Nonlinear Predictive Cost Adaptive Control of Pseudo-Linear Input-Output Models Using Polynomial, Fourier, and Cubic Spline Observables

TL;DR

This paper introduces a novel adaptive nonlinear model predictive control method that employs online system identification with various basis functions, enabling effective control of uncertain nonlinear systems without prior models.

Contribution

It proposes a new nonlinear predictive cost adaptive control approach using recursive least squares with basis functions for online identification, extending generalized predictive control.

Findings

Effective control of uncertain nonlinear systems demonstrated.

Comparison of polynomial, Fourier, and spline basis functions.

No prior system modeling or training required.

Abstract

Control of nonlinear systems with high levels of uncertainty is practically relevant and theoretically challenging. This paper presents a numerical investigation of an adaptive nonlinear model predictive control (MPC) technique that relies entirely on online system identification without prior modeling, training, or data collection. In particular, the paper considers predictive cost adaptive control (PCAC), which is an extension of generalized predictive control. Nonlinear PCAC (NPCAC) uses recursive least squares (RLS) with subspace of information forgetting (SIFt) to identify a discrete-time, pseudo-linear, input-output model, which is used with iterative MPC for nonlinear receding-horizon optimization. The performance of NPCAC is illustrated using polynomial, Fourier, and cubic-spline basis functions.