Fal!2001 16.31 Optimization -1 This control design problem is a constrained optimization, with the constraints being the dynamics of the system The standard way of handling the constraints in an optimization is to add them to the cost using a lagrange multiplier Results in an unconstrained optimization Example: min f(, y)=a2 +y2 subject to the constraint that c(x,y)=x+y+2=0 Figure 1: Optimization results Clearly the unconstrained minimum is at a=y=0Fall 2001 16.31 Optimization-1 • This control design problem is a constrained optimization, with the constraints being the dynamics of the system. • The standard way of handling the constraints in an optimization is to add them to the cost using a Lagrange multiplier — Results in an unconstrained optimization. • Example: min f(x, y) = x2 + y2 subject to the constraint that c(x, y) = x + y + 2 = 0 2 1.5 1 0.5 0 −0.5 −1 −1.5 −2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 x Figure 1: Optimization results y • Clearly the unconstrained minimum is at x = y = 0