Additional notes on the TORA example: a filtering approach to eliminate velocity measurements

This is an addendum to the control design solutions presented by Jankovic et al. (1996) for the benchmark TORA system. A high-pass filter is proposed to approximately differentiate the input position signal, thereby yielding an approximate velocity signal for use in the input control. The filter and control input are designed through a Lyapunov analysis, thus accounting for the effect of the pseudo-velocity signal in the closed-loop system (in spite of the fact that the filter output is not guaranteed to fully recreate the true velocity). The stability analysis shows that the closed-loop system is globally asymptotically stable. Computer simulations illustrate that the transient behavior of the controllers designed here is nearly equivalent to those proposed by Jankovic et al.