Fall 2001 163115-5 Linear Quadratic Regulator An alternative approach is to place the pole locations so that the closed-loop(SISO)system optimizes the cost function LQR (t)(CC)(t)+ru(t)dt Where y'y=a(CC)c assuming D=0) is called the State Cost ul is called the control cost and r is the Control Penalty Simple form of the Linear Quadratic Regulator Problem Can show that the optimal control is a linear state feedback ()=-Kq(t Klgr found by solving an Algebraic Riccati Equation(Are) We will look at the details of this solution procedure later. For now let's just look at the optimal closed-loop pole locationsFall 2001 16.31 15—5 Linear Quadratic Regulator • An alternative approach is to place the pole locations so that the closed-loop (SISO) system optimizes the cost function: JLQR = Z ∞ 0 £ xT (t)(CTC)x(t) + r u(t) 2 ¤ dt Where: — yT y = xT (CTC)x {assuming D = 0} is called the State Cost — u2 is called the Control Cost, and — r is the Control Penalty — Simple form of the Linear Quadratic Regulator Problem. • Can show that the optimal control is a linear state feedback: u(t) = −Klqrx(t) — Klqr found by solving an Algebraic Riccati Equation (ARE). • We will look at the details of this solution procedure later. For now, let’s just look at the optimal closed-loop pole locations