Locally optimal risk-sensitive controllers for strict-feedback nonlinear systems

For a class of risk-sensitive nonlinear stochastic control problems with dy namics in strict-feedback form, we obtain through a constructive derivation state-feedback controllers which (i) are locally optimal, (ii) are globall y inverse optimal, and (iii) lead to closed-loop system trajectories that a re bounded in probability. The first feature implies that a linearized vers ion of these controllers solve a linear exponential-quadratic Gaussian (LEQ G) problem, and the second feature says that there exists an appropriate co st function according to which these controllers are optimal.