
57 Linear Tangent Steering Problem
58 Linear Gas Absorber
59 Linear Pendulum
60 Linear Problem with Bang Bang Control
61 LQR Problem
62 Marine Population Dynamics
63 Max Radius Orbit Transfer
64 Methanol to Hydrocarbons
65 Min Energy Orbit Transfer
66 Missile Intercept
67 Moonlander Example
68 Nagurka Problem
69 Nishida problem
70 Nondifferentiable system
71 Nonlinear CSTR
72 Obstacle Avoidance
73 Oil Shale Pyrolysis
74 One Dimensional Rocket Ascent
75 Parametric Sensitivity Control
76 Parallel Reactions in Tubular Reactor
77 Parameter Estimation Problem
78 Park-Ramirez bioreactor
79 Path Tracking Robot
80 Path Tracking Robot (Two-Phase)
81 Pendulum Gravity Estimation
82 Penicillin Plant
83 Plug-Flow Tubular Reactor
84 Quadratic constraint problem
85 Quadruple Integral
86 Radio telescope
87 Rayleigh Unconstrained
88 Rigid Body Rotation
89 Robot Arm Movement
90 Time-optimal Trajectories for Robot Manipulators
91 Satellite Control
92 Second Order System
93 Simple Bang Bang Problem
94 Singular Arc Problem
95 Singular CSTR
96 Singular Control 1
97 Singular Control 2
98 Singular Control 3
99 Singular Control 4
100 Singular Control 5
101 Singular Control 6
102 Spring Mass Damper (2 Degree Freedom)
103 Stirred Tank
104 Temperature Control
105 A Simple Terminal Constraint Problem
106 Third order system
107 Time Delay 1
108 Time Delay 1 (Approximate)
109 Time Delay 2
110 Time Delay 2 (Approximate)
111 Transfer Min Swing
112 Tubular Reactor
113 Turbo Generator
114 Two-Link Robot
115 Two-Link Robotic Arm
116 Two-Phase Schwartz
117 Two Stage CSTR
118 Van der Pol Oscillator
119 Zermelos problem (version 1)
120 Zermelos problem (version 2)
References
Notes

5 Scaling of optimal control problems

Scaling of optimal control problems are best done after they are defined. The level of the cost function, variables, states and controls should be balanced around 1.

batchFermentor.m exemplifies a very basic way of scaling an optimal control problem.

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