3 results about "Matrix differential equation" patented technology

This invention provides an adaptive admittance method and system based on the optimal control LQR theory, including constructing an environmental dynamics model and a robotic arm admittance control model, and deriving their interactive dynamics model; defining state variables and control inputs, and establishing a standard form state-space equation; constructing a quadratic performance index function, transforming admittance parameter optimization into an LQR problem; substituting the linear quadratic regulator framework into the quadratic performance index function, transforming the LQR problem into solving the Riccati matrix differential equation, and deriving analytical expressions for virtual optimal stiffness and virtual optimal damping; within the robotic arm control sampling frequency, inputting real-time collected environmental contact forces and the actual pose of the robotic arm end effector, along with set weighting coefficients, into the analytical expressions to calculate optimal virtual stiffness and damping; and then calculating pose corrections based on the admittance control model to correct the robotic arm's motion trajectory.

Disclosed is a method for digitally simulating polymerase chain amplification of at least one target, comprising simulating a plurality of successive amplification cycles, each cycle comprising: a hybridization stage; an extension stage; then, a denaturation stage; wherein the hybridization phase comprises, for each cycle: obtaining, for said cycle, initial values of a concentration vector of a plurality of nucleic acid molecules in the form of a single strand; initializing a concentration matrix of a duplex formed by hybridization of a plurality of nucleic acid molecules in a single strand form; the evolution of the concentration matrix during the hybridization phase is calculated by applying to the concentration matrix a matrix differential equation representative of the kinetics formed by the duplex according to the concentrations of the plurality of nucleic acid molecules.

The application is directed to the non-cooperative target observation task with large navigation information error and low update frequency, thereby a strong security efficient non-cooperative target active observation trajectory planning method is provided, and the application relates to the field of spacecraft orbit optimization technology. The state gain reachable set is calculated from the navigation initial error by the matrix differential equation, and the spacecraft structure size compensation is carried out, the boundary of the safety strategy is taken as the path inequality constraint, the optimization model with the path fuel consumption and the path length as the composite performance index, the optimization variable is the observation path state and the corresponding control, and the trajectory planning model is established comprehensively, and then the model prediction control is used to solve the optimization problem, so as to obtain the corresponding path state. The application is suitable for the trajectory planning of the non-cooperative target active observation in the space orbit optimization.