This paper studies the design of efficient model predictive controllers for fast-sampling linear time-invariant systems subject to\r\ninput constraints to track a set of periodic references. The problem is decomposed into a steady-state subproblem that determines\r\nthe optimal asymptotic operating point and a transient subproblem that drives the given plant to this operating point. While the\r\ntransient subproblem is a small-sized quadratic program, the steady-state subproblem can easily involve hundreds of variables\r\nand constraints. The decomposition allows these two subproblems of very different computational complexities to be solved in\r\nparallel with different sampling rates.Moreover, a receding horizon approach is adopted for the steady-state subproblem to spread\r\nthe optimization over time in an efficient manner, making its solution possible for fast-sampling systems. Besides the conventional\r\nformulation based on the control inputs as variables, a parameterization using a dynamic policy on the inputs is introduced, which\r\nfurther reduces the online computational requirements. Both proposed algorithms possess nice convergence properties, which are\r\nalso verified with computer simulations.
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