Abstract: 

A key enabler for machine learning lies in the use of massive parallel simulation. The goal of this presentation is to demonstrate how this paradigm—massive parallel simulation—can be paired with model-based safety-critical controllers. In particular, we will talk about the fusion of data-driven methods with CBS MPC, and layered architectures. These ideas will be demonstrated on a wide variety of robotic systems.

Abstract: 

This part of the workshop will describe a novel approach for computationally tractable, data-driven, optimisation-based control for applications in which safety is critical.

Starting with a brief introduction to the main concepts and challenges, the discussion will motivate recent work on Model Predictive Control (MPC) and the convex-concave procedure for finding locally optimal solutions of nonconvex problems.

We will consider how to use differences of convex (DC) functions to derive convex conditions that allow control system performance to be optimized as a sequence of convex sub-problems.

Using sequences of sets (tubes) to bound predicted trajectory, the method can provide guaranteed robustness to uncertainty, and it allows warm-starting and early-termination at feasible suboptimal solutions. Key properties and theoretical results, including feasibility, convergence, optimality and closed loop stability will be discussed.

The talk will explain how DC representations can be computed directly from data and how model estimation can be performed online simultaneously with control to define safe learning-based control algorithms. We will discuss data-driven techniques using neural networks, machine learning and sum-of-squares polynomials to obtain systematic DC decompositions of nonlinear system dynamics.

As an application of these ideas, we will describe the problem of controlling the transitions of a tiltwing vertical take-off and landing (VTOL) aircraft subject to wind disturbances and model uncertainty. Results of a case study will be discussed involving a VTOL aircraft model with unknown wind gusts and aerodynamics defined by experimental data.

Abstract: In this talk, I will draw together three threads of work on learning for control-affine dynamical systems, sketching a roadmap for a theory of sample complexity for this class of nonlinear control problems. First, I will discuss data-driven robust control using Control Certificate Functions (CCFs) and non-parametric set-based representations of unknown dynamics. Then, focusing on the question of identification, I will turn to more classic machine learning methods of kernel regression and random features. Finally, I will discuss recent work on the sample complexity of learning partially observed bilinear dynamical systems. Throughout, I will highlight open questions that remain unanswered. Based on work done with Andrew Taylor, Victor Dorobantu, Ben Recht, Yisong Yue, Aaron Ames, Kimia Kazemian, Yahya Sattar, Yassir Jedra, and Maryam Fazel.

Abstract: This talk focuses on uncertainty set estimation for unknown control systems. Un-certainty sets are crucial for the quality of robust control since they directly influence the conservativeness of the control design. Departing from the confidence region analysis of least squares estimation, this talk focuses on set membership estimation (SME), which is a classical uncertainty-set estimation method in the control literature. Though good numerical performances have attracted applications of SME in robust control, the non-asymptotic convergence rate of SME for dynamical systems remains an open question. This talk will discuss the convergence rate bounds for SME for both linear control systems and nonlinear systems. We also provide numerical results demonstrating SME’s practical promise.

Abstract: Set invariance in the presence of uncertainty and disturbance is of central importance for the safety of control systems. In this talk I will explain a data-driven method to compute an approximation of a minimal robust control invariant set from experimental data. Minimal control invariant sets are relevant in precise target tracking problems under uncertainty. Specifically, given a model structure, including both additive and multiplicative uncertainties, our method begins by identifying the set of admissible models with constraints extracted from the experimental data. Each model in the set of admissible models contains information about the nominal model and the characterization of the model uncertainties. I will illustrate some trade-offs between uncertainty characterizations and make connections to  unfalsified control. I will also highlight several open problems. Finally, I will show an experimental demonstration of the method on a real autonomous vehicle lane-keeping controller in Mcity, University of Michigan’s autonomous vehicle testing facility.

Abstract: Despite recent advances in Machine Learning (ML), the goal of designing control systems capable of fully exploiting the potential of these methods to learn from the environment and safely achieve complex specifications remains elusive: we have been told that ”fully autonomous vehicles are less than 5 years away”...since 2015. Modern ML methods can leverage large amounts of data to learn powerful predictive models, but such models are not designed to operate in a closed-loop environment. Recent results on reinforcement learning offer a tantalizing view of the potential of a rapprochement between control and learning, but so far proofs of performance are restricted to limited cases (e.g. finite horizon LQR/LQG). Thus, in most cases learning elements are used as black boxes within the loop, with less than completely understood properties. Further progress hinges on the development of a principled understanding of the properties and limitations of ML algorithms when used in a control systems context.

In the first portion of the talk we argue that when the goal is to learn models that can be used for control, loss functions based on open loop metrics are not adequate. Rather, what is needed are metrics that capture closed-loop distances, such as the gap metric introduced in the 1990’s. We will conclude this portion of the talk by presenting some recent results on gap-metric based learning and discuss generalizations.

In the second part of the talk we will address the problem of designing non-linear controller directly from data, bypassing the identification steps. We will start by presenting some simple examples where commonly used ML techniques (e.g. Deep Learning, Reinforcement Learning) will provably fail to find a stabilizing controller and discuss the implications of these results for the type of architectures needed for control. We will conclude the talk by presenting an overview of data-driven safe control of non-linear systems and point out to open problems.

Abstract: I will present two threads of research from my group related to uncertainty quantification. In the first part, I will focus on how to generate provably correct uncertainty sets for black-box ML models under arbitrary distribution shifts. Based on the framework of conformal prediction (CP), we present a Bayesian CP algorithm that can answer multiple arbitrary confidence level queries online with provably low regret. In the second part, I will focus on the problem of set-membership estimation in control and perception, and present computationally tractable inner and outer approximations of the true parameter uncertainty set in the form of ellipsoids. The inner approximation uses a fast GPU-based sampling strategy and the outer approximation leverages sums-of-squares relaxations.

Abstract: The next generation of Cyber-Physical Systems (CPS) is large-scale, safety-critical, and time-varying. Therefore, we must design practical control algorithms that enable CPS that are scalable and robust to uncertainties, with fast adaptation. Towards this, I will introduce a novel uncertainty set-based online adaptive control framework that leverages online learning techniques (e.g., convex online optimization) and control methods (e.g., distributed control and MPC) that enable novel safety guarantees for unknown systems under non-stochastic and potentially adversarial disturbances. 

I will outline adversarial stability results for learning-based control in (i) unknown time-varying systems and (ii) unknown large-scale networked systems with communication constraints. Applications of the framework include voltage regulation in power distribution grids and comfort-constrained HVAC control. Experiments on realistic nonlinear simulations with real-world data confirm that the approach remains effective under practical conditions.