CN111061294B - Trajectory optimization self-adaptive optimal control system for nonstationary hypersonic aircraft - Google Patents
Trajectory optimization self-adaptive optimal control system for nonstationary hypersonic aircraft Download PDFInfo
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Abstract
The invention discloses a non-stationary hypersonic aircraft trajectory optimization self-adaptive optimal control system, which is used for controlling an aircraft trajectory. The aircraft attitude and heading angle sensor is composed of an aircraft altitude sensor, an aircraft speed sensor, an aircraft flight channel inclination angle sensor, an aircraft horizontal flight distance sensor, an aircraft micro control unit MCU and an aircraft attack angle controller. After the hypersonic aircraft reaches the reentry airspace, the aircraft micro-control unit MCU automatically executes an internal self-adaptive optimization algorithm to obtain a track optimization control strategy which enables the hypersonic aircraft to have the farthest range, and the aircraft micro-control unit MCU converts the obtained control strategy into a control command and sends the control command to the aircraft attack angle controller for execution. The method can quickly obtain a track optimization control strategy according to different states of the hypersonic aerocraft such as altitude, speed, flight channel inclination angle and flight horizontal distance, so that the hypersonic aerocraft can obtain a longer range.
Description
Technical Field
The invention relates to the field of trajectory optimization of reentry sections of hypersonic aircrafts, in particular to a non-stationary hypersonic aircraft trajectory optimization self-adaptive optimal control system. After the hypersonic aircraft reaches the reentry section, a trajectory optimization control strategy of the hypersonic aircraft can be given and converted into an aircraft attack angle control command, and the hypersonic aircraft can obtain a longer horizontal flight distance under the condition of meeting the safety requirement.
Background
The hypersonic aircraft is a novel aircraft for realizing remote rapid and accurate strike and global rapid arrival, has very important strategic position in future military, politics and economy, becomes an extremely important development direction in the world aerospace field, and is one of the competitive fields of major aerospace countries in the world. The research and development of the hypersonic flight vehicle have very important significance in the aspects of developing space and national safety.
In the research of hypersonic flight vehicles, trajectory optimization is an important content of modern flight vehicle design and control, is not only beneficial to improving the flight quality of the flight vehicle to meet the requirements of established missions, but also is a necessary condition for completing important guarantee of flight missions and realizing maneuvering flight, has been paid attention to by military and strong countries at home and abroad in recent years, and is a hotspot and difficulty of current research at home and abroad.
The hypersonic flight vehicle enters the atmosphere from the outer edge, the change range of the altitude and the speed is large, the hypersonic flight vehicle faces various severe reentry environments, the reentry section track optimization technology is the key for ensuring the hypersonic flight vehicle to complete the flight task smoothly, and the hypersonic flight vehicle has important practical value for improving the hitting range and the landing precision. Therefore, it is very important to research an efficient hypersonic aircraft reentry section trajectory optimization method.
Disclosure of Invention
In order to enable the hypersonic aerocraft to obtain a longer range and improve the hitting range of the hypersonic aerocraft, the invention aims to provide a non-stable hypersonic aerocraft track optimization self-adaptive optimal control system. The controller uses MCU as the carrier for realizing the optimal control method. The hypersonic aircraft reentry section trajectory optimization problem flight process can be described by a mathematical model as follows:
where t represents time, t0Represents the starting time, t, of the flight process of the trajectory optimization problem of the reentry section of the hypersonic aircraftfRepresenting the flight process end time of the trajectory optimization problem of the reentry section of the hypersonic aircraft, and tfNot fixing;
is called state variable and sequentially represents physical parameters of an aircraft such as altitude, aircraft speed, aircraft flight channel inclination angle, aircraft horizontal flight distance and the like, nxIs the dimension of the state variable, where nx＝4。x0Is the initial value of the state vector and,
is its first derivative; u (t) represents the angle of attack control of the hypersonic flight vehicle, and is the control variable of the problem, ul、uuRespectively as its lower limit and upper limit;
the method is characterized in that a differential equation set is established according to energy conservation and a mechanical principle; g [ u (t), x (t), t)]Is an inequality path constraint condition which must be met in the reentry section process of the hypersonic aircraft.
For the reentry segment process of the hypersonic flight vehicle, the mathematical model for maximizing the flight distance can be expressed as:
wherein J [ u (t) ] represents the objective function J determined by the angle of attack manipulated variable u (t). This problem is essentially an optimal control problem.
The technical scheme adopted by the invention for solving the technical problems is as follows: a non-stationary hypersonic aircraft track optimization self-adaptive optimal control system is composed of an aircraft altitude sensor, an aircraft speed sensor, an aircraft flight channel inclination angle sensor, an aircraft horizontal flight distance sensor, an aircraft micro control unit MCU and an aircraft attack angle controller. The aircraft altitude sensor, the aircraft speed sensor, the aircraft flight channel inclination angle sensor, the aircraft horizontal flight distance sensor and the aircraft attack angle controller are all connected with an aircraft micro control unit MCU through a data bus, and the aircraft micro control unit MCU is formed by sequentially connecting an information acquisition module, an initialization module, an Ordinary Differential Equations (ODE) discretization module, a nonlinear Programming problem (NLP) solving module, an adaptive module and a control instruction output module;
the operation process of the non-stationary hypersonic aircraft trajectory optimization self-adaptive optimal control system is as follows:
step 1: inputting a pneumatic coefficient model, an aircraft performance constraint condition and a specified optimization target corresponding to the aircraft into an aircraft Micro Control Unit (MCU);
step 2: after the hypersonic aircraft reaches the reentry section, starting an aircraft altitude sensor, an aircraft speed sensor, an aircraft flight channel inclination angle sensor and an aircraft horizontal flight distance sensor to obtain the current state information of the hypersonic aircraft on altitude, speed, flight channel inclination angle and flight horizontal distance;
and step 3: the aircraft micro control unit MCU executes an internal state variable parameterization optimization algorithm according to the set altitude, speed and flight channel inclination angle requirements to obtain a track optimization control strategy for enabling the hypersonic aircraft to have the longest horizontal flight distance;
the method specifically comprises the following substeps:
step 3.1: the information acquisition module acquires the current state information of the hypersonic aircraft, such as the altitude, the speed, the flight channel inclination angle and the flight horizontal distance, obtained in the step 2;
step 3.2: an initialization module sets the discrete segment number of the time of the track optimization process and the initial guess value u of the attack angle control quantity(0)(t), setting an optimization precision requirement tol, and setting the iteration number k to zero;
step 3.3: the discretization module of the ordinary differential equation set is used for forming the ordinary differential equation set on a time axis t0,tf]All the components are dispersed;
step 3.4: the nonlinear programming problem solving module carries out optimization direction solving, optimization step length solving and optimization correction in sequence to obtain a control vector u(k)(t) and a state vector x(k)(t) then controlling the obtained gainQuantity u(k)(t) and a state vector x(k)(t) judging the convergence of NLP, and if the convergence condition is satisfied, controlling the attack angle u(k)(t) processing by a self-adaptive module and then using the processed signal as a track optimization control instruction; otherwise, the adaptive module processes the data.
And 4, step 4: and the aircraft micro control unit MCU converts the obtained track optimization control instruction into a control instruction and sends the control instruction to the aircraft attack angle controller for execution.
Said step 3.3 comprises the following sub-steps:
step 3.3.1: discretizing the attack angle control quantity u (t) and the state track x (t) by adopting the following interpolation formula:
where N is for the time interval t0,tf]Performing a discrete number of stages, MiAlpha (t) and beta (t) satisfy the condition that the number of configuration points on the ith segment
And
discretization coefficient ui,jAnd si,jU (t) and x (t), respectively, at configuration point ti,jValue of s'i,jIs composed of
At the configuration point ti,jS 'is determined by the specific equation of state through u (t) and x (t)'i,j＝f(ui,j,si,j,ti,j) Where f is the equation of state.
Step 3.3.2: increasing non-uniformly distributed detection points at non-configured points
The number of detection points on the ith segment. Determining the values of the control variables and the state variables at the test points by step 3.3.1, obtaining a first representation of the derivative values at the test points by means of the state equation
On the other hand, a second expression of the derivative value at the detection point is obtained by the derivative expression of the expression (2):
will be provided with
As a new constraint to make state variable discretization conform to the state equation at the detection point to get higher solution accuracy.
Said step 3.4 comprises the following sub-steps:
step 3.4.1: controlling the angle of attack u(k-1)(t) as a point in vector space, denoted P1，P1The corresponding objective function value is J [ u ](k-1)(t)]；
Step 3.4.2: from point P1Starting from the selected NLP algorithm, a optimizing direction d in the vector space is constructed(k-1)And step length lambda(k-1)；
Step 3.4.3: passing formula u(k)(t)＝u(k-1)(t)+λ(k-1)d(k-1)Constructing a correspondence u in vector space(k)Another point P of2So that P is2Corresponding objective function value J [ u ](k)(t)]Ratio J [ u ](k-1)(t)]More preferably.
Step 3.4.4: using optimization correction u(k)(t) obtaining corrected dots
Is marked as a point P3Simultaneously order
So that P is3Corresponding objective function value J [ u ](k)(t)]Ratio J [ u ](k-1)(t)]The better is;
step 3.4.5: if the objective function value J [ u ] of this iteration(k)(t)]The value of objective function J [ u ] of last iteration(k-1)(t)]If the difference between the absolute values of the two-dimensional data is less than the accuracy tol, the convergence is judged to be satisfied, and the control instruction u obtained by the iteration is processed(k)(t) outputting to a control instruction output module; if the convergence is not satisfied, the iteration number k is increased by 1, and u is added(k)(t) is set to the initial value and execution continues at step 3.4.5.
In step 3.4, the adaptive module processing includes the following sub-steps:
step A: setting initial conditions u0Initial time node distribution T0Setting the tolerance e of the objective functionJMaximum number of iterations lmaxElimination criterion constant εminRefinement criterion constant εmax. Set l ═ 0.
And B: in time segments TlSolving by adopting an NLP solving module to obtain the currently optimized control variable ulAnd corresponding time node distribution TlL is 0 or satisfies the termination condition
Go to step C, otherwise go to step D.
And C: obtaining IMF function by EMD decomposition
Distribution T for time segmentslIf, if
Then the corresponding time node is eliminated, the number of time nodes is reduced, if so
The corresponding time nodes are refined, the time node number is increased, and the new time node distribution T is obtainedl+1Obtaining a control variable set u corresponding to the new time node by interpolationl+1. Setting l ═ l +1, if l < lmaxReturning to the step B, and adding Tl+1And ul+1And D, taking the initial value as an initial value of the NLP solving module in the (l + 1) th iteration, and otherwise, turning to the step D.
Step D: stopping the adaptation and outputting u*＝ulAnd J*＝J[ul]。
The invention has the following beneficial effects: the non-stationary hypersonic aircraft trajectory optimization self-adaptive optimal control system controls the hypersonic aircraft, overcomes the defects that the conventional hypersonic aircraft trajectory optimization controller cannot meet the constraint in the whole course under non-Gaussian and non-stationary conditions when facing various severe flight environments, has low solving precision and low solving efficiency and the like, obtains a trajectory optimization attack angle control instruction for enabling the hypersonic aircraft to have longer horizontal flight distance, improves the attack range of the hypersonic aircraft, improves the autonomous guidance capability of the aircraft, improves the guidance precision of the aircraft, and enhances the robustness of a guidance system.
Drawings
FIG. 1 is a schematic structural diagram of a non-stationary hypersonic vehicle trajectory optimization adaptive optimal control system;
FIG. 2 is a structural diagram of an internal module of an MCU of a non-stationary hypersonic flight vehicle trajectory optimization self-adaptive optimal control system.
Detailed Description
Example 1
The structure of the non-stationary hypersonic flight vehicle trajectory optimization adaptive optimal control system is shown in figure 1. And when the hypersonic aircraft arrives at the reentry section airspace, the hypersonic aircraft altitude sensor 13, the aircraft speed sensor 14, the aircraft flight channel inclination angle sensor 15, the aircraft horizontal flight distance sensor 16 and the aircraft micro-control unit MCU 12 are all started. The information acquisition module immediately acquires the initial altitude of the aircraft when the aircraft enters the reentry sectionThe height, the speed, the flight channel inclination angle and the horizontal flight distance are set at the current initial time t00s, the altitude of the altitude sensor transmitted into the MCU is h080000 m, the speed of the speed sensor transmitted into the MCU is v06400m/s, the flight channel inclination angle of the flight channel inclination angle sensor transmitted into the MCU is gamma0The horizontal flying distance of the sensor into the MCU is r00 m; end time tfThe hypersonic flight vehicle needs to meet the condition that the altitude is set as hf24000m, speed set vf760m/s, the flight path inclination angle is set to gammaf-0.08 rad; combining a three-dimensional space motion equation, a pneumatic coefficient model, an aircraft performance constraint condition and a specified optimization target of the aircraft to obtain a mathematical model of the problem as follows:
max J[u(t)]＝x4(tf)
s.t.
CL＝-0.15+3.44u(t)
CD＝0.29-1.51u(t)+5.87u(t)2
x1(0)＝80×103,x1(tf)＝24×103
x2(0)＝6.4×103,x2(tf)＝760
x3(0)＝-0.052,x3(tf)＝-0.08
x4(0)＝0
wherein L represents lift, D represents drag, CLDenotes the coefficient of lift, CDRepresenting the drag coefficient. For convenience of description, F (x (t), u (t), and t) are used to represent a mathematical model of a differential equation set established by a hypersonic aircraft reentry section three-dimensional space motion equation, that is:
g [ u (t), x (t), t ] is adopted to represent constraint conditions of the reentry section process of the hypersonic aerocraft, and the constraint conditions are as follows:
in addition, J [ u (t) ] represents the objective function of the hypersonic flight vehicle trajectory optimization, namely the horizontal flight distance of the flight vehicle at the optimization ending moment.
The information acquisition module 21 is configured to acquire a current altitude and a current speed of the aircraft, a current channel inclination angle and a current flight level distance of the aircraft, an altitude and a speed setting of the aircraft, information of the channel inclination angle of the aircraft, a pneumatic coefficient model and a performance constraint condition of the aircraft, and a specified optimization target parameter.
The non-stationary hypersonic aircraft trajectory optimization self-adaptive optimization method for automatically generating an attack angle control instruction by an aircraft Micro Control Unit (MCU) is shown in FIG. 2, and the operation steps are as follows:
step 1): after the hypersonic aircraft arrives at the reentry section, the aircraft altitude sensor, the aircraft speed sensor, the aircraft flight channel inclination angle sensor and the aircraft horizontal flight distance sensor are started, and the information acquisition module 21 acquires the initial time t0Altitude h of hypersonic aerocraft at 0s080000 m, velocity v06400m/s, the flight path inclination angle is gamma0The horizontal flying distance of the sensor is set as r00 m; end time tfThe altitude requirement of the hypersonic flight vehicle is set as hf24000m, speed requirement set to vf760m/s, the flight path inclination angle requirement is set to γf＝-0.08rad；
Step 2): the initialization module 22 starts to operate, sets the discrete segment number of the time of the track optimization process and the initial guess value u of the attack angle control quantity(0)(t), setting an optimization precision requirement tol, and setting the iteration number k to zero;
step 3): the ordinary differential equation set is discretized on the time axis t by the ordinary differential equation set discretization module 230,tf]All the components are dispersed;
step 4): the NLP problem solving module 24 obtains the required attack angle control strategy and corresponding state trajectory, and this process includes multiple internal iterations, each iteration requires solving the optimization direction and optimization step length, and performing optimization correction. Control quantity u of attack angle obtained for a certain iteration(k)(t) if it corresponds to the objective function value J [ u ](k)(t)]The value of objective function J [ u ] of previous iteration(k-1)(t)]If the difference is smaller than the accuracy requirement tol, judging whether the convergence is met, and if so, outputting the command to the control command output module 26; otherwise, carrying out the next iteration;
step 5): for the obtained control vector u(k)(t) and a state vector x(k)(t) analyzing, satisfying convergence condition, and controlling the attack angle u(k)(t) output as an instruction; otherwise the next adaptation module processing 25 is performed.
The operation of the ordinary differential equation set discretization module 23 is as follows:
step 1): discretizing the attack angle control quantity u (t) and the state track x (t) by adopting the following interpolation formula:
where N is for the time interval t0,tf]Performing a discrete number of stages, MiAlpha (t) and beta (t) satisfy the condition that the number of configuration points on the ith segment
And
discretization coefficient ui,jAnd si,jU (t) and x (t), respectively, at configuration point ti,jValue of s'i,jIs composed of
At the configuration point ti,jS 'is determined by the specific equation of state through u (t) and x (t)'i,j＝f(ui,j,si,j,ti,j) Where f is the equation of state.
Step 2): increasing non-uniformly distributed detection points at non-configured points
The number of detection points on the ith segment.Determining the control variable value and the state variable value at the detection point by the step 1, and obtaining a first expression of the derivative value at the detection point by the state equation
On the other hand, the second expression of the derivative value at the detection point is obtained by the derivative expression of (2)
Will be provided with
As a new constraint to make state variable discretization conform to the state equation at the detection point to get higher solution accuracy.
The NLP solving module 24 includes four sub-modules of optimizing direction solving, optimizing step solving, optimizing correction and NLP convergence judgment, and the operation process is as follows:
step 1): controlling the angle of attack u(k-1)(t) as a point in vector space, denoted P1，P1The corresponding objective function value is J [ u ](k-1)(t)]；
Step 2): from point P1Starting from the selected NLP algorithm, a optimizing direction d in the vector space is constructed(k -1)And step length lambda(k-1)；
Step 3): passing formula u(k)(t)＝u(k-1)(t)+λ(k-1)d(k-1)Constructing a correspondence u in vector space(k)Another point P of2So that P is2Corresponding objective function value J [ u ](k)(t)]Ratio J [ u ](k-1)(t)]More preferably.
Step 4): using optimization correction u(k)(t) obtaining corrected dots
Is marked as a point P3Simultaneously order
So that P is3Corresponding objective function value J [ u ](k)(t)]Ratio J [ u ](k-1)(t)]The better is;
step 5): if the objective function value J [ u ] of this iteration(k)(t)]The value of objective function J [ u ] of last iteration(k -1)(t)]If the difference between the absolute values of the two is less than the accuracy tol, the convergence is judged to be satisfied, and the control strategy u obtained by the iteration is used(k)(t) output to the control command output module 26; if the convergence is not satisfied, the iteration number k is increased by 1, and u is added(k)(t) set to the initial value, proceed to step 2).
The operation of the adaptation module 25 is as follows:
step 1): setting initial conditions u0Initial time node distribution T0Setting the tolerance e of the objective functionJMaximum number of iterations lmaxElimination criterion constant εminRefinement criterion constant εmax. Set l ═ 0.
Step 2): in time segments TlSolving by adopting an NLP solving module to obtain the currently optimized control variable ulAnd corresponding time node distribution TlL is 0 or satisfies the termination condition
Go to step 3, otherwise go to step 4.
Step 3): obtaining IMF function by EMD decomposition
Distribution T for time segmentslIf, if
Then the corresponding time node is eliminated, the number of time nodes is reduced, if so
The corresponding time sectionPoints are refined, the time node number is increased, and new time node distribution T is obtainedl+1Obtaining a control variable set u corresponding to the new time node by interpolationl+1. Setting l ═ l +1, if l < lmaxReturning to the step 2, adding Tl+1And ul+1And (4) serving as an initial value of the NLP solving module in the (l + 1) th iteration, and otherwise, turning to the step 4.
Step 4): stopping the adaptation and outputting u*＝ulAnd J*＝J[ul]。
And finally, the obtained optimized track is output to a control instruction output module as an instruction by the MCU of the aircraft, the optimized track is converted into a control instruction and is sent to the attack angle controller, and the track optimization is executed.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and is not intended to limit the practice of the invention to these embodiments. For those skilled in the art to which the invention pertains, several simple deductions or substitutions may be made without departing from the inventive concept, which should be construed as falling within the scope of the present invention.
Claims (1)
1. A non-stationary hypersonic aircraft track optimization self-adaptive optimal control system is characterized by comprising an aircraft altitude sensor, an aircraft speed sensor, an aircraft flight channel inclination angle sensor, an aircraft horizontal flight distance sensor, an aircraft micro control unit MCU and an aircraft attack angle controller; the aircraft altitude sensor, the aircraft speed sensor, the aircraft flight channel inclination angle sensor, the aircraft horizontal flight distance sensor and the aircraft attack angle controller are all connected with an aircraft micro control unit MCU through a data bus, and the aircraft micro control unit MCU is formed by sequentially connecting an information acquisition module, an initialization module, a constant differential equation set discretization module, a nonlinear programming problem solving module, an adaptive module and a control instruction output module;
the operation process of the non-stationary hypersonic aircraft trajectory optimization self-adaptive optimal control system is as follows:
step 1: inputting a pneumatic coefficient model, an aircraft performance constraint condition and a specified optimization target corresponding to the aircraft into an aircraft Micro Control Unit (MCU);
step 2: after the hypersonic aircraft reaches the reentry section, starting an aircraft altitude sensor, an aircraft speed sensor, an aircraft flight channel inclination angle sensor and an aircraft horizontal flight distance sensor to obtain the current state information of the hypersonic aircraft on altitude, speed, flight channel inclination angle and flight horizontal distance;
and step 3: the aircraft micro control unit MCU executes an internal state variable parameterization optimization algorithm according to the set altitude, speed and flight channel inclination angle requirements to obtain a track optimization control strategy for enabling the hypersonic aircraft to have the longest horizontal flight distance;
the method specifically comprises the following substeps:
step 3.1: the information acquisition module acquires the current state information of the hypersonic aircraft, such as the altitude, the speed, the flight channel inclination angle and the flight horizontal distance, obtained in the step 2;
step 3.2: an initialization module sets the discrete segment number of the time of the track optimization process and the initial guess value u of the attack angle control vector(0)(t), setting an optimization precision requirement tol, and setting the iteration number k to zero;
step 3.3: the discretization module of the ordinary differential equation set is used for forming the ordinary differential equation set on a time axis t0,tf]All the components are dispersed;
step 3.4: the nonlinear programming problem solving module carries out optimization direction solving, optimization step length solving and optimization correction in sequence to obtain an attack angle control vector u(k)(t) and a state variable x(k)(t) then obtaining angle of attack control vector u(k)(t) and a state variable x(k)(t) performing non-linear programming convergence judgment, and if the convergence condition is met, controlling the angle of attack to the vector u(k)(t) processing by a self-adaptive module and then using the processed signal as a track optimization control instruction; otherwise, processing by the self-adaptive module;
and 4, step 4: the aircraft micro control unit MCU converts the obtained track optimization control instruction into a control instruction and sends the control instruction to the aircraft attack angle controller for execution;
said step 3.3 comprises the following sub-steps:
step 3.3.1: control the angle of attack by a vector u(k)(t) discretizing the state variable x (t) by adopting the following interpolation formula:
where N is for the time interval t0,tf]Performing a discrete number of stages, MiAlpha (t) and beta (t) satisfy the condition that the number of configuration points on the ith segment
And
discretization coefficient ui,jAnd si,jU (t) and x (t), respectively, at configuration point ti,jValue of s'i,jIs composed of
At the configuration point ti,jS 'is determined by the specific equation of state through u (t) and x (t)'i,j＝f(ui,j,si,j,ti,j) Wherein f is an equation of state;
step 3.3.2: increasing non-uniformly distributed detection points at non-configured points
The number of detection points on the ith section; determining the values of the control variables and the state variables at the test points by step 3.3.1, obtaining a first representation of the derivative values at the test points by means of the state equation
On the other hand, a second expression of the derivative value at the detection point is obtained by the derivative expression of the expression (2):
will be provided with
Serving as a new constraint to enable the state variable discretization to accord with a state equation at the detection point so as to obtain higher solving precision;
said step 3.4 comprises the following sub-steps:
step 3.4.1: control the angle of attack by a vector u(k-1)(t) as a point in vector space, denoted P1，P1The corresponding objective function value is J [ u ](k-1)(t)]；
Step 3.4.2: from point P1Starting from the non-linear programming algorithm, an optimization direction d in the vector space is constructed(k-1)And step length lambda(k-1)；
Step 3.4.3: passing formula u(k)(t)＝u(k-1)(t)+λ(k-1)d(k-1)Constructing a correspondence u in vector space(k)Another point P of2So that P is2Corresponding objective function value J [ u ](k)(t)]Ratio J [ u ](k-1)(t)]The better is;
step 3.4.4: using optimization correction u(k)(t) obtaining corrected dots
Is marked as a point P3Simultaneously order
So that P is3Corresponding objective function value J [ u ](k)(t)]Ratio J [ u ](k-1)(t)]The better is;
step 3.4.5: if the objective function value J [ u ] of this iteration(k)(t)]The value of objective function J [ u ] of last iteration(k-1)(t)]If the difference between the absolute values of the two-dimensional data is less than the accuracy tol, the convergence is judged to be satisfied, and the control instruction u obtained by the iteration is processed(k)(t) outputting to a control instruction output module; if the convergence is not satisfied, the iteration number k is increased by 1, and u is added(k)(t) setting to an initial value, and continuing to execute the step 3.4.5;
in step 3.4, the adaptive module processing includes the following sub-steps:
step A: setting initial conditions u0Initial time node distribution T0Setting the tolerance e of the objective functionJMaximum number of iterations lmaxElimination criterion constant εminRefinement criterion constant εmax(ii) a Setting l as 0;
and B: in time segments TlSolving by adopting a nonlinear programming solving module to obtain the currently optimized control variable ulAnd corresponding time node distribution TlL is 0 or satisfies the termination condition
Turning to the step C, otherwise turning to the step D;
and C: obtaining IMF function by EMD decomposition
Distribution T for time segmentslIf, if
Then the corresponding time node is eliminated, the number of time nodes is reduced, if so
The corresponding time nodes are refined, the time node number is increased, and the new time node distribution T is obtainedl+1Obtaining a control variable set u corresponding to the new time node by interpolationl+1(ii) a Setting l ═ l +1, if l < lmaxReturning to the step B, and adding Tl+1And ul+1Taking the initial value as an initial value of a nonlinear programming solving module in the (l + 1) th iteration, otherwise, turning to the step D;
step D: stopping the adaptation and outputting u*＝ulAnd J*＝J[ul]。
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