Locally optimal risk-sensitive controllers for strict-feedback nonlinear systems (Q1586797)

This paper deals with risk-sensitive control of nonlinear stochastic systems whose dynamics are in strict feedback form. Using a backstepping procedure, the authors constructed the state-feedback control \(\mu^*\), which satisfies the following 3 conditions. 1. \(\mu^*\) is optimal for the linearized risk-sensitive design, which implies that the linear exponential quadratic Gaussian problem is solved. Namely, \(\mu^*\) is locally optimal. 2. For a given nonlinear systems there exists an appropriate cost function, according to which \(\mu^*\) is optimal. Namely, \(\mu^*\) is globally inverse optimal. 3. \(\mu^*\) leads to closed-loop system trajectories that are bounded in probability.