On nonlinear \(H_\infty\)-control via state feedback (Q2712478)

This paper deals with the disturbance attenuation problem with prefixed level \(\gamma\) for a nonlinear system of the form: NEWLINE\[NEWLINE\dot x= f(x)+ g(x)u+ a(x)w,\quad y= x,\quad z={h(x)\choose u}.NEWLINE\]NEWLINE Under some suitable assumptions the control which provides the prescribed attenuation level is given by NEWLINE\[NEWLINE\widehat u(x)= -g^T(x)\Biggl({\partial V\over\partial x}\Biggr)^T,NEWLINE\]NEWLINE where \(V(x)\) is the solution to the Hamilton-Jacobi equation NEWLINE\[NEWLINE{\partial V\over\partial x} f(x)+{1\over 2} {\partial V\over\partial x} \Biggl[{1\over\gamma^2} a^Ta- g^Tg\Biggr] \Biggl({\partial V\over\partial x}\Biggr)^T+{1\over 2} h^Th= 0.NEWLINE\]NEWLINE The paper provides an iterative procedure, which allows to compute the \(-g^T(x)({\partial V\over\partial x})^T\).