Bounded control of random vibration: Hybrid solution to HJB equations (Q1868316)

The authors examine a mathematical model of a randomly excited mass-spring system. It is supposed that the excitation is a stationary Gaussian white noise, the cost functionals being the response energies of several types. The problem is studied by dynamical programming method. The solution to Hamilton-Jacobi-Bellman equation is combined of two different parts: the solution in `inner' domain, found numerically, and that in `outer' domain generated as a `dry-friction' control law. The efficiency of obtained long-time control is studied in terms of the system response by means of two approaches: direct energy balance and stochastic averaging. The control is used both for single-degree-of-freedom and multi-degree-of-freedom systems. The results of Monte Carlo simulation illustrate reasonable accuracy of the expected response energy. Certain potential extensions of the proposed procedure are mentioned.