Time-optimal output regulators for linear multivariate discrete-time systems Part 2. All classes of right-invertible systems
Titel:
Time-optimal output regulators for linear multivariate discrete-time systems Part 2. All classes of right-invertible systems
Auteur:
Amin, M. H. Hassan, M. M.
Verschenen in:
International journal of control
Paginering:
Jaargang 46 (1987) nr. 4 pagina's 1411-1428
Jaar:
1987
Inhoud:
In Part 1 of this paper (Hassan and Amin 1987) a simple algebraic solution for the time-optimal output regulator problem was presented. This solution, which consists of a state feedback control law, has been obtained for all classes of right-invertible decouplable systems S(A, B, C, E). The results of Part 1 are here extended to all classes of right-invertible systems S(A, B, C, E). A set of optimal output deadbeat indices (called the 'optimal set') is defined and related to the observability indices of the optimal closed-loop system. The time-optimal output regulator problem for a right-invertible non-decouplable system S(A, B, C, E) is resolved by transforming S into a decouplable system Sc(A, B, Cc, Ec) having the optimal output deadbeat index σ* of S. First, an algorithm is presented to construct iteratively, in a well-defined optimal sense, a unimodular left compensator L(z) and a compensated decouplable system Sc(A, B, Cc, Ec) from the state-space parameters of S. Then, a family of optimal state feedback matrices Fc*, which attains the optimal set of Sc, is given as the optimal solution F* of S. For any right-invertible system S(A, B, C, E), it is shown that the optimal number of control iterations required at most to zero its outputs is equal to the associated uniquely defined μ 1 index of the right Wiener-Hopf factorization at infinity of H(z) (the transfer function matrix of the system). A numerical example is worked out to illustrate the design procedures of time-optimal output regulators for non-decouplable systems.
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