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This notebook contains material from cbe30338-2021; content is available on Github.

< 6.4 Implementing Predictive Control | Contents | Tag Index | 7.0 Discrete Event Systems >

6.5 Quiz Review for Chapters 5 and 6

6.5.1 Material covered

• Optimization: 5.1, 5.2, 5.3, 5.5,
• Predictive Control: 6.1, 6.2, 6.3, 6.4

6.5.2 Learning Goals

You should be able to:

1. Describe elements of an optimization problem:

   • Decision variables.
     • What are decision variables?
     • Types of decision variables: Real, Nonnegative, boolean, integer.
     • Typical onstraints on decision variables: Upper and lower bounds.
   • Constraints
     • Inequalities
     • Equalitis
     • Algebraic
     • Differential equations
     • Feasible regions
     • Active vs inactive constraints
   • Objective function
     • Types: Minimize, maximize
     • Objective functions are scalar functions of the decision variables
   • Types of optimization problems
     • Linear, Nonlinear
     • Integer
   • Outcomes
     • Feasible vs infeasible
     • Unbounded
     • Optimal solution

2. Formulating Optimization problems

   • Blending problems
     • Decision variables represent how much of something will be used or created
     • There is usually a collection of underlying materials or resourcds that will be combined.
     • The objective function typically represents overall cost, profit, or property.
   • Procedure
     • Identify the index sets.
     • Create decision variables, one for each member of the index set
     • Establish upper and lower bounds, if they exist, for the decision variables
     • Define objective function
     • Define constraints
     • Create problem and solve
     • Display solution in ways that are meaningful to the application
   • Sensitivity Studies

3. Predictive Control

   • Open-Loop optimization
     • Formulate and solve for the control trajectory
     • The state-space model provide equality constraints
   • Closed-loop predictive control
     • Observer/Estimator required to provide current values of the state
     • Solve an open-loop optimization to find control policy
     • Apply new control policy
     • Repeat the procedure when new measurement information is available

6.5.3 Exercises

1. Study questions from Notebook 5.2.3
2. Review the sensitivity analysis for Homework 4
3. Review the medical application in this notebook https://jckantor.github.io/CBE30338/07.01-Simulation-and-Optimal-Control-in-Pharmacokinetics.html.
   • Be sure you can recode the same problem in CVXPY.
   • As stated, this is an open-loop opimization problem. Be sure you would know how to formulate the problem for predictive control. What would be the objective function? The constraints? The bounds on the decision variables?

< 6.4 Implementing Predictive Control | Contents | Tag Index | 7.0 Discrete Event Systems >