Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics

Castañeda, Fernando; Choi, Jason J.; Zhang, Bike; Tomlin, Claire J.; Sreenath, Koushil

doi:10.23919/acc50511.2021.9483420

Cited by 32 publications

(37 citation statements)

References 17 publications

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“…CLF or CBF-based controllers that use GP regression to learn the model uncertainty terms have been proposed before [16], [17], [18]. However, these works do not consider uncertainty in the input effects, which is significant for many systems [7]. In [19], this problem is tackled by using Matrix-Variate GP regression.…”

Section: B Related Workmentioning

confidence: 99%

“…First, we extend the GP-CLF-SOCP controller presented in [7] to the safety-critical control case by including an uncertainty-aware CBF chance constraint. This results in the formulation of the so-called Gaussian Process-based Control Barrier Function and Control Lyapunov Function Second-Order Cone Program (GP-CBF-CLF-SOCP).…”

Section: Contributions and Organizationmentioning

confidence: 99%

“…In general, the nominal model vector fields ( f , g) do not perfectly match the true plant vector fields (f , g) due to model uncertainty. We start by designing a locally exponentially stabilizing CLF V and a CBF B, based on the nominal model (7). These functions are assumed to be a locally exponentially stabilizing CLF and a CBF, respectively, also for the true plant (1).…”

Section: Adverse Effects Of Model Uncertaintymentioning

confidence: 99%

“…This section gives an overview of Gaussian Processes and how they are used for regression in this paper. We utilize a compound kernel, which was introduced in our previous work [7], to exploit the affine nature of the problem.…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

“…However, CBF-based controllers suffer from the problem of model uncertainty, which we tackle using Gaussian Process (GP) regression. We build on our previous work [7], where we used GP regression to address model uncertainty in Control Lyapunov Functions (CLFs, [8]). We propose an optimization-based safety-critical controller, and we conduct an analysis of its feasibility.…”

Section: Introduction a Motivationmentioning

confidence: 99%

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Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty

Castañeda

Choi

Zhang

et al. 2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a min-norm quadratic program (CBF-CLF-QP) which solves for a safety-critical control input. However, since these constraints rely on a model of the system, when this model is inaccurate the guarantees of safety and stability can be easily lost. In this paper, we present a Gaussian Process (GP)based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs. The considered model uncertainty is affected by both state and control input. We derive probabilistic bounds on the effects that such model uncertainty has on the dynamics of the CBF and CLF. Then, we use these bounds to build safety and stability chance constraints that can be incorporated in a min-norm convex optimization program, called GP-CBF-CLF-SOCP. As the main theoretical result of the paper, we present necessary and sufficient conditions for pointwise feasibility of the proposed optimization problem. We believe that these conditions could serve as a starting point towards understanding what are the minimal requirements on the distribution of data collected from the real system in order to guarantee safety. Finally, we validate the proposed framework with numerical simulations of an adaptive cruise controller for an automotive system.

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