Question: Consider the following optimal control problem x = u, x(0) = 1 1 - = 45 (u - qx) dt where q is a

Consider the following optimal control problem x = u, x(0) = 1 1 - = 45 (u - qx) dt where q is a constant. (a) Explain whether or not this is a linear quadratic regulator problem if q > 0. (b) Let q = 0 in this part. Pretend that you have not taken this course and learned the Minimum Principle. Determine the solution (u*(t) and x*(t)) to the problem by using just logic and observation. (c) Solve the problem with a q = 8 by finding the optimal pair {x*(t), u* (t)} Hint: the solution of differential equation * + kx = 0 with k > 0 is x(t) = c sin(at) + C cos(at) where = k

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Finance Questions!

THE PRISON SERVICE The prison service provides an excellent example of the complexity of stakeholder requirements, to some extent reflecting the mixed task it faces. Society requires the service to...

A researcher conducts a study that examines the relationship between dementia and restraint use. A 95% confidence interval is selected (alpha=.05). If the p-value = 0.03, what is the correct...

List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...

For the standardnormal distribution, compute Z subscript .03. Use Excel and round the answer to two decimal places.

In a receiver operating characteristic analysis, sensitivity is defined as a: Question 35 options: false positive false negative predicted positive true negative true positive

Please use hamiltonian Problem 5 (30 points). Consider the following optimal control problem: 1 max (ty (1?) % (u(t))2) dt \"(331318) 0 subject to y(t] = 11505), 7.56) E R, 9(0) 2 07 y(1) is free....

1.Explain the three varying characteristics of common shares. 2.What are flotation costs? 3.How is cost of common equity computed for no growth stock? for constant growth stock? 4.What is a dividend...

1. 2. Consider the following elliptic PDE: au z2 = x2 1, = [0, 1]; y= [0, 1] ay? Using finite difference methd with step size h = 0.25 for both x-and y-domains, determine u(x, y) at all nodes of the...

Consider a financial market with a riskless asset and a risky asset. The price of the riskless asset S follows dS = Serdt, where r is a constant. The price of the risky asset S follows dS. = Studt +...

my economics assign Consider the following economy. There are two periods, 0 and 1, and a single consumption good. The economy is populated by two types of agents: nanciers (F) and entrepreneurs (E)....

A project is about placing reinforcing steel for a cast-in-situ footing. The project manager needs to plan job clock time, labor productivity and labor cost estimate by employing two skilled steel...

Describe a variable- or adjustable-rate loan. List four features that should be compared when shopping for this type of loan. What is a convertible loan?

Mr. and Mrs. Martinez hope to send their daughter to college in eleven years. How much money should they invest now at an interest rate of 8% per year, compounded continuously , in order to be able...

The following financial information is available for Plummer Corporation. The weighted-average number of shares of common stock outstanding was 80,000 for 2016 and 100,000 for 2017. Instructions...

During the design and development stages of a remote meter reading system for residential electricity use, the two engineers working on the project for the City of Forest Ridge noted something...

On its issue date, an investor paid $99,760 for a $100,000 face value, 98-day Government of Canada T-bill. What was the investor's required rate of return?

The data below shows the average hourly megawatts of electricity used in New York City for the years 1993 through 2004. a. Plot the series and explain what can be learned from this plot. b. Calculate...

Set up a ratio problem. If the ratio cannot be reduced to an equivalent ratio in terms of small integers, then express it as a ratio of decimal equivalents with the smallest term set at 1. Maintain...

Which term refers to the formal process for addressing any factor such as wages, hours, or conditions of employment that is used as a complaint against the employer?

An Algorithm for Management of Change (MoC). List three things that would not have occurred if the MoC algorithm had been followed.

The catalytic dehydration of methanol (ME) to form dimethyl ether (DME) and water was carried out over an ion exchange catalyst (K. Klusacek, Collection Czech. Chem. Commun., 49, 170 (1984)). The...

Prepare a list of safety considerations for designing and operating chemical reactors. What would be the first four items on your list? For example, what safety concerns would you have for operating...

=+b. What proportion of fasteners pass inspection?

=+a. What is the probability that a randomly chosen person from the population does not have the same blood type as that found at the crime scene?

=+John Wiley, New York, 1995). Suppose that a suspect is found whose blood type matches a rare blood type found at a crime scene. Let denote the frequency with which people in the population have...