Combining Robust Control and Machine Learning for Uncertain Nonlinear Systems Subject to Persistent Disturbances

Abstract

This paper proposes a control strategy consisting of a robust controller and an Echo State Network (ESN) based control law for stabilizing a class of uncertain nonlinear discrete-time systems subject to persistent disturbances. Firstly, the robust controller is designed to ensure that the closed-loop system is Input-to-State Stable (ISS) with a guaranteed stability region regardless of the ESN control action and exogenous disturbances. Then, the ESN based controller is trained in order to mitigate the effects of disturbances on the system output. A numerical example demonstrates the potentials of the proposed control design method.

Figures (5)

• Figure 1: Proposed Control Setup.
• Figure 2: General set-up for learning the inverse model.
• Figure 3: General set-up for inverse model control.
• Figure 4: System closed-loop response (at the top of figure) considering $u=u_1$ (red dashed line) and $u=u_1+u_2$ (black solid line) for $x_0^T = [ -0.0225 \;\;0.252 \;\; 0.005]$, $\theta=0.75$ and the disturbance signal (depicted at the bottom of the figure) defined as $d(t) = 0.25\sqrt{2}(\sin(t) + \sin(2t))$.
• Figure 5: Reachable set estimate and phase portrait of state trajectories for $x_0^T = [ -0.0225 \;\;0.252 \;\; 0.005]$, $\theta=0.75$ and $d(t) = 0.25\sqrt{2}(\sin(t) + \sin(2t))$, considering the control laws $u = u_1$ (state trajectory in red solid line) and $u = u_1 + u_2$ (state trajectory in black solid line).

Theorems & Definitions (1)

• proof