Optimal Solutions of Linear Control Systems with Nonperiodic Convex Integrands

In this work we study the existence and asymptotic behaviour of overtaking optimal trajectories for a linear system with a nonperiodic convex cost function. We extend the results obtained by Leizarowitz Leizarowitz, A. 1986. Tracking nonperiodic trajectories with the overtaking criterion. Appl. Math. Opt.14 155--171. for a problem of tracking a prescribed nonperiodic trajectory with a quadratic cost function and establish the existence and uniqueness of optimal trajectories on an infinite horizon. The asymptotic dynamics of finite time optimizers is examined.

[1]  A. Leizarowitz.  Tracking nonperiodic trajectories with the overtaking criterion , 1986 .

[2]  D. Gale.  On Optimal Development in a Multi-Sector Economy , 1967 .

[3]  B. Anderson,et al.  Linear Optimal Control , 1971 .

[4]  Z. Artstein,et al.  Tracking periodic signals with the overtaking criterion , 1985 .

[5]  von Weizäscker,et al.  Existence of Optimal Programs of Accumulation for an Infinite Time Horizon , 1965 .

[6]  Bernard D. Coleman,et al.  On the thermodynamics of periodic phases , 1992 .

[7]  A. Leizarowitz.  Infinite horizon autonomous systems with unbounded cost , 1985 .

[8]  A. Haurie,et al.  Infinite Horizon Optimal Control: Theory and Applications , 1987 .

[9]  Dean A. Carlson,et al.  The existence of catching-up optimal solutions for a class of infinite horizon control problems with time delay , 1990 .

[10]  Alain Haurie,et al.  On Existence of Overtaking Optimal Trajectories Over an Infinite Time Horizon , 1976, Math. Oper. Res..

[11]  A. Haurie,et al.  Infinite Horizon Optimal Control , 1987 .

[12]  R. Rockafellar.  Saddle points of hamiltonian systems in convex problems of Lagrange , 1973 .

[13]  C. Zălinescu.  On uniformly convex functions , 1983 .

[14]  A. Leizarowitz.  Optimal trajectories of infinite-horizon deterministic control systems , 1989 .

[15]  Optimal Solutions of Linear Periodic Control Systems with Convex Integrands , 1998 .

[16]  Alain Haurie,et al.  Existence of overtaking solutions to infinite dimensional control problems on unbounded time intervals , 1987 .