Switching-time computation for bang-bang control laws

We obtain improvements and give extensions to the switching time computation (STC) method, which is used to compute the switching times for bang-bang control laws. We first report a considerable computational improvement on the STC method as applied to a nonlinear system with one control input. The second contribution of this paper is the extension and implementation of the STC method for two control inputs. In bang-bang control calculations it is a usual practice to consider all possible combinations of the switchings and then carry out the computations with a large set of switching parameters. We introduce a novel scheme for the switching times for two inputs which results in far fewer switching parameters to calculate.

[1]  Mordechai Shacham,et al.  Numerical solution of constrained non‐linear algebraic equations , 1986 .

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

[3]  Eric King-wah Chu,et al.  A nonmonotone inexact Newton algorithm for nonlinear systems of equations , 1995, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[4]  Kok Lay Teo,et al.  A Unified Computational Approach to Optimal Control Problems , 1991 .

[5]  K. Teo,et al.  Control parametrization enhancing technique for time optimal control problems , 1997 .

[6]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[7]  H. Walker,et al.  Least-change secant update methods for undetermined systems , 1990 .

[8]  C. Yalçın Kaya,et al.  Computations and time-optimal controls , 1996 .

[9]  John T. Wen,et al.  An algorithm for obtaining bang-bang control laws , 1987 .

[10]  C. Kaya,et al.  Computational Method for Time-Optimal Switching Control , 2003 .

[11]  D. Clements,et al.  Optimal control computation for nonlinear time-lag systems , 1985 .

[12]  R. R. Mohler,et al.  Nonlinear systems (vol. 2): applications to bilinear control , 1991 .

[13]  Françoise Lamnabhi-Lagarrigue,et al.  Bang-Bang Solutions for a Class of Problems Arising in Thermal Control , 1986 .

[14]  G. J. Lastman,et al.  A shooting method for solving two-point boundary-value problems arising from non-singular bang-bang optimal control problems , 1978 .