Robust Quadratic Gaussian Control of Continuous-time Nonlinear Systems

TL;DR

This paper introduces a robust nonlinear quadratic Gaussian controller for continuous-time systems that accounts for noise and disturbances, using an approximation technique to reduce computational complexity, demonstrated on an inverted pendulum.

Contribution

It presents a novel RNQG controller based on SDRE that incorporates noise and disturbance, with an efficient approximation method for real-time implementation.

Findings

Controller effectively manages noise and disturbance in nonlinear systems.

Approximation reduces computational burden for real-time control.

Successful application demonstrated on an inertially stabilized inverted pendulum.

Abstract

In this paper, we propose a new Robust Nonlinear Quadratic Gaussian (RNQG) controller based on State-Dependent Riccati Equation (SDRE) scheme for continuous-time nonlinear systems. Existing controllers do not account for combined noise and disturbance acting on the system. The proposed controller is based on a Lyapunov function and a cost function includes states, inputs, outputs, disturbance, and the noise acting on the system. We express the RNQG control law in the form of a traditional Riccati equation. Real-time applications of the controller place high computational burden on system implementation. This is mainly due to the nonlinear and complex form of the cost function. In order to solve this problem, this cost function is approximated by a weighted polynomial. The weights are found by using a least-squares technique and a neural network. The approximate cost function is incorporated into the controller by employing a method based on Bellman's principle of optimality. Finally, an inertially stabilized inverted pendulum example is used to verify the utility of the proposed control approach.