Newton's method for a rational matrix equation occurring in stochastic control

By Tobias Damm, Diederich Hinrichsen. 2001

66 citations recorded by the source corpus.

We study a general class of rational matrix equations, which contains the continuous (CARE) and discrete (DARE) algebraic Riccati equations as special cases. Equations of this type were encountered in [SIAM J. Control and Optimization 36 (1998) 1504–1538; Stochastics and Stochastics Reports, 65 (1999) 255–297], where H∞-type problems of disturbance attenuation for stochastic linear systems were studied. We develop a unifying framework for the analysis of these equations based on the theory of (resolvent) positive operators and show that they can be solved by Newton's method starting at an arbitrary stabilizing matrix.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/241df918ca7fef456174083ea4633089515366bc

Citations in the corpus

• Online adaptive optimal control for continuous-time Markov jump linear systems using a novel policy iteration algorithm (2015, unknown): “In [4], the author has pointed out that the iteration algorithm (10) equals to the standard Newton's algorithm [14][3][20] with the form: P i (k + 1) = P i (k) − (R Pi(k) ) −1 R(P i (k)), (29) where R(P i (k)) = A T i P i (k) + P i (k)A i − P i (k)B i R −1 i B T i P i (k) + N j=1 π ij P j (k) + Q i…”