PDF-EE Winter Lecture Linear Quadratic Stochastic Control with Partial State Observation

N with state input and process noise linear noise corrupted observations Cx t 0 N is output is measurement noise 8764N 0 X 8764N 0 W 8764N 0 V all independent Linear Quadratic Stochastic Control with Partial State Obser vation 102 br. We start with the most general from that of time varying system matrices and 64257nite horizon 41 Time varying and 64257nite horizon case Consider the dynamical system 41 We are interested in 64257nding a control such that the following cost e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations 01 01 10 20 15 10 5 02 04 06 08 y brPage 4br EE392m Winter 2003 Control Engineering 44 Example Servosystem command More stepper motor flow through a valve motor torque I control Introduce integrator into control Closedloop dynamics gk gk gk This PowerPoint . was adapted from . http://. www.purplemath.com/modules/quadform2.htm. and . http://. teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/6-4/2006_6_4.ppt. Looking Back…. In our previous lesson, we solved quadratic function by . Division of Student Assessment & School Improvement. Virginia Department of Education. New . Partially Accredited . Ratings. Partially . Accredited: Approaching Benchmark-Graduation and Completion Index. Michel . Gendreau. CIRRELT and MAGI. École Polytechnique de Montréal. SESO 2015 International Thematic. . Week. ENSTA and ENPC .  Paris, June 22-26, 2015. Effective solution approaches for stochastic and integer problems. Essential Questions . and Quadratics review. Function, relation, domain, range, perfect square trinomial, difference of perfect squares, roots/zeroes, real and complex roots, extrema, minimum, maximum, y-intercept, line or Axis of symmetry, standard form, vertex form, intercept form, 1. Perfect Square Trinomials. Examples. x. 2. + 6x + 9. x. 2. - 10x + 25. x. 2. + 12x + 36. Creating a Perfect . Square Trinomial. X. 2. . + 14x + ____ . Find the constant term by squaring half . Recall, we have used the quadratic formula previously. Gives the location of the roots (x-intercepts) of the graph of a parabola. Function must be in standard form; f(x) = ax. 2. + . bx. + c. Example. Find the roots for the function f(x) = 2x. Find the roots:. 1) x. 2. – 64 = 0 . 2) 8x. 2. – 64x = 0. 3) x. 2. – 16x + 64 = 0. 1) Ensure the quadratic equation is set to zero.. 2) Factor the quadratic equation (GCF, perfect square binomial [DOTS], trinomial). There are many uses of parabolas in real-world applications.. Graphs of Quadratic Functions. Plotting quadratic curves. If you remember a relation is a correspondence between two sets of numbers called the . General Equation. Y = ax². What if A was positive?. Test in your calculator. What if A Was negative?. Test in your calculator.. Y = ax². What if A was greater than 1?. Test in your calculator. What if A Was less than 1?. December 5. , 2016. Quadratic functions are polynomial equations that have an __________ in the equation and ____________ is the highest exponent of x. . The standard form of a quadratic equation is :. LL2 section 50. m. onochromatic plane wave. Constant. complex vector,. defines polarization state,. which is definite (elliptical). Approximately monochromatic plane wave. Contains frequencies in some interval .