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In reinforcement learning, the TD($\lambda$) algorithm is a fundamental policy evaluation method with an efficient online implementation that is suitable for large-scale problems. One practical drawback of TD($\lambda$) is its sensitivity…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
In this paper, we investigate the problem of Model Predictive Control (MPC) of dynamic systems for high-level specifications described by Signal Temporal Logic (STL) formulae. Recent works show that MPC has the great potential in handling…
In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
We investigate the task and motion planning problem for Signal Temporal Logic (STL) specifications in robotics. Existing STL methods rely on pre-defined maps or mobility representations, which are ineffective in unstructured real-world…
In this work, we present a novel robustness measure for continuous-time stochastic trajectories with respect to Signal Temporal Logic (STL) specifications. We show the soundness of the measure and develop a monitor for reasoning about…
The performance of model-based control techniques strongly depends on the quality of the employed dynamics model. If strong guarantees are desired, it is therefore common to robustly treat all possible sources of uncertainty, such as model…
Signal temporal logic (STL) is a powerful tool for describing complex behaviors for dynamical systems. Among many approaches, the control problem for systems under STL task constraints is well suited for learning-based solutions, because…
This work studies the planning problem for robotic systems under both quantifiable and unquantifiable uncertainty. The objective is to enable the robotic systems to optimally fulfill high-level tasks specified by Linear Temporal Logic (LTL)…
This paper presents a spatiotemporal tube (STT)-based control framework for satisfying Signal Temporal Logic (STL) specifications in unknown control-affine systems. We formulate STL constraints as a robust optimization problem (ROP) and…
Researchers have previously proposed augmenting Signal Temporal Logic (STL) with the value freezing operator in order to express engineering properties that cannot be expressed in STL. This augmented logic is known as STL*. The previous…
We present a framework to interpret signal temporal logic (STL) formulas over discrete-time stochastic processes in terms of the induced risk. Each realization of a stochastic process either satisfies or violates an STL formula. In fact, we…
An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels if the time-step ratios…
Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from signal temporal logic (STL)…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much…
In this paper, we study the control of dynamical systems under temporal logic task specifications using gradient-based methods relying on quantitative measures that express the extent to which the tasks are satisfied. A class of controllers…
We propose a signal temporal logic (STL)-based framework that rigorously verifies the feasibility of a mission described in STL and synthesizes control to safely execute it. The proposed framework ensures safe and reliable operation through…
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL) that is…