A new approach to linearly perturbed Riccati equations arising in stochastic control

Applied Mathematics and Optimization

Volumn 37, Issue 1, 1998, Pages 99-126

  Fragoso, M D ^a   Costa, O L V ^b   De Souza, C E ^c  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Linearly perturbed Riccati equation; Mean square stabilizability; Nonobservable systems; Stochastic control; Strong solution

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; PERTURBATION TECHNIQUES; STOCHASTIC CONTROL SYSTEMS;

LINEARLY PERTURBED RICCATI EQUATIONS; MEAN SQUARE STABILIZABILITY;

RICCATI EQUATIONS;

EID: 0031673832     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900070     Document Type: Article

References (27)

1. Bitmead RR, Gevers MR, Petersen IR, Kaye RJ (1985) Monotonicity and stability properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples, Systems Control Lett 5:309-315
2. Bittanti S, Colaneri P (1986) Lyapunov and Riccati equations: Periodic inertia theorems, IEEE Trans Automat Control 31:659-661
3. Bittanti S, Colaneri P, Guardabassi G (1986) Analysis of the periodic Lyapunov and Riccati equations via canonical decomposition, SIAM J Control 24:1138-1149
4. Chan SW, Goodwin GC, Sin KS (1984) Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems, IEEE Trans Automat Control 29:110-118
5. Costa OLV, Fragoso MD (1993) Stability results for discrete-time linear systems with Markovian jumping parameters, J Math Anal Appl 179:154-178
6. Costa OLV, Fragoso MD (1995) On the discrete-time infinite coupled Riccati equations which arises in a certain optimal control problem, IEEE Trans Automat Control 40:2076-2088
7. Delchamps DF (1980) A note on the Analyticity of the Riccati Metric, Lectures in Applied Mathematics, Vol 18, American Mathematical Society, Providence, RI, pp 37-41
8. De Souza CE(1987) Riccati differential equation in optimal filtering of periodic non-stabilizable systems, Internat J Control 46:1235-1250
9. De Souza CE, Fragoso MD (1990) Results on generalized Riccati equations arising in stochastic control, in Progress in Systems and Control Theory, Vol II, MA Kaashoek, JH Van Schuppen, ACM Ran, eds., Birkhäuser, Boston, pp 95-102
10. De Souza CE, Fragoso MD (1990) On the existence of maximal solution for generalized algebraic Riccati equations arising in stochastic control, Systems Control Lett 14:233-239
11. De Souza CE, Gevers MR, Goodwin GC (1986) Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices, IEEE Trans Automat Control 31:831-838
12. Fragoso MD (1988) On a partially observable LQG problem for systems with Markovian jumping parameters, Systems Control Lett 14:349-356
13. Fragoso MD (1990) A small random perturbation analysis of a partially observable LQG problem for systems with Markovian jumping parameters, IMA J Math Control Inform 7:293-305
14. Fragoso MD, Hemerly EM (1991) Optimal control for a class of noisy linear systems with Markovian jumping parameters and quadratic cost, Internat J Systems Sci 22(12):2553-2561
15. Fragoso MD, Souza CE (1992) Maximal solution of a certain class of periodic Riccati differential equations, Linear Algebra Appl 169:61-73
16. Gohberg I, Lancaster P, Rodman L (1986) On Hermitian solutions of symmetric algebraic Riccati equations, SIAM J Control 24:1323-1334
17. Hager WW, Horowitz LL (1976) Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems, SIAM J Control 14:295-312
18. Hewer GA (1975) Periodicity, detectability and matrix Riccati equations, SIAM J Control 13:1235-1251
19. Kubrusly CS (1985) Mean square stability for discrete bounded linear systems in Hilbert space, SIAM J Control 23:19-29
20. Naylor AW, Sell GR (1982) Linear Operator Theory in Engineering and Science, 2nd edn, Springer-Verlag, Berlin
21. Ran ACM, Vreugdenhil R (1988) Existence and comparison theorems for algebraic Riccati equations for continuous and discrete-time systems, Linear Algebra Appl 99:63-83
22. Shayman MA (1985) On the phase portrait of the matrix Riccati equation arising from the periodic control problem, SIAM J Control 23:717-751
23. Sontag ED (1990) Mathematical Control Theory, Springer-Verlag, New York
24. Weidmann J (1980) Linear Operators in Hilbert Spaces, Springer-Verlag, New York
25. Wimmer HK (1985) Monotonicity of maximal solutions of algebraic Riccati equations, Systems Control Lett 5:317-319
26. Wonham WM (1968) On a matrix Riccati equation of stochastic control, SIAM J Control 4:681-697
27. Wonham WM (1970) Random differential equations in control theory, in Probabilistic Methods in Applied Mathematics, AT Bharucha Reid, ed, Vol 2, Academic Press, New York, pp 131-212