CN115586721A - Short-range accurate guidance method based on model predictive control - Google Patents
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Abstract
A short-range accurate guidance method based on model predictive control relates to a solid fuel missile. The method comprises the following steps: 1) Establishing a re-entry guidance model and constraining; 2) Adopting linearization to optimize the reentry guidance model and the constraint convex; 3) Discretizing a state equation and constraint; 4) And the model prediction control algorithm restrains the control increment to realize the prediction of the model. The model need not be decoupled in advance. The model prediction control has the characteristics of prediction model and feedback correction, so that the model prediction control has larger tolerance degree to external disturbance and self various uncertainties and strong robustness. The model prediction control system has the characteristic of rolling optimization, and meets the requirement of real-time property. The traditional guidance problem is subjected to convex optimization, so that the control law obtained through the performance function J is the optimal control rate which meets the constraint of the performance function J in the feasible domain of the performance function J, and the requirement of reliable convergence is met.
Description
Technical Field
The invention relates to a solid fuel missile, in particular to a short-range accurate guidance method based on model predictive control.
Background
The solid fuel missile has the advantages of short launching period, compact structure, small volume, good maneuverability, fast combat response and the like, and is paid attention by various countries. In actual operation, due to the variability of the situation of a battle field, a missile launching troop is often required to launch a missile on site to destroy important strategic places of an enemy as soon as possible, such as a frontier airport, a cannon place and the like. There may be special circumstances when it is desirable for my mid-range missile to strike precisely at short range within its minimum range. The control quantity of guidance is generally attack angle and roll angle, that is, a two-dimensional control quantity is used to solve the three-degree-of-freedom guidance problem. The under-actuated problem is not only large in design difficulty but also low in guidance precision. In current guidance research, the longitudinal and transverse guidance of the system is generally realized by neglecting the roll angle. However, in the actual missile launching process, the speed, the distance to be flown and the height of the missile need to meet certain constraint conditions to enable the missile to enter the hitting section from the gliding section. Therefore, in order to achieve the purpose of short-range target hitting of the medium-range missile, the missile is required to rapidly reduce the speed to achieve the requirement of entering the hitting section through the overturning of the roll angle in the gliding section. Because the value of the roll angle is relatively large, the missile cannot be guided in the longitudinal and transverse directions by a method of neglecting the roll angle. How to realize the short-range high-precision guidance of the medium-range missile without simplifying the model is a big problem troubling the engineering world. Although the linear quadratic controller (LQR) and the rolling time domain controller (RHC) based on optimal control which are started in recent years can solve the problem, the two methods have the defects of large online calculation amount and long time for solving a performance function, and cannot be applied to online guidance.
The literature (Mease K D, kremer J. Shuttle entry guiding used non-linear geometrical methods [ J ]. Journal of guiding Control and dynamics.1994, 17-1356) realizes the Guidance of the longitudinal plane through resistance acceleration, and the literature (Zhujian, liuluhua, tang nationality, and the like. The nose-down maneuver Guidance method based on feedback linearization and sliding mode Control [ J ]. University of defense science and technology, 2014,36 (02): 24-29) realizes the tracking Guidance of the longitudinal state by combining the method of sliding mode Control. The literature (Bharadwaj S, rao A V, mease K D. Entry track tracking laboratory view feedback linearization [ J ]. Journal of Guidance Control and dynamics, 1998, 726-732) presents a method of approximate feedback linearization that converts a three-dimensional trajectory into two-dimensional trajectories, the horizontal and the vertical. The above documents mostly focus on how to decouple the system, and guidance is realized by transverse and longitudinal separation, but rarely consider the situation that the missile speed needs to be reduced as soon as possible by a large inclination angle to realize short-range striking on an actual battlefield. In the literature (Dukeman G A, fogle F R.Profile-following entry guiding using linear equation [ C ]// AIAA strategy, navigation, and Control reference and inhibition. Reston: AIAA Inc.,2002, 1-10), the optimal Control rate is obtained by converting an originally nonlinear system into a linear error system by using a linear quadratic regulator Control and directly obtaining a feedback gain by solving a performance function. A method for approximating rolling time domain Control is proposed in the literature (Lu P. Adjustment out time-varying objectives: precision entry accuracy governed [ J ]. Journal of Guidance Control and dynamics.1999, 22. The above documents achieve the problem of short-range accurate guidance of medium-range missiles. But the solution computation time is long and cannot be used in an online system. The literature (water honored teacher, army, george. Reentry vehicle prediction correction guidance method research based on Gaussian pseudo-spectrum method [ J ]. Astronavigation report.2011, 32 (06): 1249-1255) uses Gaussian pseudo-spectrum method to convert the nonlinear differential equation into an algebraic equation with constraints through discretization, thereby reducing the solving time. However, the article does not consider the problem that the actual guidance is mostly non-convex, and the required optimal control law is not necessarily the minimum value of the performance function under the constraint, so that the guidance precision is not high.
Disclosure of Invention
The invention aims to solve the problems that the short-range accurate guidance of a medium-range missile in the prior art is lack of consideration, the solving is difficult to improve and the like, and provides a short-range accurate guidance method based on model predictive control, which is suitable for an under-actuated system.
The invention discloses a short-range accurate guidance method based on model predictive control, which comprises the following steps:
1) Performing first-order Taylor expansion on the state equation and the constraint;
2) Carrying out linearization and convexity treatment on the state equation and the constraint;
3) Discretizing a state equation and constraint;
4) Obtaining state quantity in a future period of time through model prediction;
5) Obtaining an optimal control quantity through rolling optimization;
in step 1), the equation of state is combined with constraints:
wherein f is s Representing equation of state, f c A constraint equation is represented.
Performing a first order taylor expansion at any point can result in:
where x denotes the state variables, u denotes the control variables and the subscript r denotes the projected quantity.
In step 2), subtracting the first-order taylor expansion expression of the state equation and the constraint obtained in step 1) from the planning quantity to obtain:
A 1 Δx+B 1 Δu≤0
wherein
Δx＝x-x r ,Δu＝u-u r
In step 3), discretizing by an euler forward method according to the state equation and constraint which are already linearized and embossed in step 2), so as to obtain:
Δx(k+1)＝(TA+E)Δx(k)+TBu(k)
A 1 Δx(k)+B 1 Δu(k)≤0
where T represents a discretized period value, E is an identity matrix, and Δ x (k) and Δ u (k) represent a state error value and a control error value at time k.
In step 4), model prediction is performed on the discretized state equation obtained in step 3), so as to obtain state variables within a period of time, wherein a specific numerical calculation method is as follows:
wherein, the first and the second end of the pipe are connected with each other,
N p ,N c respectively a prediction time domain and a control time domain,
in step 5), all the state quantities within a future period of time obtained in step 4) are subjected to rolling optimization to obtain an optimal control quantity:
s.t.f s (x(k+i),u(k+j))-f s (x(k),u(k))＝0
A 1 Δx(k)+B 1 Δu(k)≤0
the invention realizes accurate guidance under the full state and avoids the phenomenon of control accuracy reduction of the solid fuel missile caused by the violent change of the inclination angle under the short range. Meanwhile, the method uses convex optimization processing on the state equation and the constraint, and compared with the traditional optimal control, the method has the advantages of higher solving speed and higher reliable convergence.
Compared with the prior art, the invention has the advantages that:
the guidance method obtains the guidance instruction by using an optimal control method, and compared with the traditional guidance method, the guidance method does not need to decouple the model in advance. For the special condition faced by the guidance, the missile faces the change of a relatively complex sideslip angle in the flight process, the decoupling difficulty is relatively high, even if the decoupling is forced, the calculation time of the algorithm can be greatly increased, the requirement of rapidity cannot be met, and meanwhile, a certain error exists between the decoupled model and the original model under the condition, so that the guidance precision is influenced.
Compared with the traditional guidance method, the model prediction control has the characteristics of prediction model and feedback correction, and has larger tolerance degree on external disturbance and self various uncertainties and strong robustness.
Compared with the traditional guidance method, the MPC is the optimal control for continuous and repeated online operation, and the traditional guidance method generally adopts off-line characteristic point tuning to follow the planned track, so the MPC meets the requirement of real-time performance.
The invention carries out convex optimization on the traditional guidance problem, so that the control law obtained by the performance function J must meet the constrained optimal control rate in the feasible domain and meet the requirement of reliable convergence.
Drawings
FIG. 1 is a schematic block diagram of a model predictive control algorithm.
Fig. 2 is a course tracking curve.
Fig. 3 is a height tracking curve.
Fig. 4 is a lateral distance tracking curve.
Fig. 5 is a monte carlo bias three-dimensional ballistic targeting curve.
Fig. 6 is a graph of monte carlo bias velocity versus time.
Figure 7 is a monte carlo ballistic dip-time curve.
Fig. 8 is a monte carlo deviation angle of attack versus time plot.
FIG. 9 is a graph of Monte Carlo bias pressure versus time.
Fig. 10 is a control timing chart.
Detailed Description
The following examples will further illustrate the present invention with reference to the accompanying drawings.
1. Model, constraint and optimization problem description
Generally, missile modeling in the guidance problem is a three-degree-of-freedom particle motion equation which is recorded as:
the state variable is x = [ x ] 1 x 2 x 3 x 4 x 5 x 6 ] T ＝[x y z v θ ψ v ] T X, y and z are the three-axis positions of the missile in the ground coordinate system, v is the speed, theta and psi v The trajectory inclination angle and the trajectory deflection angle. Control variable quantity taking u = [ ] 1 u 2 ]＝[α γ v ]Where α is angle of attack γ v Is the sideslip angle. For convenience of the following representation, note:
then equation (1.1) may be changed to:
the constraints on the state variable x and the control variable u of the missile can be expressed as:
the initial and final state constraints of missile flight are as follows:
during missile flight, due to the influence of materials, structures and external environments, the missile needs to meet certain path constraints in the flight process, and the path constraints of the missiles in most guidance researches are as follows:
the constraint of overload N is used for total overload constraint in the missile flying process, but normal overload in the missile flying process is far greater than tangential overload, the consideration on the reliability of missile structure and thermal protection is carried out, the normal overload constraint is selected to replace the total overload constraint so as to achieve the purpose of reducing the upper limit of the overload constraint as far as possible, and the new path constraint is as follows:
wherein, the normal direction is overloaded by N y Is of the original form
Due to the roll angle gamma of the general missile during guidance v Is generally 0, so most scholars discard cos γ when considering overload constraints v An item. However, in the case of short-range precision guidance of the medium-range missile considered in the present invention, this is due to the roll angle γ v The value of (A) is relatively large, and cos gamma needs to be reserved v An item. That is, for a generic missile guidance scheme, the angle of attack α and the roll angle γ v Only the upper limit and the lower limit of the value range are separately restricted. For the present invention, the angle of attack α and the roll angle γ v Not only the upper and lower limits of the value range need to be restrained, but also the normal overload N y Of angle of attack alpha and angle of inclination gamma v An inequality constraint is also required to be satisfied, and the specific path constraint is as follows:
note book
Wherein
P、N y Respectively, heat flow rate, dynamic pressure, normal overload.
In the study of missile guidance using optimal control, the performance function uses the position error of the missile under the ground coordinate system as a performance index for realizing the rapid tracking of the track:
J＝(x 1 -x 1f ) 2 +(x 2 -x 2f ) 2 +(x 3 -x 3f ) 2 (1.8)
or in order to facilitate the control of an actual missile control system, the missile flies more stably, and the control quantity is the attack angle of the missile
And the slip angular rate
The integral of the square of (d) is taken as a performance indicator:
the invention focuses on the tactical consideration of short-range accurate hitting of the medium-range missile, the requirement on the stability of lateral control is higher compared with the general missile guidance scheme, and meanwhile, the concept of the weight coefficient is introduced to balance the smoothness of the control quantity and the minimum tracking error of the track; the final performance index function is:
wherein x is r And u r For planned values, Q, RThe diagonal weight matrix has a larger value of one element in the diagonal line compared with other elements, and the function value of the corresponding item is smaller.
Thus, the guidance problem to be studied by the present invention is described as: in the case of satisfying the constraints (1.2), the state variable and control variable constraints (1.3), the initial and final state constraints (1.4) of the flight, and the path constraints (1.7) given by the model, an appropriate control quantity is found so that the performance function (1.10) is minimum, namely:
the guidance problem described above only considers the generation of guidance laws in the off-line case. Considering that the actual missile flight has model errors and uncertain external disturbance influence in the missile flight process, if the missile still flies according to the guidance law generated under the offline condition, the guidance accuracy may deviate from the designed optimal track, and the guidance accuracy is greatly reduced. Meanwhile, since the equation (1.11) is non-convex, whether the solution is the global optimal solution or not must be considered, and the solution time is increased. The present invention addresses the above problems.
2. Guidance strategy
2.1 model and constrained convex optimization
Because the motion model and the partial constraint of the missile are not convex, if the MPC algorithm is continuously used for solving, the solving time is greatly increased, the solved optimal control quantity is probably not the global optimal solution under the constraint, and the requirements on the instantaneity, the rapidity and the reliable convergence of the missile guidance algorithm in engineering are not met. The above algebraic expression is subjected to convex transformation, linearization is a special convex method, and the above algebraic expression is subjected to linearization in order to simplify subsequent numerical calculation to meet the real-time requirement.
With equation (1.1) at an arbitrary point, the state equation of the system can be:
reference track x r Satisfies the following conditions:
subtracting the two equations (1.12) and (1.13) to obtain a linear state space equation composed of errors:
wherein:
heat flow rate
The dynamic pressure P is obtained by interpolation of height and speed, and the first-order Taylor expansion must be obtained at any point:
linearized heat flow rate
The dynamic pressure P is constrained to:
normal overload N y The magnitude of the coefficient is mainly influenced by the lift-drag coefficient of the missile, the lift-drag coefficient is mainly selected by interpolation of the height h, the velocity v and the attack angle alpha, and the linearized constraint is as follows:
the medium heat flow rate in the formulas (1.17) and (1.18)
Dynamic pressure P and normal overload N y The independent variables of (1) are state variables or control variables of the guidance model, so that the linearized constraint equations thereof must be written in the following form:
A 1 Δx+B 1 Δu≤0 (1.19)
wherein:
2.2 discretization of equations of state and constraints
The algorithm of model predictive control must be performed in a discretization mode, so equations (1.3), (1.8) and (1.13) are discretized and obtained by a forward euler method:
Δx(k+1)＝(TA+E)Δx(k)+TBu(k) (1.21)
the constraint equation can be directly discretized at the current point, which can be:
the state equation and the constraint are converted into a form satisfying the convex function definition, and a specific implementation form of the model predictive control algorithm is given below.
2.3 guidance Algorithm implementation
For a common unmanned automobile, the stable operation of the unmanned automobile can be realized by obtaining the control quantity u through the performance index, but the requirement on the control quantity is higher because the flight speed of the hypersonic missile is too high. And a new state equation is constructed to further constrain the control increment delta u, so that the missile flies more stably in the guidance process.
Note the book
Then ξ (k + 1) at the next moment is:
the model prediction schematic block diagram is shown in fig. 1. The model prediction control principle is that the state quantity x obtained by planning r (k) The difference between the actual state quantity x (k) measured by the missile-borne sensor is used as an initial quantity to predict a period of time N in the future p The error delta x of the internal state quantity is substituted into a performance function J by a series of delta x to obtain N c Increment of a series of control increments over time
However, since the external disturbance of the future time is unknown, the control quantity of the next time is not optimal, and only the current time needs to be adjusted
Inputting, calculating the state quantity error delta x at the next moment, and repeating the calculation until the solution is completed. N is a radical of p N c Respectively a prediction time domain and a control time domain. In general, the idea of model predictive control is mainly divided into three aspects, namely predictive model, rolling optimization and feedback correction.
The prediction model embodies:
i.e. by the state quantity error deltax at the present moment and the increment of the control increment
The error state quantity delta x (k + 1) at the next moment can be solved, by analogy, the error state quantities at all time points in the prediction time domain can be obtained by repeating the calculation process, and the model can be predicted.
The rolling optimization is embodied by performance indexes, which are divided into: the new state variable term added for realizing accurate tracking of the planned track, and the control increment variable term added for enabling the guided missile to fly more stably. The specific expression is as follows:
the performance index J is simplified by the equation (1.18) to the following form:
wherein the content of the first and second substances,
since the aim is to minimize the performance index J in order to obtain an optimum control rate u, E is left out T The QE item further simplifies the performance index J to obtain:
the performance index J can be approximately regarded as a quadratic programming form, and according to the inherent property of the quadratic programming, when Q and R are positive definite symmetric matrixes, the performance index J is a convex function, so that the non-convex problem of the guidance control can be changed into the optimal control problem of convex optimization.
As can be seen from the equation (1.27), the performance index J is not a global performance function, and due to the fact that Δ x changes along with the external disturbance at each moment and the performance index J changes along with the external disturbance at each moment, MPC optimization is a rolling optimization process which is continuously repeated and online, and due to the advantages, compared with other guidance methods, the MPC optimization method has stronger robustness.
A specific example is given below using a three-degree-of-freedom missile model.
1. System modeling and constraints
The three-degree-of-freedom missile model is specifically used as follows:
wherein x, y and z are three-axis positions of the missile under the ground coordinate system, v is the speed of the missile, and theta, psi v The control quantities are attack angle alpha and inclination angle gamma of the missile v . For convenience of representation, note that state variable x = [ x ] 1 x 2 x 3 x 4 x 5 x 6 ] T ＝[x y z v θ ψ v ] T Control variable u = [ u ] 1 u 2 ]＝[α γ v ]，
Then equation (1.28) may be changed to
The attack angle alpha is an implicit function of the whole state equation, the magnitude of the lift L and the resistance D is determined, and a specific calculation formula is as follows:
the CN and CA are non-dimensionalized normal force and axial force, and CL and CD are lift coefficient and drag coefficient of the missile.
The state quantity x and control quantity u constraint in the guidance process can be expressed as follows:
the missile is subjected to the following path constraints during guidance:
note the book
2. Model and constrained convex optimization
The expression after (1.29) convex optimization is as follows:
order to
The original form can be simplified into
The expression after the formula (1.32) is embossed is as follows:
order to
The original formula can be simplified to A 1 Δx+B 1 Δu≤0。
3. Discretization of equations of state and constraints
The formula (1.33) is discretized by using the forward Euler method to obtain the following formula:
Δx(k+1)＝(TA+E)Δx(k)+TBu(k) (1.35)
discretizing a constraint equation to obtain:
4. implementation of predictive algorithms
The control increment delta u is constrained by constructing a new state equation
Then it can be deduced
Then the mathematical model of the prediction model is as follows:
the proposed performance indexes are as follows:
wherein
The final solution must be the global optimal solution
By passing
The optimal control rate u can be obtained, and the accurate guidance of the missile can be realized.
5. Pulling deflection simulation
In order to achieve the maximum uncertainty met by live-action flight as far as possible, dynamic pressure and pneumatic parameters are all biased to 20% in a positive and negative mode, and under the condition, model prediction guidance and traditional proportional feedback guidance are compared and simulated, wherein the weight matrix of model prediction control is shown in the figures 2-4, and the simulation result is shown in the figure. Compared with the traditional proportional feedback guidance, the model prediction guidance has better tracking performance under the influence of external disturbance and has higher robustness under dynamic disturbance. Meanwhile, the robustness of the real verification model is predicted, under the condition of the same bias pulling condition, 1000 Monte Carlo bias simulations are carried out on the real verification model, and the target shooting graphs are shown in figures 5-9. The satisfaction degree of each constraint is given in table 1, all the constraints meet the pre-designed value through data statistics of 1000 times of deviation simulation, and the guidance scheme based on model prediction control is proved to be capable of achieving accurate guidance under strong uncertainty of an under-actuated system.
TABLE 1
| Constraint type | Unit of | Required value | Meet the situation |
| Maximum penetration height | km | ≯80 | Satisfy the requirements of |
| Full range angle of attack | ° | ≯25° | Satisfy the requirement of |
| Full-range dynamic pressure | pa | ≯300000 | Satisfy the requirement of |
| Inclination angle of landing trajectory | ° | ≮80 | Satisfy the requirement of |
| Landing speed | m/s | 300～500 | Satisfy the requirements of |
6. Real-time guidance
In order to evaluate the real-time performance of model prediction guidance, the guidance method is simulated by Matlab under the conditions that the CPU main frequency is 3.10GHz and the machine band RAM is 16GB, and the calculation time is counted. Under the condition that pneumatic parameters and dynamic pressure are all positively biased by 20%, closed-loop guidance of 163 discrete nodes is simulated, a guidance timing diagram is shown in FIG. 10, the total time is 8.62s, the time given by each guidance instruction is 0.0064s on average and is less than 1s of a guidance period, and the real-time requirement is met.
Claims (6)
1. A short-range accurate guidance method based on model predictive control is characterized by comprising the following steps:
1) Performing first-order Taylor expansion on the state equation and the constraint;
2) Carrying out linearization and convexity treatment on the state equation and the constraint;
3) Discretizing a state equation and constraint;
4) Obtaining state quantity in a future period of time through model prediction;
5) And obtaining the optimal control quantity through rolling optimization.
2. The short-range accurate guidance method based on model predictive control as claimed in claim 1, wherein in step 1), the state equation and the constraint are as follows:
wherein f is s Represents the equation of state, f c Representing a constraint equation;
performing a first order taylor expansion at any point yields:
where x represents the state variable, u represents the control variable, and the subscript r represents the projected quantity.
3. The short-range accurate guidance method based on model predictive control as claimed in claim 1, wherein in step 2), the linearization and convexity processing is performed, and the equation of state and the constrained first-order taylor expansion expression obtained in step 1) are subtracted from the planning quantity to obtain:
A 1 Δx+B 1 Δu≤0
wherein the content of the first and second substances,
Δx＝x-x r ,Δu＝u-u r
4. the short-range accurate guidance method based on model predictive control as claimed in claim 1, characterized in that in step 3), the discretization of the state equation and the constraint is carried out by an euler forward method according to the state equation and the constraint which have been linearized and embossed in step 2):
Δx(k+1)＝(TA+E)Δx(k)+TBu(k)
A 1 Δx(k)+B 1 Δu(k)≤0
wherein, T represents a discretized period value, E is a unit matrix, and Δ x (k) and Δ u (k) represent a state error value and a control quantity error value at the time of k.
5. The short-range accurate guidance method based on model predictive control as claimed in claim 1, characterized in that in step 4), the state quantity in a future period of time is obtained through model prediction, the discretized state equation obtained in step 3) is subjected to model prediction to obtain the state variable in a period of time, and the specific numerical calculation method is as follows:
wherein the content of the first and second substances,
N p ,N c respectively a prediction time domain and a control time domain,
6. the short-range accurate guidance method based on model predictive control as claimed in claim 1, wherein in step 5), the obtaining of the optimal control quantity through rolling optimization is to roll optimize all the state quantities obtained in step 4) in a future period of time to obtain the optimal control quantity:
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1999010758A1 (en) * | 1997-08-22 | 1999-03-04 | Hynomics Corporation | Multiple-agent hybrid control architecture for intelligent real-time control of distributed nonlinear processes |
| US20100228409A1 (en) * | 2008-12-16 | 2010-09-09 | California Institute Of Technology | Method and apparatus for powered descent guidance |
| CN107121929A (en) * | 2017-05-23 | 2017-09-01 | 西北工业大学 | Robust reentry guidance method based on linear covariance model PREDICTIVE CONTROL |
| EP3506041A1 (en) * | 2017-12-29 | 2019-07-03 | Deutsches Zentrum für Luft- und Raumfahrt e.V. | Method, apparatus and spacecraft for constrained atmospheric entry |
| CN111930145A (en) * | 2020-08-24 | 2020-11-13 | 中国人民解放***箭军工程大学 | Hypersonic aircraft reentry trajectory optimization method based on sequence convex programming |
| CN112114521A (en) * | 2020-07-30 | 2020-12-22 | 南京航空航天大学 | Intelligent prediction control entry guidance method for spacecraft |
| CN112558475A (en) * | 2020-11-30 | 2021-03-26 | 中国运载火箭技术研究院 | Reentry guidance method considering flight time based on convex optimization |
| CN114721261A (en) * | 2022-03-14 | 2022-07-08 | 中国运载火箭技术研究院 | Rocket sublevel attitude overturning and landing online guidance method |
-
2022
- 2022-10-08 CN CN202211220550.5A patent/CN115586721A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1999010758A1 (en) * | 1997-08-22 | 1999-03-04 | Hynomics Corporation | Multiple-agent hybrid control architecture for intelligent real-time control of distributed nonlinear processes |
| US20100228409A1 (en) * | 2008-12-16 | 2010-09-09 | California Institute Of Technology | Method and apparatus for powered descent guidance |
| CN107121929A (en) * | 2017-05-23 | 2017-09-01 | 西北工业大学 | Robust reentry guidance method based on linear covariance model PREDICTIVE CONTROL |
| EP3506041A1 (en) * | 2017-12-29 | 2019-07-03 | Deutsches Zentrum für Luft- und Raumfahrt e.V. | Method, apparatus and spacecraft for constrained atmospheric entry |
| CN112114521A (en) * | 2020-07-30 | 2020-12-22 | 南京航空航天大学 | Intelligent prediction control entry guidance method for spacecraft |
| CN111930145A (en) * | 2020-08-24 | 2020-11-13 | 中国人民解放***箭军工程大学 | Hypersonic aircraft reentry trajectory optimization method based on sequence convex programming |
| CN112558475A (en) * | 2020-11-30 | 2021-03-26 | 中国运载火箭技术研究院 | Reentry guidance method considering flight time based on convex optimization |
| CN114721261A (en) * | 2022-03-14 | 2022-07-08 | 中国运载火箭技术研究院 | Rocket sublevel attitude overturning and landing online guidance method |
Non-Patent Citations (2)
| Title |
|---|
| 冯玥;王容顺;梅映雪;孙洪飞;吴了泥;: "动力增程型高超声速飞行器的再入轨迹规划", 北京航空航天大学学报, no. 08 * |
| 姚华利;孙洪飞;: "不确定非线性***的鲁棒H_∞保性能控制", 厦门大学学报(自然科学版), no. 06, 28 November 2012 (2012-11-28) * |
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