A system, computer-readable medium, and a method to operate a vehicle in a manner that minimizes a cost to travel from an origin to a destination that includes finding the input to a flight control system that minimizes direct operating cost. The approach described herein employs an energy state approximation (ESA).

A system, computer-readable medium, and a method to operate a vehicle in a manner that minimizes a cost to travel from an origin to a destination that includes finding the input to a flight control system that minimizes direct operating cost. The approach described herein employs an energy state approximation (ESA).

Embodiments relate to a computing system for solving differential equations. The system is configured to receive problem packages corresponding to problems to be solved, each comprising at least a differential equation and a domain, and to select a solver of a plurality of solvers, based upon availability of each of the plurality of solvers. Each solver comprises a coordinator that partitions the domain of the problem into a plurality of sub-domains, and assigns each of the plurality of sub-domains to a differential equation accelerator (DEA) of a plurality of DEAs. Each DEA comprises at least two memory units, and processes the sub-domain data over a plurality of time-steps by passing the sub-domain data through a selected systolic array from one memory unit, and storing the processed sub-domain data in the other memory unit, and vice versa.

Embodiments relate to a computing system for solving differential equations. The system is configured to receive problem packages corresponding to problems to be solved, each comprising at least a differential equation and a domain, and to select a solver of a plurality of solvers, based upon availability of each of the plurality of solvers. Each solver comprises a coordinator that partitions the domain of the problem into a plurality of sub-domains, and assigns each of the plurality of sub-domains to a differential equation accelerator (DEA) of a plurality of DEAs. Each DEA comprises at least two memory units, and processes the sub-domain data over a plurality of time-steps by passing the sub-domain data through a selected systolic array from one memory unit, and storing the processed sub-domain data in the other memory unit, and vice versa.

A SMT method for initialization of a hybrid equation-based dynamic system representing a dynamic behavior of a physical device, said method comprising: preparing a SMT problem, solving the SMT problem using a SMT solver, extracting a plurality of unfixed start value premises from UNSAT cores, creating a relaxed SMT problem by removing the plurality of unfixed start value premises, solving the relaxed SMT problem using the SMT solver, extracting the solution from the SMT solver and considering further algorithms to solve the relaxed SMT problem.

A SMT method for initialization of a hybrid equation-based dynamic system representing a dynamic behavior of a physical device, said method comprising: preparing a SMT problem, solving the SMT problem using a SMT solver, extracting a plurality of unfixed start value premises from UNSAT cores, creating a relaxed SMT problem by removing the plurality of unfixed start value premises, solving the relaxed SMT problem using the SMT solver, extracting the solution from the SMT solver and considering further algorithms to solve the relaxed SMT problem.

Image data corresponding to an image depicting an equation is received. The image data is processed to identify a plurality of morphological components corresponding to the equation depicted in the image. A computer readable data object is generated using the plurality of morphological components, wherein the computer readable data object is in a defined syntax computable by a computational application.

System, methods, and other embodiments described herein relate to NODE learned tire models. In one embodiment, a method includes calculating estimated tire forces based on vehicle measurements; solving a second order differential equation in a repetitive manner until an error calculation based on a tire force function and the estimated tire forces reaches a minimum value, by: using a first predictive model to provide one or more inflection points and initial conditions based on the vehicle measurements, using a second and third predictive model to act as, respectively, exponents to a positive and a negative exponential equation based on the one or more inflection points, the initial conditions, and the vehicle measurements, and integrating the exponential equations to obtain the tire force function; and applying the tire force function to new vehicle measurements to estimate current tire forces.

System, methods, and other embodiments described herein relate to NODE learned tire models. In one embodiment, a method includes calculating estimated tire forces based on vehicle measurements; solving a second order differential equation in a repetitive manner until an error calculation based on a tire force function and the estimated tire forces reaches a minimum value, by: using a first predictive model to provide one or more inflection points and initial conditions based on the vehicle measurements, using a second and third predictive model to act as, respectively, exponents to a positive and a negative exponential equation based on the one or more inflection points, the initial conditions, and the vehicle measurements, and integrating the exponential equations to obtain the tire force function; and applying the tire force function to new vehicle measurements to estimate current tire forces.

Certain aspects of the present disclosure generally relate to a sampling network of a switched-capacitor integrator and a clocking scheme associated therewith, which may be used in an analog-to-digital converter (ADC), for example. The integrator generally includes five sets of switches which allow for a decreased switching frequency (e.g., halved) at an input stage of the integrator compared to conventional double sampling networks. As a result, the input impedance of the integrator may be increased (e.g., doubled), resulting in lower power consumption and reduced strain on driving circuitry.