A lagrange approach to set-theoretic control synthesis

A Lagrange approach to solving the nonlinear constrained optimization problem arising in the set-theoretic control problem is described. By introducing matrix Lagrange multipliers, the problem is reduced to that of solving a set of nonlinear simultaneous matrix equations, one of which is the familiar matrix Riccati equation frequently encountered in linear-quadratic control theory. The structural similarities and differences between set-theoretic and linear-quadratic control methods are identified. The results obtained from the set-theoretic control approach are compared with those obtained from the linear-quadratic control approach.