Hamilton-Jacobi theory for periodic control problems

Optimal Control of Mechanical Oscillations

“…A detailed bibliography dedicated to the periodic control can be found in reviews [123,124,157,163,184,185,187]. A search for an optimal control is based either on a solution of a two-point problem of the maximum principle [187] or on a solution of a dynamic programming equation [158,183]. Such problems have rarely an analytical solution; so the approximate methods for determination of a quasi-optimal control are of special interest.…”

“…A solution for a linear system with a mean-square quality criterion was constructed in the form of a linear feedback, coefficients of which satisfied a periodic Riccati equation [ 151,183] with a subsequent averaging of the Riccati equation.…”

Periodic and Recursive Control Theoretic Smoothing Splines

“…This may be viewed as a smoothing problem with continuous data z(t) or as a problem of tracking a curve given by z(t). Optimality conditions for problems of this type were derived in [8]. A review of the results follows.…”

“…This paper examines a similar LQ problem, with the important distinction that we optimize over all periodic solutions. Again, results for periodic LQ problems can be found in papers dating back to the 1970s, [8,9], but these do not cover the point-to-point problem.…”

Systematic performance analysis of continuous processes subject to multiple input cycling

“…The two major approaches taken for analysis of forced periodic operations (Guardabassi et al, 1974;Sterman and Ydstie, 1990a) are: (1) the Hamilton-Jacobi approach based on the maximum principle (Bailey and Horn, 1971;Bailey, 1973;Guardabassi et al, 1974;Ma ezoni, 1974;Noldus, 1977) or relaxed steady state analysis (Bailey and Horn, 1971;Bailey, 1973) suitable for high forcing frequencies, and (2) a frequency-domain approach using * Tel. : +1-312-567-3044; fax: +1-312-567-8874.…”