Some approaches to ergodic and adaptive control of stochastic semilinear systems
The author considers some ergodic and adaptive control problems for the stochastic semilinear system NEWLINE\[NEWLINEdX(t)= (AX(t)+ f(\alpha, X(t))- u(t)) dt+ Q^{1/2} dW(t),NEWLINE\]NEWLINE where \(X(t)\), \(t\geq 0\), is an \(H\)-valued process, \(H\) is a Hilbert space, \(A\) is an infinitesimal operator of a Hilbert-Schmidt exponentially stable semigroup of contractions, \(W(t)\), \(t\geq 0\), is a standard cylindrical \(H\)-valued Wiener process, \(Q= (Q^{1/2})^* Q^{1/2}\) is an invertible linear operator, \(u\) is a control, and \(f(\alpha,\cdot):H\to H\) is a nonlinear function for each \(\alpha\) from a finite-dimensional compact set.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].
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