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Abstract
The design of a piecewise constant feedback control for the linear regulator problem from the standpoint of fixing the gains a priori and optimizing the system with respect to the location of the discontinuities in control is considered. The gains, available as an extra set of parameters, may be chosen to ‘approximate’ the optimal Riccati gain matrix or by some other criterion. The discontinuities induced by the assumed form of the control are treated using the theory of distributions, and the optimal set of discontinuities is found by a second-variation algorithm. In addition, the Cayley-Hamilton technique is found to be a viable computational alternative for arbitrary time-invariant systems.
Notes
† Communicated by the Author.