Rotor unmanned aerial vehicle fixed time control method for unknown environment

Abstract

The invention discloses an unknown environment-oriented rotor unmanned aerial vehicle fixed time control method, which comprises the following steps of: 1, simultaneously considering output constraint and unknown external interference under the condition of system uncertainty, and constructing a rotor unmanned aerial vehicle position ring and attitude ring nonlinear system model; 2, designing a safety expectation tracking signal # imgabs0 #, obtaining other expectation signals # imgabs1 # through inverse solution, calculating an error # imgabs2 # of a position ring and an error # imgabs3 # of an attitude ring, combining nonlinear system model characteristics of the position ring and the attitude ring of the rotor unmanned aerial vehicle, designing a barrier Lyapunov function, and selecting proper upper and lower bounds; and 3, designing a tracking controller based on the obstacle Lyapunov function in combination with a fuzzy logic system, a fixed time disturbance observer, a filter and a self-adaptive backstepping method. The method has the advantage that the rotor unmanned aerial vehicle can complete tracking of the preset expected tracking signal within fixed time on the basis of ensuring the system safety and stability under the condition that the influence of output constraint, system uncertainty and unknown external interference is considered.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicles, and in particular to a fixed-time control method for a rotary-wing unmanned aerial vehicle facing an unknown environment. Background Art

[0002] In recent years, rotary-wing UAVs have achieved remarkable performance in high-altitude photography, waterway inspection, earthquake prevention and disaster relief, epidemic prevention and disinfection, and fixed-point material delivery, relying on their advantages such as fixed-point hovering, vertical take-off and landing, wide application environment, and flight in any direction. Rotary-wing UAV systems have the characteristics of high nonlinearity, strong coupling, time variation, and open-loop instability. It is very difficult to achieve the flight goals of rotary-wing UAV systems such as fixed-point hovering, forward and backward flight, and autonomous take-off and landing. However, since rotary-wing UAVs have extremely high application value in many fields in the real world, the development of autonomous flight control technology for rotary-wing UAVs is of far-reaching significance. There is no doubt that advanced autonomous flight control technology is the core of solving the above problems.

[0003] During the flight of a rotorcraft UAV, factors such as engine jitter and changes in the external environment (such as gusts of wind) may cause problems with the stability of the system. Especially when the flight control system is running, if the impact of system uncertainty and external disturbances is not considered, the system performance may deteriorate. In addition, there must be various safety protection mechanisms during the flight of a rotorcraft UAV, such as position constraints. Therefore, the designed controller must ensure that the system state quantity always remains within the safety boundary in order to complete the preset tasks safely and effectively. If the restricted problems during the flight of the UAV cannot be solved in time, it may lead to irreversible losses such as system loss of control and crash.

[0004] In addition, since drones need to respond quickly to complex working environments, the response speed of the controller is particularly important. This problem is usually not considered in traditional control. The final control result is that the drone system reaches asymptotic stability, and the stabilization time cannot be guaranteed. Therefore, it is urgent to design a control strategy that can control the system stabilization time. Summary of the invention

[0005] To solve the above problems, the present invention provides a fixed-time control method for a rotorcraft UAV in an unknown environment, which has the advantages of enabling the rotorcraft UAV to complete tracking of a preset expected tracking signal within a fixed time while ensuring system safety and stability, taking into account output constraints, system uncertainties and the influence of unknown external interference, and on this basis, can solve the problem of output limitation during flight.

[0006] The present invention is achieved through the following technical solutions:

[0007] A fixed-time control method for a rotary-wing UAV in an unknown environment comprises the following steps:

[0008] Step 1: Considering the system uncertainty, output constraints and unknown external interference, a nonlinear system model of the position loop and attitude loop of the rotorcraft is constructed;

[0009] Step 2: Design safety expectation tracking signal X d ,Y d ,Z d ,ψ d , and obtain the remaining expected signal φ by inverse solution d ,θ d , calculate the errors z1,z2 of the position loop and z3,z4 of the attitude loop, combine the nonlinear system model characteristics of the position loop and attitude loop of the rotorcraft, design the corresponding obstacle Lyapunov function, and select the appropriate upper and lower bounds according to the output requirements;

[0010] Step 3: Based on the barrier Lyapunov function in step 2, a tracking controller is designed by combining the fuzzy logic system with the fixed-time disturbance observer, filter and adaptive backstepping method.

[0011] Furthermore, in step 1, the nonlinear system model of the position loop and attitude loop of the rotorcraft is constructed as follows:

[0012]

[0013] Where: P = [X, Y, Z] T , X, Y, Z are the positions in three directions in the geodetic coordinate system, ε=[u,v,w] T ,u,v,w,respectively, are the velocities of the X,Y,Z axes in the geodetic coordinate system, Ξ=[φ,θ,ψ] T , φ, θ, ψ are the roll angle, pitch angle and yaw angle of the three axes X, Y and Z in the body coordinate system, ν = [p, q, r] T , p, q, r are the roll angular velocity, pitch angular velocity and yaw angular velocity of the X, Y, and Z axes in the body coordinate system, is the rotation matrix, F m is the main rotor thrust, G = [0,0,mg] T is the weight of the rotorcraft, J is the moment of inertia matrix, is the system uncertainty, is the unknown disturbance vector under attitude angle and attitude angular velocity.

[0014] Furthermore, the barrier Lyapunov function in step 2 is designed as:

[0015]

[0016] Where: b i >0, (i=1,2,3) is the pre-designed error constraint, z 1i represents the i-th column of z1, which is b i ,(i=1,2,3)pre-designed error safety margin.

[0017] Further, the controller selection is as follows:

[0018]

[0019] Among them: u1 is the controller of the position loop, u2 is the controller of the attitude loop, 0<ι<1,ρ>1ζ1>0,ζ2>0 are the parameters to be designed, is the matrix to be designed, is the output of the dynamic surface, is an estimate under system uncertainty, is the estimate of the position loop and attitude loop disturbance, are the parameters of the barrier Lyapunov function.

[0020] Furthermore, the fixed-time disturbance observer is:

[0021]

[0022] in is the estimate of the position loop and attitude loop disturbance is an auxiliary variable, It is a parameter to be designed.

[0023] The present invention also provides a device, including a memory and a processor, wherein the memory is used to store computer programs; the processor is used to execute the above-mentioned fixed-time control method for a rotorcraft in an unknown environment.

[0024] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program can control the rotary-wing UAV at a fixed time when executed by a processor.

[0025] The beneficial effects of the present invention are:

[0026] 1. The present invention aims at the output constraints of the UAV, selects reasonable upper and lower bounds of the error, and uses the barrier Lyapunov function to constrain the output to ensure the safe flight of the rotor UAV. For system uncertainty and unknown external interference, the fuzzy logic system and fixed-time disturbance observer are used for estimation, and the fixed-time stability theory is used to ensure the response time of the UAV. It has been verified that the fixed-time anti-disturbance tracking controller designed by the present invention can complete the tracking of the preset expected tracking signal on the basis of ensuring the safety and stability of the system.

[0027] 2. The present invention simultaneously considers output constraints, system uncertainty and unknown external interference, and constructs a nonlinear system model of the position loop and attitude loop of a rotorcraft UAV that requires fast response; the present invention designs a class of adaptive fixed-time algorithms with the help of the real-time output and output constraints of the rotorcraft UAV system; the present invention uses fuzzy logic system and fixed-time disturbance observer method to approximate the problems of system uncertainty, unknown external interference, response time, etc., and adopts fixed-time stability theory to design an adaptive fixed-time tracking controller to realize the safe flight intention of the rotorcraft UAV system. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a system control flow chart of the present invention. DETAILED DESCRIPTION

[0029] A fixed-time control method for a rotary-wing UAV in an unknown environment comprises the following steps:

[0030] Step 1: Considering the system uncertainty, output constraints and unknown external interference, a nonlinear system model of the position loop and attitude loop of the rotorcraft is constructed;

[0031]

[0032] Where: P = [X, Y, Z] T , X, Y, Z are the positions in three directions in the geodetic coordinate system, ε=[u,v,w] T ,u,v,w,respectively, are the velocities of the X,Y,Z axes in the geodetic coordinate system, Ξ=[φ,θ,ψ] T , φ, θ, ψ are the roll angle, pitch angle and yaw angle of the three axes X, Y and Z in the body coordinate system, ν = [p, q, r] T , p, q, r are the roll angular velocity, pitch angular velocity and yaw angular velocity of the X, Y, and Z axes in the body coordinate system, is the rotation matrix, F m is the main rotor thrust, G = [0,0,mg] T is the weight of the rotorcraft, J is the moment of inertia matrix, is the system uncertainty, is the unknown disturbance vector under attitude angle and attitude angular velocity;

[0033] Step 2: Ensure that the position X, Y, Z and the yaw angle ψ correspond to the expected tracking signal X d ,Y d ,Z d ,ψ d and its first-order derivative is bounded, and the remaining desired signal φ is obtained by inverse solution d ,θd , calculate the position loop errors z1, z2 (specifically P and P d The error z1, ε and the virtual control law α1 error z2) and the attitude loop error z3, z4 (specifically Ξ and Ξ d The error z3 of ν and the error z4 of the virtual control law α2), combined with the nonlinear system model characteristics of the rotor UAV position loop and attitude loop, design the corresponding obstacle Lyapunov function to constrain the output error z1, and select the appropriate upper and lower bounds according to the output requirements;

[0034] The barrier Lyapunov function is:

[0035]

[0036] b i >0, (i=1,2,3) is the pre-designed error constraint, z 1i represents the i-th column of z1, which is

[0037] in

[0038] b i ,(i=1,2,3)pre-designed error safety margin.

[0039] Step 3: Based on the barrier Lyapunov function in step 2, a tracking controller is designed by combining the fuzzy logic system with the fixed-time disturbance observer, filter and adaptive backstepping method.

[0040] The controller selections are as follows:

[0041]

[0042] Among them, u1 is the controller of the position loop, u2 is the controller of the attitude loop, 0<ι<1,ρ>1ζ1>0,ζ2>0 are the parameters to be designed, is the matrix to be designed, is the output of the dynamic surface, is an estimate under system uncertainty, is the estimate of the position loop and attitude loop disturbance, are the parameters of the barrier Lyapunov function.

[0043] The fixed-time disturbance observer is:

[0044]

[0045] in is an auxiliary variable, It is a parameter to be designed.

[0046] The controller design process is as follows:

[0047] (1) Position subsystem for drones;

[0048] a. Design virtual control law α1:

[0049]

[0050] Among them, 0<ι<1,ρ>1,a 1i1 >0,a 1i2 >0 is the parameter to be designed; α 1i ,P di Represents α1,P d Column of

[0051] b. Design the fixed-time disturbance observer form:

[0052] c. Design filter:

[0053]

[0054] Where λ1 is the filter output signal, is the time derivative of λ1, τ1 is a positive definite diagonal matrix;

[0055] d. Design fuzzy adaptive law

[0056]

[0057] Among them, γ1>0,ξ1>0 are the parameters to be designed;

[0058] e. Design a fixed time controller;

[0059] (2) For the attitude subsystem, the controller design process is as follows:

[0060] a. Design the virtual control law α2 as follows:

[0061]

[0062] in, is the matrix to be designed;

[0063] b. Design a fixed-time disturbance observer;

[0064] C. Design filter:

[0065]

[0066] Where λ2 is the filter output signal, is the time derivative of λ2, τ2 is a positive definite diagonal matrix;

[0067] d. Combine the attitude subsystem, disturbance observer and filter to design the fuzzy adaptive law

[0068]

[0069] Among them, γ2>0,ξ2>0 are parameters to be designed.

[0070] e. Design a fixed-time controller.

[0071] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below according to the accompanying drawings.

[0072] Example 1

[0073] See also Figure 1 , a fixed time control method for a rotary wing UAV in an unknown environment, comprising the following steps:

[0074] Step 1: Considering the output constraints, system uncertainty and unknown external interference, a nonlinear system model of the rotorcraft position loop and attitude loop is constructed.

[0075] The process of establishing the nonlinear system model of the position loop and attitude loop of the rotary-wing UAV in step 1 is as follows:

[0076] a. Nonlinear model of the position loop and attitude loop of a rotary-wing UAV

[0077] Considering the output constraints, system uncertainty and unknown external disturbances, combined with the aerodynamics and kinematics of the rotorcraft, the nonlinear model of the position loop and attitude loop is described as:

[0078]

[0079] Where: P = [X, Y, Z] T ,ε=[u,v,w] T The position and velocity vectors of the rotorcraft, Ξ=[φ,θ,ψ] T , ν=[p,q,r] T are the attitude angle and attitude angular velocity vector of the rotorcraft, is the rotation matrix, F m is the main rotor thrust, G = [0,0,mg] T is the weight of the rotorcraft, J is the moment of inertia matrix, is the system uncertainty, is the unknown interference vector under attitude angle and attitude angular velocity; the attitude rotation matrix is

[0080]

[0081] To facilitate controller design, system (1) can be rewritten as a position subsystem and an attitude subsystem:

[0082] The position subsystem is expressed as follows:

[0083]

[0084] The attitude subsystem is expressed as follows:

[0085]

[0086] Where u1=RF m , F ν =J -1 ν×Jν,

[0087] Before controller design, the following assumptions and lemmas are required:

[0088] Assumption 1: The derivative of the external disturbance vector d1, d2 is bounded, that is, there exists a positive constant β such that the following is true about the disturbance vector d i ,(i=1,2) time derivative The inequality holds:

[0089] Assumption 2: The expected tracking signal Θ is d =[X d ,Y d ,Z d ,ψ d ] T and its r-order derivative are bounded (r = 1, 2), that is, there exists a positive constant δ j (j=1,...,4) so ​​that the following inequality always holds:

[0090]

[0091] Assumption 3: The roll angle and pitch angle of the rotorcraft always remain within a reasonable range (-π / 2, π / 2).

[0092] Lemma 1: For any variable If a3>0,a4>0,a5>0, then the following inequality holds

[0093]

[0094] Lemma 2: For ρ>1,0<ι<1,a i >0, then

[0095]

[0096] Lemma 3: For b i >0, The following inequality always holds true

[0097]

[0098] Lemma 4: For o1≥o2>0,ρ>1, there always exists the following inequality

[0099]

[0100] Considering that rotorcraft UAVs are often subject to output constraints, the upper and lower bounds of the system output error are defined as z 1,up =[b1,b2,b3] T With z 1,low =[-b1,-b2,-b3] T .

[0101] In addition, during the flight of the rotorcraft, the existence of factors such as engine jitter and changes in the external environment (such as gust interference) will cause problems to the stability of the system. The unknown external interference signal d(t) satisfies the norm bounded condition, that is, there is a positive constant β that makes the following inequality hold

[0102] In order to deal with system uncertainty, a fuzzy logic system will be used to approximate it, and the design is as follows

[0103]

[0104] in is the matrix to be designed, is the approximation error, σ i is a positive real number.

[0105] Substitute it into the position subsystem and attitude subsystem to get

[0106]

[0107] and

[0108]

[0109] in It is a composite disturbance.

[0110] The tracking error of the position subsystem is designed as follows:

[0111] z1 = PP d (14)

[0112] z2 = ε-α1 (15)

[0113] Among them, α1 is the virtual control law of the position subsystem.

[0114] In order to realize the output constraint, the obstacle Lyapunov function is designed as follows:

[0115]

[0116] where z 1i represents the i-th column of z1, which is b i ,(i=1,2,3)pre-designed error safety margin.

[0117] Step 3: Combining the barrier Lyapunov function, fuzzy logic system, fixed-time disturbance observer and fixed-time stability theory, design a tracking controller based on the adaptive backstepping method; the controller design process of step 3 is as follows:

[0118] a. For the position subsystem of the UAV, the virtual control law α1 is designed as follows:

[0119]

[0120] Among them, 0<ι<1,ρ>1,a 1i1 >0,a 1i2 >0 is the parameter to be designed; α 1i ,P di Represents α1,P d Column of .

[0121] To compensate for unknown disturbances, a fixed-time disturbance observer is designed as follows:

[0122]

[0123] in, is an auxiliary variable, is the matrix to be designed, β1>0 is the parameter to be designed, and the error variable is defined Then there is

[0124]

[0125] b. To avoid direct derivation of the virtual control law α1, let it pass through the following form of filter:

[0126]

[0127] Where λ1 is the filter output signal, is the time derivative of λ1, τ1 is a positive definite diagonal matrix, and the error variable is defined Then there is

[0128]

[0129] Wherein, B1 is a continuous function vector and satisfies ‖B1(·)‖≤B1 under the condition of given initial value.

[0130] Combining the position subsystem (12), the obstacle Lyapunov function (16), the disturbance observer (18) and the filter (20), the fuzzy adaptive law is designed. With fixed time controller u1 as follows:

[0131]

[0132] Among them, γ1>0,ξ1>0 are the parameters to be designed. is the matrix to be designed,

[0133] For the attitude subsystem, a tracking controller based on adaptive backstepping method is designed by combining fuzzy logic system, fixed-time disturbance observer and fixed-time stability theory. The controller design process is as follows:

[0134] a. For the position subsystem of the rotorcraft UAV, the virtual control law α2 is designed as follows:

[0135]

[0136] in, is the matrix to be designed.

[0137] To compensate for unknown disturbances, a fixed-time disturbance observer is designed as follows:

[0138]

[0139] in, is an auxiliary variable, is the matrix to be designed, β2>0 is the parameter to be designed, and the error variable is defined Then there is

[0140]

[0141] b. To avoid direct derivation of the virtual control law α2, let it pass through a filter of the following form:

[0142]

[0143] Where λ2 is the filter output signal, is the time derivative of λ2, τ2 is a positive definite diagonal matrix, and the error variable is defined Then there is

[0144]

[0145] Wherein, B2 is a continuous function vector and satisfies ||B2(·)||≤B2 under the condition of given initial value.

[0146] Combining the attitude subsystem (21), the disturbance observer (25) and the filter (27), the fuzzy adaptive law is designed. With fixed time controller u2 as follows:

[0147]

[0148] Among them, γ2>0,ξ2>0 are the parameters to be designed. is the matrix to be designed.

[0149] After the above analysis and discussion, the following conclusions are drawn:

[0150] Conclusion 1: For a rotorcraft UAV system with output constraints, system uncertainty and external disturbances, the obstacle Lyapunov function is considered to be (16), the fixed-time disturbance observer is designed as (18) and (25), the virtual control input is designed as (17) and (24), the control input is designed as (23) and (30), the fuzzy adaptive law is designed as (22) and (29), the filter is designed as (20) and (27), and the system is actually fixed-time bounded. The tracking error of the system and the observer error of the observer can converge within a fixed time, the convergence time does not depend on the initial conditions of the system, and the observer convergence speed can be made faster than the state convergence speed by adjusting the parameters.

[0151] Proof: Take the Lyapunov function as

[0152]

[0153] Taking the derivative of V with respect to time t, we get

[0154]

[0155] in in Yes D i >0 upper bound.

[0156] From Lemma 2, we can get

[0157]

[0158] Substituting (33) into (32) we can get

[0159]

[0160] in

[0161] From Lemma 3, we can get

[0162]

[0163] Substituting (35)-(38) into (34), we obtain

[0164]

[0165] where c2 = min{c1,2c1,3 1-ρ c1}.

[0166] After further transformation, we can get

[0167]

[0168] From Lemma 2, we can get the following inequality:

[0169]

[0170] Substituting (41)-(43) into (40), we obtain

[0171]

[0172] in

[0173] Assumptions Then we can get

[0174]

[0175] Then (44) can be rewritten as

[0176]

[0177] Where B=c2,S=5 1-ρ c2,W=W3.

[0178] In order to ensure the stability of the closed-loop system, it is necessary to design relevant parameters ι,ρ,Λ1,Λ2,a 111 ,a 121 ,a 131 ,ζ1,ζ2,a 112 ,a 122 ,

[0179] a 132 ,a 21 ,a 22 ,a 31 ,a 32 ,a 41 ,a 42,β1,β2,Γ1,Γ2,ξ1,ξ2,γ1,γ2,b1,b2,b3 make (47) true and the conclusion is proved.

[0180] The obstacle Lyapunov function designed by the present invention can keep the output error within a preset safety range at all times. The fuzzy logic system and the fixed-time disturbance observer are used to approximate the system uncertainty and external disturbance of the system. The observer error can be designed to reach an ideal state before the system stabilizes by designing parameters, further improving the stability of the system. All states of the system are bounded and can track the expected signal. In addition, the stabilization time is determined only by the design parameters.

[0181] According to the above steps, the rotorcraft UAV can complete the tracking of the preset expected tracking signal while considering the constant attitude angle and altitude constraints and the influence of unknown external interference and ensuring the safety and stability of the system.

[0182] The present invention also provides a device, comprising: a memory and a processor, wherein the memory is used to store a computer program; the processor is used to implement a fixed-time control method for a rotorcraft drone facing an unknown environment when executing the computer program.

[0183] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, a rotary-wing unmanned aerial vehicle can be controlled at a fixed time.

[0184] It should be noted that although the present invention is described by the above embodiments, the present invention may also have other various embodiments. Without departing from the spirit and scope of the present invention, it is obvious that those skilled in the art may make various corresponding changes and deformations to the present invention, but these changes and deformations should all fall within the scope of protection of the appended claims of the present invention and their equivalents.

Claims

1. A fixed-time control method for a rotary-wing UAV in an unknown environment, characterized in that: The following steps are involved: Step 1: Considering the system uncertainty, output constraints and unknown external interference, a nonlinear system model of the position loop and attitude loop of the rotorcraft is constructed; Step 2: Design safety expectation tracking signal X d ,Y d ,Z d ,ψ d , and obtain the remaining expected signal φ by inverse solution d ,θ d , calculate the errors z1,z2 of the position loop and z3,z4 of the attitude loop, combine the nonlinear system model characteristics of the position loop and attitude loop of the rotorcraft, design the corresponding obstacle Lyapunov function, and select the appropriate upper and lower bounds according to the output requirements; Step 3: Based on the barrier Lyapunov function in step 2, a tracking controller is designed by combining the fuzzy logic system with the fixed-time disturbance observer, filter and adaptive backstepping method.

2. The method for controlling a rotary-wing UAV in an unknown environment according to claim 1, characterized in that: In step 1, the nonlinear system model of the position loop and attitude loop of the rotorcraft is constructed as follows: Where: P = [X, Y, Z] T , X, Y, Z are the positions in three directions in the geodetic coordinate system, ε=[u,v,w] T ,u,v,w,respectively, are the velocities of the X,Y,Z axes in the geodetic coordinate system, Ξ=[φ,θ,ψ] T , φ, θ, ψ are the roll angle, pitch angle and yaw angle of the three axes X, Y and Z in the body coordinate system, ν = [p, q, r] T , p, q, r are the roll angular velocity, pitch angular velocity and yaw angular velocity of the X, Y, and Z axes in the body coordinate system, is the rotation matrix, F m is the main rotor thrust, G = [0,0,mg] T is the weight of the rotorcraft, J is the moment of inertia matrix, is the system uncertainty, is the unknown disturbance vector under attitude angle and attitude angular velocity.

3. The method for controlling a rotary-wing UAV in an unknown environment according to claim 1, characterized in that: The barrier Lyapunov function in step 2 is: Where: b i >0, (i=1,2,3) is the pre-designed error constraint, z 1i represents the i-th column of z1, which is b i ,(i=1,2,3)pre-designed error safety margin.

4. The method for controlling a rotary wing UAV in an unknown environment according to claim 1, characterized in that: The controller selections are as follows: Among them, u1 is the controller of the position loop, u2 is the controller of the attitude loop, 0<ι<1,ρ>1ζ1>0,ζ2>0 are the parameters to be designed, is the matrix to be designed, is the output of the dynamic surface, is an estimate under system uncertainty, is the estimate of the position loop and attitude loop disturbance, are the parameters of the barrier Lyapunov function.

5. The method for controlling a rotary-wing UAV in an unknown environment according to claim 1, characterized in that: The fixed-time disturbance observer is: in is the estimate of the position loop and attitude loop disturbance, is an auxiliary variable, It is a parameter to be designed.

6. A device, characterized in that: It comprises a memory and a processor, wherein the memory is used to store a computer program; the processor is used to execute any one of the above-mentioned methods for fixed-time control of a rotary-wing UAV in an unknown environment as claimed in claims 1 to 5.

7. A computer-readable storage medium, characterized in that: It stores a computer program, which can control the rotary-wing UAV at a fixed time when executed by a processor.

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