On a general optimal algorithm for multirate output feedback controllers for linear stochastic periodic systems

• Published in: IEEE transactions on automatic control Vol. 38; no. 6; pp. 939 - 943
• Main Authors: Yen, Nie-Zen, Wu, Yung-Chun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.1993; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Control systems; Control theory. Systems; Exact sciences and technology; Linear feedback control systems; Optimal control; Output feedback; Performance analysis; Riccati equations; Steady-state; Stochastic processes; Stochastic systems; Transient response; Optimal algorithm; Control system; Stochastic system; Regulation(control); LQ control; Linear system; Optimal control; Sampling rate; Stochastic control; Multiple sampling; Riccati equation; Output feedback; Periodic system
• ISSN: 0018-9286
• DOI: 10.1109/9.222306

A modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed. By combining the discrete-time linear quadratic regulation (LQR) control problem and the discrete-time stochastic linear quadratic regulation (SLQR) control problem to obtain an extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages of the optimal transient response of the LQR control problem and the optimal steady-state regulation of the SLQR control problem. In general, the solution of this algorithm is obtained by solving a set of coupled matrix equations. Special cases for which the coupled matrix equations can be reduced to a discrete-time algebraic Riccati equation are discussed. A reducable case is the optimal algorithm derived by H.M. Al-Rahmani and G.F. Franklin (1990), where the system has complete state information and the discrete-time quadratic performance index is transformed from a continuous-time one.< >