Improved MPC design for constrained linear periodic systems

Reference governors and maximal output admissible sets for linear periodic systems

“…Therefore, Total memory saved = 4(N − 1)(n + 1)(m − n) bytes. (23) Clearly, if m > n, memory savings are positive. Therefore, partial storage should only be used for systems in which m > n (which is typically the case).…”

“…For a complete modern treatment of periodic systems and their control methods, please see [19]. Recently, with the availability of high speed computers, many optimizationbased and predictive control methods have been developed for periodic systems [9], [20]- [23].…”

“…In the literature for linear periodic systems, MAS has been previously characterized for asymptotically stable systems. Specifically, it is shown in [21]- [23], [28] that, in contrast to LTI systems, which only require one set to describe MAS, periodic systems require N sets, where N is the system period. However, the relationship between these sets remains unexplored.…”

Fast model predictive control for linear periodic systems with state and control constraints

“…There exists a unique solution P k to the problem (23), (24). In addition, the solution is of the form…”

“…where 8 < : Now, the state at the end of the prediction horizon x.t C N / is decomposed according to (9), and u.t C N /; u.t C N C 1/; : : : are computed according to (15). Using (24), one has, for i D 0; 1; 2; ::.…”