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A State-Dependent Riccati Equation-Based Robust Control Approach for Nonlinear Systems with Parametric Uncertainties

In this paper, a novel generalized polynomial chaos expansion-based control framework is presented for continuous-time nonlinear systems with probabilistic parametric uncertainties. We consider an infinite-horizon expectation performance index for the stochastic system. To this end, we first derive a pseudo-linear description of the nonlinear system using the state-dependent coefficient parameterization. Using a sampling-based pseudospectral collocation technique in the generalized polynomial chaos expansion framework, the stochastic performance index is converted into a deterministic cost function. Synthesis of state feedback controller is then presented as the solution of a state-dependent algebraic Riccati equation and state-dependent linear matrix inequality. Finally, the theoretical results are applied to regulate the rotational dynamics of a spacecraft with an uncertain inertia matrix.