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Daily Overview |
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OC3: Optimisation and Control Location: A702 Session Chair: Behzad Azmi | |
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Stabilization of Stochastic Parabolic Equations by Finite-Dimensional Feedback 1: Dep. Math. Stat., Univ. Konstanz, Germany; 2: Inst. Comput. Appl. Math., öAW, Austria We present recent results on stabilizing nonlinear, time-dependent stochastic parabolic equations by finite-dimensional feedback. The feedback acts through a finite number of localized indicator-type actuators whose supports may cover an arbitrarily small fraction of the domain and is constructed via oblique projections onto finite-dimensional subspaces. Its offline computation requires only the actuator geometry, independently of the equation's coefficients. Our main result shows that, for any prescribed exponential decay rate $\mu > 0$, a suitable actuator configuration and feedback gain achieve mean-square exponential stabilization, with almost-sure exponential decay in the pure multiplicative noise case. We complement the theoretical findings with numerical experiments illustrating the influence of the number of actuators, noise intensity, and nonlinear effects on stabilization behavior. | |
