A receding-horizon approach to the nonlinear \(H_{\infty}\) control problem (Q5930065)

The receding horizon (RH) methodology is extended to the design of a robust controller of \(H_\infty\) type for nonlinear systems of the form: NEWLINE\[NEWLINE\dot x= a(x)+ b(x)u+ g(x)d,\quad z= {h(x)\choose u},NEWLINE\]NEWLINE where \(x\in\mathbb{R}^n\) is the state vector, \(u\in \mathbb{R}^m\) is the control vector, \(d\in\mathbb{R}^p\) denotes the vector of exogenous disturbances, \(h(x)\in \mathbb{R}^q\) is an output which must be controlled, \(a(0)= 0\), \(h(0)= 0\).NEWLINENEWLINENEWLINEUsing the nonlinear analogue of the fake \(H_\infty\) algebraic Riccati equation, one derives an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded \(L_2\)-gain. Robustness properties of the nonlinear \(H_\infty\) control law in face of dynamic input uncertainty are considered.