On the control of a two-dimensional uniform multi-link inverted pendulum: the enumeration and identification of equilibrium states
Peter J. Larcombe, Bernard Torsney · International Journal of Systems Science · 1992
The standard control task of balancing a horizontally translating inverted pendulum is discussed within the wider context of other balancing-type control problems which may be set by the same system. Defining a ‘physically realizable’ state as one which contains, and provides a variant on, the standard control task associated with the system, an explicit general result is proposed for the computation of all such possible states. The result is validated by a concordant result arising from an interesting theoretical probabilistic analogy—the symmetric random walk of single dimension—which is also utilized to provide two direct proofs. The enumerative theory is then developed to accommodate further, rather more non-standard, control problems, and results given concerning the automatic generation and identification of states by computer.