Nonlinear stochastic optimal control of offshore platforms under wave loading

A nonlinear stochastic optimal (NSO) control strategy for wave-excited jacket-type offshore platforms is proposed. Wave force is determined according to linearized Morison equation. Spectral density functions of water particle velocity and acceleration are approximated by some rational forms, respectively. Wave force vector is then treated as output of a linear filter driven by white noise. A set of partially averaged Itô equations for controlled modal energies are derived by applying stochastic averaging method for quasi-integrable Hamiltonian systems. Optimal control law is then determined by using stochastic dynamical programming principle. To demonstrate the effectiveness and efficiency of the proposed control strategy, performances of uncontrolled, linear quadratic Gaussian (LQG)-controlled and NSO-controlled example platforms under different sea states are evaluated. Numerical results show that the NSO controller has better control effectiveness and efficiency than the LQG controller.