In this article, the problem of trajectory design and tracking of non-periodic tracking-transition switching for non-minimum phase linear systems is considered. Such a trajectory design and tracking problem exists in applications such as nanomanipulation, robotic operation, and hard-disk control, where the whole trajectory consists of tracking sessions with the application-specified desired trajectory to be tracked, and transition sessions with the output trajectory to be designed. This problem becomes challenging as multiple control objectives need to be achieved. The proposed approach extends the previous work that attained smooth output transition and smooth tracking-transition switching to further achieve amplitude-constrained input-energy minimization and transition time minimization. First, the constrained input optimization problem is converted to an unconstrained input minimization problem. Then the optimal output and input are obtained by using an improved conjugate gradient method. Finally, the total transition time is further minimized via one dimensional search. The proposed approach is illustrated through a simulation example in probe-based nanomanipulation utilizing a piezoelectric actuator.

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