automotive control teams

Abstract: This article presents a time-aware hybrid model predictive control (MPC) framework that simultaneously optimizes the objective with respect to both continuous control inputs and event switching times. Rather than relying on a fixed time grid, the switching instant is lifted into the decision vector and treated as an explicit optimization variable. The resulting transcription is a smooth nonlinear program whose Karush-Kuhn-Tucker (KKT) conditions are consistent with the Hybrid Minimum Principle (HMP) event-time stationarity condition, so first-order hybrid sensitivities are recovered implicitly through the KKT system rather than by evaluating saltation matrices. Each MPC step solves a single sparse Quadratic Program (QP), jointly optimizing control inputs and impact timing in real time. On a bouncing mass landing on an oscillating platform, the method attaches in half the time of fixed-grid saltation MPC, reduces cumulative control effort by 30%, and removes the post-impact rebounds, at a 15% increase in per-cycle solve time. It matches the cumulative effort of offline time-aware solvers to within 4% while running at 2.4 ms per cycle against 281 ms for a complementarity-based formulation of the same problem, of which a 10.6x reduction is attributable to the transcription alone at a fixed solver.

Abstract: The Lipschitz property of a deep neural network provides a direct measure of its sensitivity to input perturbations and, when explicitly controlled, offers a principled way to limit the propagation of errors and improve robustness. Over the past decade, Lipschitz-bounded layers have been incorporated into increasingly expressive and high-performing deep models, narrowing the gap between empirical robustness and formal, by-design guarantees of stability. This article introduces the fundamental concepts underlying Lipschitz-bounded neural networks, explaining the principles behind Lipschitz-constrained layers, the mechanisms used to enforce their bounds, and how they yield robustness certificates at the cost of a single forward pass. The tutorial concludes by discussing emerging and open directions, highlighting Lipschitz control as a general framework for offering guaranteed, by-design stability.

Abstract: We present sparse dictionary differentiable predictive control (SD-DPC), a framework for learning sparse, interpretable feedback policies for nonlinear systems from data. A prediction model is first identified by rollout-based sparse identification of nonlinear dynamics (SINDy), building on gradient-based and multistep formulations. The policy is then parameterized as a sparse combination of dictionary functions and trained by differentiating a constrained finite-horizon predictive-control objective through this model, so that its terms are selected by closed-loop performance rather than by imitating a previously trained controller. The result is an explicit feedback law with only a handful of terms. Across three benchmark control problems, SD-DPC satisfies the constraints in all test scenarios, outperforms a policy distilled onto the same terms by up to an order of magnitude, and requires orders of magnitude less memory and online computation than an optimization benchmark, while admitting explicit sensitivity bounds.

Abstract: Real-time and cyber-physical systems are developed through successive refinements from abstract requirements to platform deployments. While timing knowledge evolves throughout this process, existing stochastic real-time formalisms typically require uncertainty to be embedded from the outset or necessitate model reconstruction when new timing information becomes available, hindering iterative timing engineering. This paper presents a refinement-oriented timing specification framework built upon the Clock Constraint Specification Language (CCSL). It supports the progressive introduction of timing knowledge across three levels: logical timing relations, quantitative real-time constraints, and stochastic timing models. Instead of altering behavioural semantics, stochastic information is attached directly to timing quantities as a refinement. This enables implementation measurements and operational observations to be incorporated incrementally within a unified declarative framework. We implement our approach in an OCaml-based simulation tool and evaluate it on a simplified but representative Software-Defined Vehicle use case.