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Suppose we are to guide a plant with a square transfer matrix through a series of way points. This can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner. Each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof. Our technique is to compute: 1) a noncausal "particular solution" based on the desired trajectory over each segment and the movement from one segment to the next, and this "particular solution" consists of a "particular control" and a "particular state trajectory"; and 2) a regulator to handle modeling errors, disturbances, etc. We concentrate on the "particular solution".
Hunt et al. (Mon,) studied this question.