158 results about "Second-order cone programming" patented technology

The invention provides a robust beam forming method based on a robust least-square. The method has the following steps: decomposing the weight of a beam forming device into two parts of static stage weight and self-adaptive weight by utilizing a generalized sidelobe cancellation device, transforming the standard MVDR (Minimum Variance Distortionless Response) beam forming device expression into a least-square form, acquiring data covariance matrix in the worst condition under the norm restrict of real data covariance matrix and estimated data covariance matrix error, utilizing the data covariance matrix to modify the least-square problem and to transform the problem into a robust least-square problem, further transforming the problem into a second order cone planning problem, and acquiring an optimal solution by utilizing an efficient interior point method. The method has better performances in the following aspects: (1) the output signal interference noise ratio and the power estimated accuracy when the existence conditions are mismatched, (2) the nulling depth of the interference direction in the beam pattern, (3) low mismatching sensibility to the parameter needed to be estimated in advance in the arithmetic. The method has certain the oretical meaning and utility value.

The invention discloses a day-ahead economic scheduling method for an electric-pneumatic coupled system based on mixed integer second-order cone programming. A function whose all-day energy and spareall-in cost are minimum is used as a target function, and constraint conditions of a power system and a natural gas system, and electric-pneumatic coupling and conversion relations are considered, toestablish an optimization model of electric-pneumatic coupled system day-ahead economic scheduling. On the basis of the model, through second-order cone relaxation of a steady-state airflow equation of a gas pipeline, a mixed integer second-order cone programming model of day-ahead economic scheduling of the electric-pneumatic coupled system is established, and an initial operation scheme is solved and obtained. Aimed at a problem that an initial scheduling result of a natural gas system is not accurate, a calibration model based on a steady-state power flow calculation method of a natural gassystem is established, so as to modify an initial operation scheme. The method realizes accurate solution of a non-convex nonlinear optimization problem, and provides a feasible, economical and accurate optimal operation scheme for electric-pneumatic coupled system day-ahead scheduling.

The invention particularly relates to a modeling and system planning method for a gas power grid combined multi-region comprehensive energy system. The method comprises the following steps: S1, establishing a coupling model of a power grid, a gas net, and a power grid-gas net and a multi-region comprehensive energy system model combined with constrained gas net-power grid; S2, establishing a planning model for optimal economic operation of a gas net-power grid combined multi-region comprehensive energy system, aiming at minimizing the total system operation cost; S3, converting the mixed integer nonlinear programming model in the model into a mixed integer second-order cone programming model by using a second-order cone programming method; performing nonlinear quantity linearization processing in the incremental piecewise linearization method model; and therefore, a large-scale mixed integer second-order cone programming model is established by taking the minimum total system operationcost as a target; and S4, a commercial planning problem solver is adopted to solve the large-scale mixed integer second-order cone programming model, and the optimal output and the total system operation cost of each unit in the multi-region comprehensive energy system are obtained.

The invention discloses an unmanned aerial vehicle flight time optimal real-time trajectory optimization method capable of ensuring convergence, and belongs to the field of trajectory optimization. According to the method, an unmanned aerial vehicle kinematics model is established under the consideration of gravity action, speed and acceleration factors, and a three-dimensional dimensionless motion equation is established. Constraint conditions of speed and control quantity are established according to specific requirements of obstacle avoidance flight of the unmanned aerial vehicle, and the minimum time is selected as an optimization target to establish an optimal control problem P0 of flight path planning of the unmanned aerial vehicle. Nonlinear dynamics in the problem P0 is transformedinto linear dynamics to obtain a fixed initial and end time trajectory optimization problem P1; and the P1 problem is relaxed into an approximate convex optimization problem P2 through convex relaxation, so that the robustness and robustness of real-time solving of the unmanned aerial vehicle are improved. And the problem P2 is discretized to form a second-order cone programming problem P3, and asecond-order cone programming problem P3 is solved iteratively for finite times to obtain an optimal solution, namely the optimal flight time trajectory of the unmanned aerial vehicle. The task response capability of the unmanned aerial vehicle can be further improved.

The invention provides an obstacle avoidance method for soft landing of an object outside the earth under a multi-obstacle constraint environment, and belongs to the technical field of navigation, guidance and control. The invention provides an improved optimum soft landing guidance method based on convex optimization for the problem of optimum guidance under the multi-obstacle constraint environment on the basis of the previous achievements. The method is characterized by, to begin with, establishing an optimal second-order cone programming model without obstacle constraint, and standardizing the model; then, carrying out analysis modeling on bulge obstacles on the surface of the Mars, and carrying out linear conversion to enable nonconvex constraints to be converted into convex constraints; fusing an obtained bulge obstacle mathematical model into second-order cone programming problems, and establishing a complete optimal second-order cone programming model with the obstacle constraints being taken into consideration; and finally, verifying the correctness of the algorithm through simulation analysis of three different types of obstacle constraints. The method can be applied to the study of lunar soft landing; the simulation result shows that the new algorithm realizes effective avoidance of three-dimensional space obstacles; available space for flying above and surrounding the obstacles is utilized reasonably; and fuel minimization is met simultaneously.

The invention discloses a time optimal rapid three-dimensional obstacle avoidance path planning method, particularly relates to an unmanned aerial vehicle obstacle avoidance path planning method, andbelongs to the field of unmanned aerial vehicle path planning. According to the invention, the method comprises the steps: establishing an unmanned optimal control model which takes the acceleration in each direction as a control variable and contains the flight time sum through considering the maximum acceleration and obstacle constraint conditions; loosening an original non-convex nonlinear optimization problem into a second-order cone programming problem; and finally, solving a series of second-order cone programming problems through iteration to obtain a solution of an original problem andobtain an optimal change strategy in the speed direction. In other words, the obstacle avoidance path planning with the optimal time is realized by coordinating the flight time and the flight speed direction, the online planning of the obstacle avoidance path and the related control quantity can be realized, and the task response capability of the unmanned aerial vehicle can be further improved through the optimized flight path with the optimal time.

The invention discloses a positioning method based on arrival time of unknown starting time in the non-line-of-sight environment. The method comprises steps of firstly establishing a model of a signal transmission distance between a target source and each sensor; obtaining a description of the measurement noise based on the model; according to the description of the measurement noise, using the robust weighted least squares method under the worst case to obtain the positioning problem in the environment of unknown signal transmission start time and non-line-of-sight errors, and converting the positioning problem into a non-convex positioning problem; by introducing auxiliary variables and using the second-order cone relaxation method, obtaining a second-order cone programming problem; and finally, using the interior point method to solve the second-order cone programming problem to get the final estimation value of the coordinate position of the target source in the reference coordinate system. The method has the advantages of being capable of simultaneously solving the problems of the unknown signal transmission start time and the non-line-of-sight errors so as to improve the positioning accuracy.

The invention provides a rapid trajectory optimization method of a rocket power lowering landing process, discloses a fuel optimal power lowering landing rapid trajectory planning method, and belongsto the field of rocket guidance. An implementation method includes the steps that dynamics modeling and dimensional normalization are conducted on power lowering flying, and a three-dimensional dimensionless dynamics equation is established; an independent variable of the dynamics equation is changed from the time to the height; by introducing constraints required for power lowering flying, an optimal control problem of fuel optimal power lowering landing is established; a nonlinear dynamics equation in the original optimal control problem is treated as a linear dynamics equation; a part of the nonlinearity is retained and transformed into a constraint, a non-convex constraint is convexified, and a convex optimal control problem is established; the convex optimal control problem is discretized at non-uniform discrete points by using a four-order Runge-Kutta method, and a second-order cone programming problem is established; and the second-order cone programming problem is solved iteratively until converging, and trajectory planning of power lowering landing flying can be achieved. According to the rapid trajectory optimization method, the advantage of high efficiency is achieved, and the safety and the reliability of landing of the rocket power lowering stage can be improved.

The invention discloses a non-line-of-sight stable positioning method based on signal arrival time in a wireless network. The method comprises the following steps: transmission distance measured values from the time when measuring signals are emitted from an unknown target source to the time when each sensor receives the measuring signals is measured; then re-describing is performed on a distance measurement model corresponding to each sensor; next, according to the re-described distance measurement model, an initial stable least square problem is established; afterwards, an epigraph is obtained according to the stable least square problem; then a second-order cone planning problem is obtained by use of a second-order cone relaxation technology relaxation constraint condition; and finally, the second-order cone planning problem is solved by use of an interior point method technology to obtain an estimated value of the position of the unknown target source. The method provided by the invention has the following advantages: a description of the second-order cone planning problem is obtained through relaxing the description of the stable least square problem by use of the second-order cone relaxation technology, it can be ensured that a global optimal solution is obtained without being affected by local convergence, and the positioning precision is high; and since the number of solved unknown optimization variables is small, and thus the calculation complexity is quite low.

The invention relates to a method for setting a centralized and local joint control strategy of an intelligent soft open point, which comprises the steps of according to a selected active power distribution system, inputting the structure and parameters of the active power distribution system; considering time sequence characteristics of the output and load of distributed generation according to the structure and parameters of the active power distribution system, and building a centralized and local joint control strategy setting model of the intelligent soft open point of the active power distribution network; performing linearization or second-order cone conversion on an objective function and nonlinear constraints in the model so as to enable the centralized and local joint control strategy setting model of the intelligent soft open point of the active power distribution network to be converted into a second-order cone model; and calculating the second-order cone model by adoptinga second-order cone programming algorithm to obtain related parameters of the centralized and local joint control strategy of the intelligent soft open point, voltage distribution conditions in the system and active regulation condition and reactive compensation conditions of the intelligent soft open point. According to the invention, the centralized and local joint control strategy setting modelof the intelligent soft open point of the active power distribution network is built by considering the randomness and the volatility of the distributed generation and the load.

The invention discloses a method for generating a flight track of a multi-rotor unmanned aerial vehicle based on second-order cone programming, belonging to the technical field of track planning. Themethod is realized by the following steps: establishing an optimal control problem model including performance indexes, kinematical constraints, state constraints, thrust constraints, inclined angle constraints and obstacle avoidance constraints aiming at the track generation problem of the multi-rotor unmanned aerial vehicle; and converting an optimal control problem into a second-order cone programming problem based on a discretization method and successive linearization, and carrying out iteration solving on the second-order cone programming problem, so as to obtain the flight track of a multi-rotor unmanned aerial vehicle which meets complex constraints. According to the method, the flight track of a multi-rotor unmanned aerial vehicle which meets complex constraints is established based on a second-order cone programming method according to the requirements of actual tasks; and the method has the advantages that the track generation efficiency is high, and the optimality of a track result is good.

The invention provides a mixed integer second-order cone planning method and system capable of realizing distribution network voltage reactive power coordination optimization. The method comprises the steps of obtaining photovoltaic power supply output power in an active distribution network; obtaining a voltage reactive power multi-object coordination optimization target function in the active distribution network; determining constraint conditions which need to be satisfied in safety operation of the active distribution network; establishing a voltage reactive power multi-object coordination optimization model of the active distribution network; performing cone conversion on the established voltage reactive power multi-object coordination optimization model of the active distribution network; solving a mixed integer second-order cone planning model; and obtaining an operating strategy of decision variables and performing coordination optimization. In the whole process, the optimality and accuracy of the optimization, and the safety operation of the electric power grid can be ensured based on the photovoltaic power supply output power, by means of considering an influence mechanism of the uncertainty of the photovoltaic power supply output on the voltage distribution and reactive power flow of the distribution network, and by virtue of the mixed integer second-order cone planning on the voltage reactive power coordination optimization of the distribution network based on a request result of the mixed integer second-order cone planning.

The invention discloses a method for computing the maximum access capacity of distributed power sources on the basis of expansion second-order cone programming. The method includes inputting related information of power distribution networks and setting the computational accuracy and the maximum number of iteration of the maximum deviation of cone relaxation; judging whether the numbers of iteration exceed the maximum number of iteration or not; taking the maximum access capacity of the distributed power sources in systems into account according to the related information of the power distribution networks and building models for computing the maximum access capacity of the distributed power sources; converting the models for computing the maximum access capacity of the distributed power sources into second-order cone programming models according to standard forms of second-order cone programming; carrying out computation and solution by the aid of mathematical solvers for solving second-order cone programming, outputting solution results and judging whether the maximum deviation of cone relaxation meets given accuracy requirements or not; adding cutting plane constraints on the basis of the second-order cone programming models and integrally forming expansion second-order cone programming models. The method has the advantages that complicated nonlinear programming problems can be solved, tedious iteration and large quantities of tests can be omitted, and the optimal access schemes for the distributed power sources can be quickly obtained.

The embodiment of the invention provides a multi-period reactive power optimization method and device for a power grid, and belongs to the technical field of power grid reactive power optimization. The method comprises the steps: calculating an objective function and a constraint condition of a day-ahead plan control stage according to line parameters and operation characteristic parameters, establishing a day-ahead plan control model, calculating an objective function and a constraint condition of an intra-day real-time control stage, and establishing an intra-day real-time control model; performing second-order conic convexity relaxation processing on power flow constraint equations of the day-ahead plan control model and the intra-day real-time control model, and determining a mixed integer second-order conic programming multi-period model; and solving the mixed integer second-order cone programming multi-period model, and determining an optimal control strategy. Due to the fact that the second-order cone relaxation technology is adopted for conducting convex relaxation processing on the alternating current power flow equation in the second-order cone relaxation technology, the non-convex nonlinear problem is converted into a linear equation with a convex feasible region, thereby greatly reducing the solving difficulty. Therefore, a global optimal solution can be rapidly calculated, and the optimal control strategy of the coordinated reactive power control equipment can be obtained.

The present invention provides an acoustic vector circular array mode-domain robust direction estimation method. The method includes the following steps that: the received signals P(t), Vx (t) and Vy (t) of an acoustic vector circular array acoustic pressure channel, an acoustic vector circular array vibration velocity x channel and an acoustic vector circular array vibration velocity y channel are obtained; the received signals Pe (t), Vex (t) and Vey(t) of a phase mode-domain acoustic pressure channel, a phase mode-domain vibration velocity x channel and a phase mode-domain vibration velocity y channel are obtained; Vex (t) and Vey(t) are rotated electronically, so that a combined vibration velocity Vec (t) can be obtained, a covariance matrix Repv is obtained based on Pe (t) and Vec (t), an unitary matrix Q is introduced to transform the matrix Repv, so that a real-value covariance matrix Rpv of mode-domain acoustic pressure and vibration velocity combined processing can be obtained; a steering vector a<~>r(Phi<~>) which has been subjected to mode-domain transformation and real-value processing is constrained, second-order cone programming is adopted to carry out solving, so that an optimal weight vector Omegarob can be obtained; and an output space spectrogram can be obtained based on the steering vector Omegarob which has been subjected to mode-domain transformation and unitary matrix real-value transformation, and a target direction can be obtained based on a spectrum peak position. With the method of the invention adopted, the problems of performance degradation and high signal-to-noise ratio processing threshold of a minimum variance distortionless response algorithm under a condition that related sound sources are difficult to distinguish and mismatching occurs can be solved. The method has the advantages of high resolution, high robustness, small amount of calculation, strong background noise suppression ability and the like.

The invention provides a soft open point (SOP)-based active power distribution network feeder load balancing method. The method comprises: inputting related information of a power distribution network, and setting cone relaxation maximum deviation computational accuracy and maximum iterative times; judging whether the iterative times exceeds the maximum iterative times; building an active power distribution network feeder load balancing model according to the related information of the power distribution network; converting the active power distribution network feeder load balancing model into a second-order cone programming (SOCP) model according to an SOCP standard form; computing and solving by utilizing a mathematical solver for solving SOCP, judging whether the cone relaxation maximum deviation meets given accuracy requirements, and outputting solving results; and adding cutting plane constraints on the basis of the obtained SOCP model, and then integrally forming a strengthened SOCP (S-SOCP) model. According to the SOP-based active power distribution network feeder load balancing method, a complex nonlinear programming problem is solved, complicated iterations and a lot of tests are avoided, computation speed is relatively largely increased, and an optimal active power distribution network feeder load balancing scheme can be quickly obtained.

The invention discloses a second-order cone programming method for power-off grid load recovery with consideration of recovery quantity uncertainty. On the basis of improvement of a load recovery robustness optimization model with consideration of uncertainty, a robust model with a mixed integer second-order cone mode is established and solving is carried out to obtain a load recovery robust plan. The method comprises: 1, establishing a power-off grid load recovery certainty model; 2, on the basis of an information gap decision-making theory, establishing a robustness optimization model with consideration of load recovery uncertainty; 3, with a second-order cone relaxation method, carrying out convex optimization relaxation processing on a non-linear power flow equation in the optimization model; 4, carrying out linear processing on the rest of nonlinear constraints; and 5, on the basis of a direct-current power flow model, invoking CPLEX at two stages to solve the optimization model, thereby obtaining a load recovery plane. With the method disclosed by the invention, a load recovery plan can be obtained rapidly and accurately; load fluctuation within a certain range can be carried; and security of the grid recovery process can be guaranteed. The method has the certain theoretical value and engineering value.

The invention discloses a robustness weighted least square positioning method in a mixed environment based on arrival time, and the method comprises the steps: building a reference coordinate system in a wireless sensor network; describing a signal transmission distance between a target source and each sensor in a mode of a sight distance model and a mode of non-sight-distance model; obtaining a positioning problem in the mixed environment based on the arrival time according to the sight distance model and the non-sight-distance model through employing the robustness weighted least square method under the worst condition, and obtaining a non-convex positioning problem; introducing an auxiliary variable to the non-convex positioning problem, employing a second-order cone relaxing method, and obtaining a second-order cone planning problem; finally solving the second-order cone planning problem through an interior point method, and obtaining a final estimation value of the coordinate position of the target source in the reference coordinate system. The method is advantageous in that the method gives full consideration to the two states: sight distance and non-sight-distance, makes the most of path state information, achieves the targeted processing of the non-sight-distance error, and is high in positioning precision.

The invention relates to a convex-difference-planning-based calculation method of the maximum access capability of a distributed power supply in a distribution network. The method comprises: distribution network structure and parameter information is inputted, and a calculation accuracy value, an initial penalty coefficient and an iteration number of times are set; according to the distribution network structure and parameter information, a distributed power supply maximum access capability calculation model is established by considering the access capability maximization of the distributed power supply in the system; for nonlinear constraints in the maximum access capacity calculation model, conversion into a second-order cone programming model is carried out by linearization and second-order cone relaxation, and the model is solved to obtain an initial solution to the distributed power supply maximum access capability calculation model; a convex difference inequation is introduced into the second-order cone programming model and linearization is carried out, an objective function is updated; a penalty item is added into the objective function, and conversion to a convex difference programming model is carried out; the convex difference programming model is solved and whether a convergence condition is satisfied is determined; an iterative penalty factor is updated and solution calculation is carried out again; and a result is outputted. According to the invention, the calculation speed is increased substantially; and the maximum access plan of the distributed power supplyis obtained quickly.

The invention discloses an arrival time-based cooperative localization method applied to a wireless sensor network, which uses a second-order cone relaxation technique and a positive semi-definite relaxation technique to relax a minimization problem obtained by constructing a maximum likelihood function to obtain a description of the problem mixing positive half-definite and second-order cone programming; thus, a global optimal solution can be ensured to obtain without the influence of local convergence, and the localization accuracy is high; the influence of measurement noise error can be effectively suppressed; meanwhile, the prior art can be used for solving an estimate value of the coordinates of an unknown target source, thereby reducing the distribution density of the anchor nodes and reducing the cost.

The invention relates to a super-directivity beam-forming method based on circular array robust sidelobe control. The super-directivity beam-forming method comprises the steps that firstly, an error sensitivity function which measures robustness is expressed as the sum of all orders of eigen-beam error sensitivity functions; secondly, according to the performance of all orders of actual eigen-beams, the maximum exponent number is estimated; finally, the maximum error sensitivity function value is obtained, and a white noise gain constraint value is found. Some symmetrical properties of a circular array with an even number of array elements are utilized, the super-directivity beam-forming method based on robust sidelobe control is expressed as a simple optimization problem, and a final result can be extremely easily figured out in combination with the second-order cone planning algorithm. According to the super-directivity beam-forming method, the defects that a robustness parameter cannot easily be determined, and sidelobe level cannot be effectively controlled are overcome, all orders of eigen-beam error sensitivity functions become larger along with the rise of the exponent number, and the maximum error sensitivity function is approximately equal to the error sensitivity function of the highest-order eigen-beam; besides, the constructed optimization problem can obtain the optimum compromise among the multiple indicators.

The invention provides a double-layer and second-order cone programming method and a system for the new energy digestion capability of a power distribution network. According to the real-time maximum output of a distributed power supply, the maximum output power of the distributed power supply, capable of being digested by the power distribution network within a scheduling period, is calculated. According to the active power resource and the reactive power resource of the power distribution network, participating in the scheduling process, the influence mechanism of the output uncertainty of the distributed power supply on the voltage distribution and the reactive power flow of the power distribution network is reflected. Therefore, the active power resource and the reactive power resource of the power distribution network are coordinated, so that the distributed power supply is fully digested. Meanwhile, based on the upper-layer planning target function and the lower-layer planning target function of the power distribution network, a constraint condition for the safe operation of the power distribution network to meet is obtained. In this way, upper-layer planning decision-making variables and lower-layer planning decision-making variables for the power distribution network are solved. That means, the digestion capability of the power distribution network for the distributed power supply is calculated and obtained. Meanwhile, the solving result of lower-layer planning decision-making variables is fed back to the upper-layer planning decision-making variables of the power distribution network. Finally, the distributed power digestion capability of the power distribution network is accurately determined.

The invention relates to an active power distribution network reactive power control method with limitation to the number of operating times of a capacitor taken into account, and belongs to the technical field of operation and control of an electric power system. The method includes the steps that a three-phase branch trend equation of an active power distribution network is provided, a reactive power control objective function is established, and various actual restraints are comprehensively taken into account; a second order cone slack technology is utilized to handle a reactive power control problem; eventually a second order cone programming algorithm is utilized to conduct calculation to acquire reactive power control values and operating moments of a disperse reactive compensation device, the capacitor, a continuous reactive compensation device and a distributed power supply, and therefore active power distribution network reactive power control with the limitation to the number of the operating times of the capacitor taken into account is achieved. The method can be used for radial and annular active power distribution network reactive power control with the limitation to the number of the operating times of the capacitor taken into account, and control accuracy is high. The second order cone slack technology and the second order cone programming algorithm are adopted, and therefore both optimality and solve efficiency of active power distribution network reactive power control are greatly improved.

The invention belongs to the technical field of signal interference resistance, and particularly relates to a method for forming a steady broadband beam based on frequency response invariability. The method comprises the steps that an overall broadband signal frequency band is divided into L sub bands; a reference frequency is selected, an optimal weight vector with a nulling control feature is designed at the reference frequency point, and a reference beam pattern is obtained; a response variable is introduced and used for providing an invariable frequency response, and therefore all frequency points of a signal on the frequency band can have continuous and consistent array responses; a second-order cone programming method is used for designing low-side-lobe optimal weight vectors of other sub bands, and therefore beam patterns of other sub bands and the reference beam pattern can be the same in main lobe width and nulling control feature; the optimal weight vectors which are finally obtained through design are used for forming the steady broadband beam based on frequency response invariability. According to the method for forming the steady broadband beam based on frequency response invariability, the response variable is introduced, so that the array degree of freedom is higher, the calculation quantity is smaller, and the manifested anti-interference performance is better.