45 results about "Lyapunov equation" patented technology

The invention relates to the technical field of remote operating robot synchronous control, specifically discloses a remote operating robot fixed time control method based on a rapid terminal sliding mode. The method includes: selecting a master robot and a slave robot to form a remote operating system, measuring system parameters of the master robot and the slave robot respectively, measuring position information of the master robot and the slave robot on line, obtaining speed information of the master robot and the slave robot, designing a rapid terminal sliding mode surface, based on the designed rapid terminal sliding mode surface, using the system parameters of the main robot and the slave robot to design a self-adaptive fixed time controller, and using a Lyapunov equation to provide a relational expression between a parameter self-adaptive law, controller parameters, sliding mode surface parameters and system convergence time, thereby determining the controller parameters and the sliding mode surface parameters according to requirements of practical application for system convergence time and a relational expression between the system parameters and the system convergence time. The remote operating robot fixed time control method based on the rapid terminal sliding mode makes up for the defects in control speed and control accuracy of an existing remote operating robot system control method.

A method of determining the location of actuators and sensors for climate control that includes providing a model of temperature and airflow within a room. A matrix for the placement of sensors is calculated using a Lyapunov equation. A Lyapunov equation includes a matrix for the transition state from the model of temperature and airflow. A trace of the matrix for the placement of sensors is maximized to provide optimum placement of the sensors. A matrix for the placement of actuators within the model is calculated using the Lyapunov equation. A variable for the Lyapunov equation includes the matrix for the transition state obtained from the model of temperature and airflow. A trace of the matrix for the placement of actuators is maximized to provide optimum placement of the actuators within the room.

The invention discloses a low-orbit flexible satellite attitude tracking control method based on a sliding-mode observer, relates to a low-orbit flexible satellite attitude tracking control method based on a sliding-mode observer, and aims at solving the problems that an existing low-orbit flexible satellite is low in satellite attitude tracking control accuracy due to relatively large aerodynamic interference torque and vibration of flexile components. The low-orbit flexible satellite attitude tracking control method based on the sliding-mode observer comprises the following steps: building a geocentric inertial coordinate system and a satellite body coordinate system; building a state space expression, and determining an upper bound of an interference signal received by the observer; solving a gain matrix of the observer, a matching matrix of the observer and a Lyapunov equation matrix variable; observing to obtain an estimated mode vibration velocity value of the sliding-mode observer and an estimated mode vibration state value of the sliding-mode observer; rewriting a kinetic equation of a flexible satellite attitude into an error attitude tracking control model; determining a sliding-mode term gain of the control law, and carrying out tracking control on the error attitude tracking model by adopting the siding-mode control law according to measured satellite attitude quaternion, attitude angular velocity information and estimated mode quantity value. The low-orbit flexible satellite attitude tracking control method is applied to satellite attitude tracking control.

Provided is a control-limited minisatellite three-axis magnetic moment attitude control method based on an algebraic Lyapunov equation. The invention relates to a control-limited minisatellite three-axis magnetic moment attitude control method based on an algebraic Lyapunov equation. The method is used to realize global stability of a minisatellite three-axis magnetic moment attitude control under control-limited conditions. The method comprises: step 1, establishing attitude kinematics and attitude kinetic models of control-limited minisatellite three-axis magnetic moment attitude control, to obtain a state-space equation; step 2, solving explicit solution P0 of the algebraic Lyapunov equation A<T>P0+P0A=-D<T>D, wherein A is a system matrix, D is a matrix in arbitrary dimensions, the system matrix A being critical stable or Lyapunov stable, ensuring the algebraic Lyapunov equation have a positive definite solution P0; step 3, and through the positive definite solution P0 of the algebraic Lyapunov equation, designing linear feedback control law under explicit control-limited conditions. The method is applied in the field of satellite control.

The invention relates to a time-varying feedback finite-time stabilization method of a control limited spacecraft rendezvous control system. The stabilization method comprises the steps of: (1), establishing an orbital dynamics model of the control limited spacecraft rendezvous control system, and obtaining a state-space equation; (2), establishing a parametric Lyapunov equation, analyzing the property thereof, according to the positive definite solution P(gamma) of the parametric Lyapunov equation, designing an explicit linear time-varying feedback control law in a control limited condition,namely, designing a state feedback controller of the control limited spacecraft rendezvous control system; and (3), designing controller parameters by constructing an explicit Lyapunov function and utilizing the property of the parametric Lyapunov equation solution, and ensuring that a tracking spacecraft and a target spacecraft complete a rendezvous task in limited time. By means of the time-varying feedback finite-time stabilization method of the control limited spacecraft rendezvous control system in the invention, limited time stabilization of the spacecraft rendezvous control system in the control limited condition can be realized.

The invention relates to a wind-power-generation-containing two-region interconnected power grid automatic generation control optimization method. The method comprises the steps of: establishing an automatic generation control space state model, wherein the model is a two-region interconnected system including hydroelectric power, a small fossil power plant and wind power; according to the established space state model, constructing a new cost function; forming a control variable by an output variable and an output feedback gain matrix so as to determine an input variable; in a closed-loop system, constructing a Lyapunov function to obtain a Lyapunov equation; and based on the Lyapunov equation, deriving a Hamilton function, and obtaining optimal values of corresponding parameters so as toobtain an automatic generation control optimization result of the established model. A control strategy disclosed by the invention has good dynamic adaptability and can reinforce coordination among aplurality of control regions. The invention solves the problem of frequency fluctuation of a power system, which is caused by ever-increasing installed capacity of wind power and inherent randomnessand fluctuation of the installed capacity of wind power.

The invention discloses a finite time fault-tolerant control method used for a remote operation system. The method specifically comprises the steps that for the remote operation system with an executor failure, according to measured parameters of main and slave robots, a nominal system is obtained; on the basis of position and speed information of the main and slave robots in the nominal system, finite time is designed for the main and slave robots, and executor failures of the main and slave robots and system uncertain information are estimated in an online manner; on the basis of the measured joint position and speed information, a terminal sliding mode surface is designed; on the basis of the terminal sliding mode surface, the executor failure and the system uncertain estimation information, the finite time control strategy is designed; and the Lyapunov equation is used for building the system convergence rate and controller parameter relation. Through executor failure and system uncertain finite time online precise estimation, the compensation of the executor failure and the system uncertainty for the system influence can be successfully achieved, and the stable running of theclosed-loop remote operation system is ensured.

A time-varying feedback finite time control method for controlling a limited satellite formation flight system comprises the steps: step 1, establishing an orbital dynamics model for controlling the limited satellite formation flight system and obtaining a state-space equation, establishing a to-be-tracked signal model and obtaining the state-space equation; step 2, establishing a parameter Lyapunov equation and analyzing the property of the parameter Lyapunov equation, designing an explicit linear time-varying feedback control law through a positive definite solution of the parameter Lyapunovequation, establishing an output adjustment equation, and designing an explicit linear time-varying feedforward control law through a solution of the output adjustment equation; and designing a time-varying state controller for controlling the limited satellite formation flight system through a linear time-varying feedback control law and a linear time-varying feedforward control law; and step 3,constructing an explicit Lyapunov function, and designing controller parameters by utilizing the properties of a parameter Lyapunov equation and an adjustment equation solution to ensure that the accompanying satellite completes a tracking task within finite time. The invention aims to realize finite time control of the satellite formation flight system under the condition of limited control.

The invention provides a consistency control method for a distributed dynamic event triggered multi-agent system, and belongs to the technical field of multi-agent system control. According to the method, a novel distributed dynamic event triggering mechanism based on the parameter Lyapunov equation is designed by utilizing the parameter Lyapunov equation, the influence of a feedback gain matrix K and a matrix B on the triggering time interval in the system can be eliminated, and meanwhile, an expression of the minimum triggering time interval is established; the minimum triggering time interval and the unique parameter gamma of the parameter Lyapunov equation have a clear and simple relationship, and the triggering time interval of the system can be dynamically adjusted by adjusting the unique parameter in the parameter Lyapunov equation, so that the balance between the control performance of the system and the triggering time interval is realized, and the stability of the system is improved. While the multi-agent system achieves the state consistency, the communication load and the mechanical loss of the actuator are effectively reduced, and the engineering realization is easy.

An adaptive fast speed tracking control method for an uncertain underwater robot comprises the following steps of designing a control target for an underwater robot kinematics model according to the actual application of a robot; estimating an uncertain part of a system model and the unknown external interference online by using a time delay estimation technology, and further designing an integralterminal sliding mode surface; designing an adaptive controller based on the integral terminal sliding mode surface and an underwater robot kinematics model, and defining a gain variable in a controllaw; utilizing a Lyapunov equation to prove the stability of the system, and verifying the rationality of the designed integral terminal sliding mode surface and the self-adaptive controller. According to the present invention, the problem that an existing controller depends on the underwater robot model information, is solved, namely the designed controller is independent of the system model, sothat the influence of the model uncertainty and the unknown interference on an underwater robot system is overcome, the robust performance of the system is improved, the controller design is simplified, and the method is conducive to being applied to the engineering practice.

The invention provides a C-RAN system resource allocation method for balancing long-term energy efficiency and network stability. The method comprises the following steps: establishing a hybrid energysupply C-RAN mathematical model in combination with energy cooperation; establishing an objective function and constraint conditions of a long-term energy efficiency optimization problem; convertinga system long-term energy efficiency optimization problem into a single time slot optimization problem based on the thought of a Lyapunov equation and a penalty function; and solving the converted single time slot optimization problem by adopting a joint resource allocation optimization algorithm. According to the method, system resources (transmission power, cooperative energy and power grid energy supply) can be optimally allocated, the balance between the long-term energy efficiency of the system and the network stability is effectively improved. The system performance is optimized, so thatthe hybrid energy supply C-RAN system adopting energy cooperation meets various long-term and instantaneous service quality requirements, and the method has a wide application prospect.

The invention discloses a robot control method, a computing device and a storage medium. The method includes the steps that position and force parameters of a robot are acquired; based on the acquiredposition and force parameters and a hybrid adaptive impedance control algorithm designed for the robot in advance, hybrid adaptive impedance control rates are obtained, wherein the hybrid adaptive impedance control algorithm is designed based on a dynamic model and a Lyapunov equation, and the hybrid adaptive impedance control rates include the inner loop adaptive impedance control rate corresponding to a position control subspace of the robot and the outer loop adaptive impedance control rate corresponding to a force control subspace of the robot; and the motion of the robot is adaptively controlled based on a control instruction obtained by dynamic inverse solution conversion of the hybrid adaptive impedance control rates. Thus, a hybrid adaptive impedance control strategy is designed in combination with a Lyapunov method so as to provide support for ensuring the stability and effectiveness of impedance control and achieving compliant, safe and reliable human-machine interaction.

The invention discloses a method for designing a discrete gain scheduling controller of a multi-balance-point saturation switching system, and relates to a method for designing a gain scheduling controller in the control field. The invention further relates to a method for controlling a BTT guided missile. The method aims at solving the problem that balance points, obtained through conversion of a design signal tracking controller, of subsystems of a practical system are not all the same. According to the method, the multi-balance-point linear switching system is built with the parameter Lyapunov equation method and the ellipsoid invariant set theory according to state vectors of the selected system, and the discrete gain scheduling controller of the multi-balance-point saturation linear switching system under a switch path related to time is designed. The method is suitable for designing the discrete gain scheduling controller of the multi-balance-point saturation switching system.

The invention discloses an all-state control method for a flexible master-slave robot system under time-varying delay. The method comprises the following steps of designing a proportional damping controller based on position error and speed and an all-state feedback controller based on a backstepping technique separately for the master robot and the slave robot in a remote operating system composed of a master robot and a slave robot through a network; designing a high-dimension consistent precise differentiator to achieve precise differentiation of a virtual controller; and constructing a Lyapunov equation, establishing a system time-lag related stability criterion, and providing a controller parameter selection standard to achieve global stability of the flexible master-slave robot system under time-varying delay. For the flexible master-slave robot system, the all-state feedback controller based on the backstepping technique and the high-dimension consistent precise differentiator is adopted, so that position precise tracking of a control system in a global range is achieved, global asymptotic convergence of the system is guaranteed, and the robustness of the system is improved.

The invention discloses a control method and device for an aircraft subjected to class gap lag and output constraint, and the method comprises the steps of building a nonlinear model of an aircraft system according to the class gap lag output; constructing a controller and an adaptive law of the aircraft system according to the nonlinear model; constructing a Lyapunov equation; verifying the stability of the aircraft system according to the Lyapunov equation; and when the stability meets a preset requirement, simulating the aircraft system to obtain a simulation result. The method is high in precision and stability and can be widely applied to the technical field of aircraft control.

The invention relates to a dynamic stability performance evaluation method for a power device, which belongs to the technical field of power devices. Based on an equivalent circuit of the power device, sample data of the power device under different working conditions are obtained, a state-space equation of the power device is established according to the sample data, so that a system matrix is obtained, and the system matrix is substituted into a Lyapunov equation to solve a matrix used for judging stability; whether the matrix is positive definite or not is judged through the Sylvester criterion, so that whether the power device is stable or not under different working conditions is obtained, the instability index of the power device can be obtained by counting the number of instability points and the number of stability points, and therefore whether the power device is stable or not is judged. According to the method, the dynamic stability of the power device can be judged according to the parameters in real-time operation of the power device, the EMI risk level of the power device can be effectively evaluated, the actual application of the power device can be guided, reference is provided for design optimization of the power device, and the method has the advantages of being simple, efficient, portable and the like.