Time-optimal control of the swing using impulse control actions

We use the necessary conditions developed previously to deal with the task of time-optimal control for the swing. For completeness we also describe briefly the main results on impulse control. The simulation results shows how to deal with this task easily by using impulse control theory including feedback impulse control action.

[1]  R. Murray,et al.  Nonholonomic systems and exponential convergence: some analysis tools , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[2]  Claude Samson,et al.  Velocity and torque feedback control of a nonholonomic cart , 1991 .

[3]  C. C. Wit,et al.  On the Construction of Stabilizing Discontinuous Controllers for Nonholonomic Systems , 1995 .

[4]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[5]  Yiyuan Zhao.  SOLUTIONS TO PARAMETER OPTIMAL CONTROL , 1994 .

[6]  Panagiotis Tsiotras,et al.  A novel approach to the attitude control of axisymmetric spacecraft , 1995, Autom..

[7]  Zhong-Ping Jiang,et al.  Iterative design of time-varying stabilizers for multi-input systems in chained form , 1996 .

[8]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[9]  B. Piccoli.  Time-optimal control problems for the swing and the ski , 1994, funct-an/9411004.

[10]  Perinkulam S. Krishnaprasad,et al.  H/sub /spl infin// control for impulsive disturbances: a state-space solution , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[11]  B. Miller.  The generalized solutions of nonlinear optimization problems with impulse control , 1996 .

[12]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[13]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[14]  Panagiotis Tsiotras,et al.  Reduced Effort Control Laws for Underactuated Rigid Spacecraft , 1997 .

[15]  A. Bressan,et al.  Impulsive control systems without commutativity assumptions , 1994 .

[16]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[17]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[18]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[19]  E.B. Lee,et al.  Two methods for constructing aggrandized disturbances using delay tactics for stabilized control systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[20]  W. Schmaedeke.  Optimal Control Theory for Nonlinear Vector Differential Equations Containing Measures , 1965 .

[21]  A. Astolfi.  Discontinuous control of nonholonomic systems , 1996 .

[22]  P. Tsiotras,et al.  Exponentially convergent controllers for n-dimensional nonholonomic systems in power form , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).