PIP optimal control with a risk sensitive criterion

The paper shows how the 'complete observations' formulation of linear exponential of quadratic Gaussian (LEQG) control theory can be applied within a nonminimal state space (NMSS) context. This complete observations solution is not restrictive within the NMSS formulation since all the NMSS states are readily available for measurement. As a result, the associated PIP-LEQG controller (proportional integral plus-LEQG) is easily implemented in practice. Indeed, we may speculate that the partial observations solution does not introduce any significant advantages in this case; and it may even result in a decrease in robustness (in a manner similar to that which occurs when a Kalman filter is introduced into an LQ controller to achieve LQG optimisation). The results obtained so far suggest that there is not much practical advantage in using the optimal PIP-LEQG design as an alternative to the previously proposed PIP-LQ design. The theory is attractive, in the sense that the LEQG formulation incorporates the LQ as a special case and can be related to the robust H design methods. But it would appear that, in practice, it is always possible to achieve good, robust, closed performance by selection of the LQ weights, particularly if the multi objective approach to PIP-LQ design (W. Tych and P.C. Young) is used to exploit the design potential of the off-diagonal elements in the weighting matrices.