Numerical Stabilization of Bilinear Control Systems

Extremal Lyapunov exponents for bilinear control systems with constrained control values are computed numerically by solving discounted optimal control problems. Based on this computation a numerical algorithm to calculate stabilizing control functions is developed.

[1]  Fabian R. Wirth,et al.  Convergence of the Value Functions of Discounted Infinite Horizon Optimal Control Problems with Low Discount Rates , 1993, Math. Oper. Res..

[2]  M. Falcone A numerical approach to the infinite horizon problem of deterministic control theory , 1987 .

[3]  I. Dolcetta On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming , 1983 .

[4]  P. Lions Generalized Solutions of Hamilton-Jacobi Equations , 1982 .

[5]  M. Falcone,et al.  An approximation scheme for the minimum time function , 1990 .

[6]  Ronald R. Mohler,et al.  Natural Bilinear Control Processes , 1970, IEEE Trans. Syst. Sci. Cybern..

[7]  Wolfgang Kliemann,et al.  Minimal and Maximal Lyapunov Exponents of Bilinear Control Systems , 1993 .

[8]  M. Falcone,et al.  Discrete Dynamic Programming and Viscosity Solutions of the Bellman Equation , 1989 .

[9]  W. Kliemann,et al.  Linear control semigroups acting on projective space , 1993 .

[10]  Wolfgang Kliemann,et al.  Infinite time optimal control and periodicity , 1989 .

[11]  R. Chabour,et al.  Stabilization of nonlinear systems: A bilinear approach , 1993, Math. Control. Signals Syst..

[12]  Wolfgang Kliemann,et al.  The Lyapunov spectrum of families of time-varying matrices , 1996 .

[13]  Wolfgang Kliemann,et al.  Asymptotic null controllability of bilinear systems , 1995 .

[14]  H. Ishii,et al.  Approximate solutions of the bellman equation of deterministic control theory , 1984 .

[15]  W. Kliemann Recurrence and invariant measures for degenerate diffusions , 1987 .

[16]  Fritz Colonius,et al.  Asymptotic Behaviour of Optimal Control Systems with Low Discount Rates , 1989, Math. Oper. Res..