Robust stabilization of nonlinear systems with Markovian jumping parameters (Q2712220)

The authors consider the \(n\)-dimensional nonlinear control problem of minimizing NEWLINE\[NEWLINEJ(u:\xi,\rho)= {\mathbf E}\Bigl(\int^\infty_0 \biggl(g \bigl(x(t)\bigr)+ h\bigl(u(t) \bigr)\biggr) dt\mid x(0)=\xi,\;r(0)=\rho\Bigr)NEWLINE\]NEWLINE under NEWLINE\[NEWLINE\dot x(t)=A\bigl(x(t), r(t)\bigr)+B \bigl(x(t),r(t) \bigr)\biggl[d \bigl(x(t),r(t) \bigr) +p\bigl(u(t) \bigr)\biggr]NEWLINE\]NEWLINE where \(r(t)\) is a continuous-time Markov chain with finite state space. Under suitable conditions, a feedback control is constructed that stabilizes the system and guarantees its robustness. No explicit proofs are given.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].