Generalised Fully Probabilistic Controller Design for Nonlinear Affine Systems

Abstract

This paper demonstrates the extension of the Fully Probabilistic Design control method to nonlinear discrete-time stochastic dynamical systems which are affine in the input signal and are also affected by multiplicative noises. As nonlinear systems do not usually have a closed form analytic control solution, many current control methods are mostly based on linearising the system equations first and then deriving the analytic control solution. To address this problem, this paper proposes a new method which does not require the linearisation of the nonlinear system equations. This will be achieved by expressing these nonlinear equations in a different variation that will be affine in the state as well as control input, thus yielding a quadratic in the state optimal performance index. This transformation of the nonlinear system equations to an affine form in the state will result into a state dependent Riccati Equation. The derived state dependent Riccati equation is a generalisation of the Riccati equation which also has additional terms due to multiplicative noise. The simulation demonstrated that the state dependent Riccati equation in the FPD framework performed better than the LQR state dependent Riccati solution in terms of achieving a better regulation to the system state results.