Provably safe and robust learning-based model predictive control

Abstract

Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to deal with growing energy constraints. This paper describes a learning-based model predictive control (LBMPC) scheme that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance; the benefits of this framework are that it handles state and input constraints, optimizes system performance with respect to a cost function, and can be designed to use a wide variety of parametric or nonparametric statistical tools. The main insight of LBMPC is that safety and performance can be decoupled under reasonable conditions in an optimization framework by maintaining two models of the system. The first is an approximate model with bounds on its uncertainty, and the second model is updated by statistical methods. LBMPC improves performance by choosing inputs that minimize a cost subject to the learned dynamics, and it ensures safety and robustness by checking whether these same inputs keep the approximate model stable when it is subject to uncertainty. Furthermore, we show that if the system is sufficiently excited, then the LBMPC control action probabilistically converges to that of an MPC computed using the true dynamics.

Controller design under safety specifications for a class of bounded hybrid automata

“…Ideally, provably safe controllers should also be least restrictive, which means in the context of a driver-assist system that the controller constrains the possible actions of the human driver as little as possible. Due to the computational complexity of the task, the design of provably safe, least restrictive controllers remains a challenge and can in general only be done approximately, see for instance [9,3,11]. However it has been shown that a number of ground transportation systems have the so-called inputoutput order preserving property, in which case exact solutions are possible, see [4,12,5] and the references therein.…”

On-board Model Predictive Control of a Quadrotor Helicopter: Design, Implementation, and Experiments

“…Like robust control, LBMPC can deal with uncertainty directly, but also allows the designer to specify performance objectives to optimize and explicitly incorporates on line model updates to further improve performance. LBMPC is compatible with many learning techniques; previous work has employed a modified NadarayaWatson estimator with Tikhonov regularization (Aswani et al, 2012a) and a semi-parametric regression estimator (Aswani et al, 2012b).…”

“…A recently developed control technique with roots in MPC, adaptive, and learning-based control is called learning based model predictive control (LBMPC) (Aswani et al, 2012a). It seeks to combine attributes of MPC (most notably, the ability to enforce constraints, which encode safety requirements) with elements of adaptive or learning schemes which promise to improve performance by improving system models based on data obtained on-line.…”

“…Learning-Based Model Predictive Control (LBMPC) (Aswani, Gonzalez, Sastry, and Tomlin, 2012a) is a new model-based control strategy that also allows for on-line updates to the model to improve performance, while maintaining certain guarantees about safety, robustness, and convergence. LBMPC combines aspects of learning-based control and model predictive control (MPC, (Langson et al, 2004)).…”

Safe Control under Uncertainty with Probabilistic Signal Temporal Logic

“…Designing controllers under reachability analysis and safe learning are well-studied methods that allow specifying safety and reachability properties, while learning the optimal strategy online [32,33,15,3,1]. However, finding the reachable set is computationally expensive, which makes these approaches impractical for most interesting tasks.…”