A concurrent learning adaptive-optimal control architecture for nonlinear systems

Abstract

A concurrent learning adaptive-optimal control architecture is presented that combines learning-focused di rect adaptive controllers with model predictive control for guaranteeing safety during adaptation for nonlinear systems. Exponential parameter convergence properties of concurrent learning adaptive controllers are leveraged to learn a feedback linearization signal that reduces a nonlinear system to an approximation of a linear system for which an optimal solution is known or can be easily computed online. Stability of the overall architecture is analyzed, and numerical simulations on a wing-rock dynamics model are presented in presence of significant system uncertainty, parameter variation, and measurement noise.

Adaptive-Optimal Control of Constrained Nonlinear Uncertain Dynamical Systems using Concurrent Learning Model Predictive Control

“…MPC) after sufficient confidence in estimated parameters has been gauged online. One such architecture was proposed in our other papers, 20,21 and is displayed in Figure 1. In that paper we showed that guarantees on finite time to switch, stability before and after the switch, and guarantees that the architecture can switch back to the adaptive controller if ideal parameters of the system change.…”

Optimizing Reference Commands for Concurrent Learning Adaptive-Optimal Control of Uncertain Dynamical Systems

“…23 In the past, we have also applied MPC successfully together with concurrent learning adaptive controllers using a switched system architecture based on a criterion on the quality of the uncertainty approximation. 24,25 Shaping various signals to improve certain performance characteristics has attracted increasing interest in recent years. Shaping the reference command in an optimal sense has become known as the reference governor.…”

“…31 In this paper we propose a non-switching concurrent learning adaptive-optimal controller where the exogenous reference commands are shaped based on an a-priori determined optimal solution of a chosen linear reference model. One of the main challenges in implementing MPC, and specifically the architectures in, 24,25 is to guarantee the feasibility of obtaining an optimal solution online on resource constrained aircraft. In this paper, this problem is tackled by solving offline the optimal control problem for the linear reference model in a predescribed parameter space.…”

Removing erroneous history stack elements in concurrent learning

“…For concurrent learning adaptive identification, we combine the current data-based update laws in (3) with the recorded data-based update laws in (5). We obtain the following theorem on the convergence of the parameter estimates.…”

“…In [5], concurrent {stefan.kersting, mb}@tum.de learning enhances a model predictive control architecture for nonlinear systems. The synchronization of agents with uncertain dynamics in a network is discussed in [6] and [7], where concurrent learning is applied to learn the desired policies in the presence of unknown dynamics.…”