Optimal Control of Linear Systems with State Equality Constraints

This paper deals with the optimal control problem for systems withstate linear equality constraints. For deterministic linearsystems, first we find various existence conditions forconstraining state feedback control and determine all constrainingfeedback gains, from which the optimal feedback gain is derived byusing the result of singular optimal control. For systems withstochastic process noises, it is shown that the same gain used forconstraining the deterministic system also optimally constrainsthe expectation of states inside the constraint subspace andminimizes the expectation of the squared constraint error. Wecompare performance between unconstrained and constrainedcontrollers for both deterministic and stochastic systems.