Refer to page 32 for solving a linear-quadratic regulator (LQR) problem. Instructions: • Formulate the cost functional and state-space representation. • Derive the Riccati equation and solve it step-by-step. Clearly explain how the optimal control law is obtained. Ensure all matrix algebra is shown in detail. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

Please look at the attached image of this problem and show steps to solve please

Find the minimum value of x +y +z² givenx+y+z=3a.,

As an Engineer, cite other instances aside from the situations given in the picture where optimization (one maximization and one minimization) can be applied.

Find the maximum and minimum of ?(?, ?) = 5? − 3?, subject to the constraint ?^ 2 + ?^ 2 = 136.

Solve only a and b manually using formulas. Show complete solution.

what about the constraints equations ?

Traffic Control  The accompanying figure shows the flow of downtown traffic during the rush hours on a typical weekday. Each avenue can handle up to 1500 vehicles/hour without causing congestion, whereas the maximum capacity of each street is 1000 vehicles/hour. The flow of traffic is controlled by traffic lights at each of the six intersections. (A) Suggest two possible traffic-flow patterns that ensure no traffic congestion. (B) Suppose the traffic flow along 9th Street between 5th and 6th Avenues, x6, is restricted due to sewer construction. What is the minimum permissible traffic flow along this road that will not result in traffic congestion?

7 a) Differentiate the multi target mode where D =0, showing that it can’t be used for low dose b) mathematically explain whether the linear quadratic model is ideal model for high doses or low dose

P.MS.AMPA x 1.GEOMETRYCP. MS.AMPARO94/_layouts/15/Doc.aspx?sourcedoc%3{cf5f1c7b-680c-4e0a-a691-ada5a1d2... Cortes, O Notebook S1.P3.GEOMETRY CP.MS.AMPARO Notebook L Immersive Reader A This page is locked and can't be edited at this time. Select the transformations that take figure F to figure . (GCO.5) F it... n... Reflect figure F across the *axis. Rotate figure F 90° clockwise around the origin. a. C. b Reflect figure F across the Y axis. d. Rotate figure F 180° counterclockwise around the origin. Enter your answer