Modeling Multi-Phase Control Problems 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 Sequential Activation of Metabolic Pathways
65 Methanol to Hydrocarbons
66 Min Energy Orbit Transfer
67 Minimum Climb Time (English Units)
68 Missile Intercept
69 Moonlander Example
70 Nagurka Problem
71 Nishida problem
72 Nondifferentiable system
73 Nonlinear CSTR
74 Obstacle Avoidance
75 Oil Shale Pyrolysis
76 One Dimensional Rocket Ascent
77 Parametric Sensitivity Control
78 Orbit Raising Maximum Radius
79 Orbit Raising Minimum Time
80 Parallel Reactions in Tubular Reactor
81 Parameter Estimation Problem
82 Park-Ramirez bioreactor
83 Path Tracking Robot
84 Path Tracking Robot (Two-Phase)
85 Pendulum Gravity Estimation
86 Penicillin Plant
87 Plug-Flow Tubular Reactor
88 Quadratic constraint problem
89 Quadruple Integral
90 Radio telescope
91 Rayleigh Unconstrained
92 Rigid Body Rotation
93 Robot Arm Movement
94 Time-optimal Trajectories for Robot Manipulators
95 Satellite Control
96 Second Order System
97 Space Shuttle Reentry
98 Simple Bang Bang Problem
99 Singular Arc Problem
100 Singular CSTR
101 Singular Control 1
102 Singular Control 2
103 Singular Control 3
104 Singular Control 4
105 Singular Control 5
106 Singular Control 6
107 Spring Mass Damper (2 Degree Freedom)
108 Stirred Tank
109 Temperature Control
110 A Simple Terminal Constraint Problem
111 Third order system
112 Time Delay 1
113 Time Delay 1 (Approximate)
114 Time Delay 2
115 Time Delay 2 (Approximate)
116 Transfer Min Swing
117 Tubular Reactor
118 Turbo Generator
119 Two-Link Robot
120 Two-Link Robotic Arm
121 Two-Phase Schwartz
122 Two Stage CSTR
123 Van der Pol Oscillator
124 Zermelos problem (version 1)
125 Zermelos problem (version 2)
References
Notes

4 Multi-phase optimal control

brysonDenhamTwoPhase.m is a good example for multi-phase optimal control. The user simply have to link the states to complete the problem formulation.

 link = {final(p1,x1p1) == initial(p2,x1p2)
         final(p1,x2p1) == initial(p2,x2p2)};

It is important to keep in mind that the costs have to be individually defined for the phases in the case that a integrating function is used.

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