Cautious Model Predictive Control using Gaussian Process Regression (1705.10702v4)

Abstract: Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.

• The paper demonstrates that integrating Gaussian Process Regression with MPC enhances robustness against nonlinear dynamics and model uncertainties.
• It introduces a novel method for dynamic selection of inducing points in sparse GP models, significantly reducing computational costs.
• Experimental results on autonomous systems validate improved constraint adherence and control performance in both simulated and real-world scenarios.

Cautious Model Predictive Control using Gaussian Process Regression

This paper investigates a Model Predictive Control (MPC) strategy implemented with Gaussian Processes (GP) to enhance the robustness against dynamics model errors in the control of nonlinear dynamic systems. The context is grounded in the necessity for reliable model estimations in control systems, particularly when dealing with highly nonlinear contexts. The paper introduces an approach that strategically integrates a linear nominal model with a GP to model the residual nonlinear dynamics.

Summary and Contributions

This research highlights several key contributions. The paper systematically reviews approximation techniques essential for propagating state distributions in the GP-enhanced MPC. The authors propose an effective reformulation of chance-constrained MPC to ensure that caution is maintained in the controller's decisions, effectively utilizing the GP's uncertainty model. This accommodates for state uncertainties resulting from dynamic model errors.

The paper provides a well-founded application guideline for using a GP model to complement nominal control frameworks. Moreover, a novel method to dynamically select inducing points in constructing sparse GP models is introduced, which effectively reduces computational costs without significantly sacrificing prediction quality. This aspect is crucial for applications where stability and quick responsiveness are vital, such as autonomous vehicle systems.

Results and Implications

The empirical demonstrations in both simulated and real-world settings are notable. Through experiments on an autonomous underwater vehicle and in hardware implementations for autonomous racing cars, the paper successfully illustrates the GP-based MPC's improvements over conventional approaches. Particularly, the results underscore the controller's capacity to respect state and input constraints more reliably, as evidenced by the reduced constraint violations compared to controllers ignoring GP-enhanced dynamics.

The experimental results are fortified with robust simulations showing that the controller could maintain an improved control performance measured through stricter adherence to dynamic constraints and effective response to system state uncertainties. The research sets a precedent for leveraging GP models within an MPC framework to boost adaptive capabilities of nonlinear control systems.

Future Directions and Developments

While the paper provides comprehensive coverage regarding the integration of GPs with MPC, there are several pathways for future research. Approaches to further optimize the placement of inducing points in sparse GPs dynamically and efficiently remain an intriguing area. Moreover, extending the method to accommodate broader classes of constraints and performance costs would expand its applicability in diverse industrial domains.

The theoretical underpinnings could also be bolstered by exploring the degrees of conservatism imposed by the chance-constrained framework and relaxing it without adverse impacts on safety. Further, real-time demonstrations across applications involving rapid dynamic changes could further validate the model.

The implementations in autonomous systems, as demonstrated, herald advancements in AI-driven control systems adhering to safety constraints, an increasingly vital consideration as AI systems permeate safety-critical sectors. The broader ramifications for self-learning control systems, particularly in AI, also align with emerging interests in domain adaptation and indeterminate environments where model inaccuracies are predominant.

In conclusion, the paper presents a cogent case for the cautious amalgamation of Gaussian Processes into Model Predictive Control architectures, delivering significant strides in enhancing model robustness and controller efficacy in unpredictable or inaccurately modeled scenarios.