Non-minimal State Dependent Riccati Equation and Pole Assignment Control of Nonlinear Systems

This paper considers pole assignment and Riccati equation control of nonlinear dynamic systems described by State Dependent Parameter (SDP) models. The approach follows from earlier research into linear Proportional-Integral-Plus (PIP) methods but, in SDP system control, the control coefficients are updated at each sampling instant on the basis of the SDP relationships. Alternatively, algebraic solutions can be derived off-line to yield a practically useful control algorithm that is relatively straightforward to implement on a digital computer, requiring only the storage of lagged system variables, coupled with straightforward arithmetic expressions in the control software. Two examples are used to illustrate the approach. In the first instance, state space matrix analysis of a first order system shows that the expected design response is obtained for specified pole positions, including dead-beat; hence, assuming pole assignability at each sample, global stability of the nonlinear system is guaranteed at the design stage. Secondly, the paper evaluates the approach for a classical, physically-based simulation model of an inverted pendulum.