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In this contribution, we derive ILEG, an iterative algorithm to find risksensitive solutions to nonlinear, stochastic optimal control problems. Thealgorithm is based on a linear quadratic approximation of an exponential risksensitive nonlinear control problem. ILEG allows to find risk sensitivepolicies and thus generalizes previous algorithms to solve nonlinear optimalcontrol based on iterative linear-quadratic methods. Depending on the settingof the parameter controlling the risk sensitivity, two different strategies onhow to cope with the risk emerge. For positive-value parameters, the controlpolicy uses high feedback gains whereas for negative-value parameters, it usesa robust feedforward control strategy (a robust plan) with low gains. Theseresults are illustrated with a simple example. This note should be consideredas a preliminary report.

Risk Sensitive, Nonlinear Optimal Control: Iterative Linear Exponential-Quadratic Optimal Control with Gaussian Noise