Partial cheap control of the time-invariant regulator

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Abstract
A singular perturbation analysis of the partial cheap control of the linear time-invariant regulator is presented, in which some but not necessarily all of the control inputs have arbitrarily small cost weighting. In the limit, the m 2 initial cheap control inputs arc impulsive, while the outer solution asymptotically approaches a singular are associated with a dynamical system and matrix Riccati equation, both of order n – m 2. A two-time-scale decomposition of the regulator problem yields a slow control and a composite control that provide near-optimal performance. Further, the partial cheap control results are used to solve the dual almost singular optimal linear filtering problem.

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