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In this article, a novel Finite Time Stability (FTS) analysis of Fractional-Order Time Delay Systems (FOTDSs) is proposed. By using the fixed point approach, sufficient conditions for the robust FTS of FOTDSs have been established. Two…
Two important enhanced sampling algorithms, simulated (ST) and parallel (PT) tempering, are commonly used when ergodic simulations may be hard to achieve, e.g, due to a phase space separated by large free-energy barriers. This is so for…
With the explosive growth of rigid-body simulators, policy learning in simulation has become the de facto standard for most rigid morphologies. In contrast, soft robotic simulation frameworks remain scarce and are seldom adopted by the soft…
We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these…
For prediction and real-time control tasks, machine-learning (ML)-based digital twins are frequently employed. However, while these models are typically accurate, they are custom-designed for individual systems, making system-to-system…
Reformulating hyperdynamics without using a transition state theory (TST) dividing surface makes it possible to accelerate conventional molecular dynamics (MD) simulation using a broader range of bias potentials. A new scheme to calculate…
Ensuring correctness of timed behaviors in cyber-physical systems (CPS) using closed-loop verification is challenging due to the hybrid dynamics in both systems and environments. Simulink and Stateflow are tools for model-based design that…
Motion planning with simple objectives, such as collision-avoidance and goal-reaching, can be solved efficiently using modern planners. However, the complexity of the allowed tasks for these planners is limited. On the other hand, signal…
We tackle the challenging problem of multi-agent cooperative motion planning for complex tasks described using signal temporal logic (STL), where robots can have nonlinear and nonholonomic dynamics. Existing methods in multi-agent motion…
Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by…
In multi-agent systems, signal temporal logic (STL) is widely used for path planning to accomplish complex objectives with formal safety guarantees. However, as the number of agents increases, existing approaches encounter significant…
Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…
We introduce a metric that can quantify the temporal relaxation of Signal Temporal Logic (STL) specifications and facilitate resilient control synthesis in the face of infeasibilities. The proposed metric quantifies a cumulative notion of…
The incompressible smoothed particle hydrodynamics method (ISPH) is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical…
Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
The present paper introduces stochastic velocity as improvement for moving particle semi-implicit (MPS) method. This improvement is to overcome energy loss caused by numerical dissipation in the basic MPS that brings about rapid decay of…
We develop an algorithm for the motion and task planning of a system comprised of multiple robots and unactuated objects under tasks expressed as Linear Temporal Logic (LTL) constraints. The robots and objects evolve subject to uncertain…
Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…