Interconnected nonlinear system distributed fault-tolerant stabilization control method simultaneously containing unknown sensor fault and output signal constraint

Abstract

The invention discloses a distributed fault-tolerant stabilization control method for an interconnected nonlinear system containing unknown sensor faults and output signal constraints at the same time. The method comprises the steps that the interconnected nonlinear system containing the unknown sensor faults and the output signal constraints at the same time serves as a research object, and a mathematical model is established; establishing an applied sensor fault and output signal constraint model; by constructing a barrier function to process an output signal constraint problem, a virtual controller with a novel structure is designed, and an actual controller and a self-adaptive parameter updating law solve the fault-tolerant stabilization control problem of sensor faults. According to the method, the adverse effect of the sensor fault on the system can be eliminated under the condition that the interconnected nonlinear system simultaneously contains the unknown sensor fault and the output signal constraint, and the output of the system is ensured to meet the preset constraint requirement. Finally, the practicability and effectiveness of the control scheme are verified through numerical simulation research.

Description

Technical Field

[0001] The invention belongs to the field of decentralized control of interconnected nonlinear systems, and in particular relates to a decentralized fault-tolerant stabilization control method for interconnected nonlinear systems under the condition that sensor failures and output constraints exist simultaneously. Background Art

[0002] With the continuous advancement of technology, the scale and complexity of control systems are increasing, and the application of interconnected nonlinear systems has become more extensive and important. Interconnected nonlinear systems can handle the strong coupling between subsystems, which is an important development direction for modern control theory. Typical applications of interconnected nonlinear systems include intelligent manufacturing, aerospace, industrial Internet and intelligent robot clusters.

[0003] Sensors are responsible for collecting and transmitting data about the environment and equipment status, and are the basis for achieving automated and intelligent control. Sensor failure may cause data distortion or loss, which in turn affects system performance, causing safety issues and economic losses. Existing research has achieved certain results in fault-tolerant control of interconnected nonlinear systems under sensor failure conditions, but there are few research results on the situation where sensor failures and output constraints exist at the same time.

[0004] Actual systems are often subject to multiple constraints due to physical limitations or safety considerations. Once these constraints are violated, it may cause system instability and performance degradation, and in serious cases, it may also induce safety incidents and endanger personnel safety. Summary of the invention

[0005] In view of the shortcomings of existing research on interconnected nonlinear systems with unknown sensor faults and output signal constraints, an improved barrier function is proposed to solve the output signal constraint problem. In order to solve the fault-tolerant stabilization control problem of sensor faults, a virtual controller, actual controller and adaptive parameter update law with novel structures are designed. This scheme can not only eliminate the adverse effects of sensor faults on closed-loop control systems, but also make the system output signal meet the given constraint requirements. Finally, the effectiveness of the proposed algorithm is verified through numerical simulation.

[0006] In order to achieve the above object, the present invention proposes a distributed fault-tolerant stabilization control method for interconnected nonlinear systems with unknown sensor faults and output signal constraints, which is implemented by the following steps:

[0007] Step 1: Consider the following interconnected nonlinear system with N subsystems:

[0008]

[0009] Among them, x ij (t)(i=1,2,...,N,j=1,2,...,ni ) represents the state of the system, u if (t) represents the control input of the system, y i (t) represents the output of the system, where N is the subsystem number, n i is the order of the subsystem; is the state variable measured by the sensor; is an unknown nonlinear function, is the unknown interconnection function; p ij (t) is the unknown failure factor; n i1 and n i2 is the preset constraint boundary.

[0010] For the sensor failure factor p ij (t) The following assumptions are made:

[0011] 0 <p ij,0 ≤p ij (t)≤1

[0012] Among them, p ij,0 is a constant; p ij (t) itself and its first-order derivative are bounded.

[0013] Step 2: The barrier function construction method is as follows:

[0014]

[0015] Among them, m ij (t) is a second-order continuously differentiable positive time-varying function and satisfies m ij (0)>m ij (t), t∈(0,+∞). i1 (y i ) is defined as follows:

[0016] ζ i1 (y i )=o i1 (y i )q i1 (y i )+o i2 (y i )q i2 (y i )

[0017] in, s i1 and i2 is a positive constant and satisfies s i1 ≤m i1 (0),s i2 ≤mi2 (0).q i1 (y i ), q i2 (y i ) is defined as follows:

[0018]

[0019] When e i1 When (t) is bounded, the system output y i (t) will be strictly constrained to n i1 (-m i1 (t)) <y i <n i2 (m i2 (t)). Among them,

[0020] The main control objective of the present invention is to design a distributed fault-tolerant stabilization control method for interconnected nonlinear systems with unknown sensor faults and output signal constraints, to ensure that all signals of the closed-loop system are bounded and that the system output signal meets the given constraint requirements.

[0021] Step 3: Perform the following coordinate transformation:

[0022] z i1 =e i1

[0023]

[0024] Among them, α ij-1 is the virtual control input.

[0025] Designing a virtual controller α ij , the actual controller u if (t) and the corresponding adaptive parameter update law The details are as follows:

[0026] Virtual Controller α i1 for:

[0027]

[0028] Virtual Controller α ij for:

[0029]

[0030] Actual controller u if (t) Designed to:

[0031]

[0032] Corresponding adaptive parameter update law for:

[0033]

[0034] in, c∈(0,1) is a constant; sgn(*) represents the sign function; and d ij is a positive design parameter.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] In interconnected nonlinear systems, existing distributed fault-tolerant control lacks a method to simultaneously solve sensor failure and output signal constraint problems. The present invention proposes an improved barrier function to solve the output signal constraint problem of interconnected nonlinear systems. The mathematical structures of the designed virtual controller, actual controller and adaptive parameter update law are different from those in previous literature. The functions implemented by the proposed controller are different from those of existing similar controllers. It can eliminate the adverse effects of unknown sensor failures on closed-loop control systems while ensuring that the system output meets the given constraint requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a simplified model diagram of an interconnected nonlinear system;

[0038] Figure 2 is a graph of the subsystem outputs and constraints;

[0039] Figure 3 is the control input curve of the subsystem;

[0040] Figure 4 It is the adaptive parameter update law curve of the subsystem; DETAILED DESCRIPTION

[0041] The specific implementation of the present invention is now described in further detail in conjunction with the accompanying drawings. In order for those skilled in the art to better understand the implementation of the present invention, the present invention also provides simulation verification results using MatlabR2023b software.

[0042] Step 1: Consider the following interconnected nonlinear system with N subsystems:

[0043]

[0044] Among them, x ij (t)(i=1,2,...,N,j=1,2,...,n i ) represents the state of the system, u if( t) represents the control input of the system, y i(t) represents the output of the system, where N is the subsystem number, n i is the order of the subsystem; is the state variable measured by the sensor; is an unknown nonlinear function, is the unknown interconnection function; p ij (t) is the unknown failure factor; n i1 and n i2 is the preset constraint boundary.

[0045] For the sensor failure factor p ij (t) The following assumptions are made:

[0046] 0 <p ij,0 ≤p ij (t)≤1

[0047] Among them, p ij,0 is a constant; p ij (t) itself and its first-order derivative are bounded.

[0048] Step 2: The barrier function construction method is as follows:

[0049]

[0050] Among them, m ij (t) is a second-order continuously differentiable positive time-varying function and satisfies m ij (0)>m ij (t), t∈(0,+∞). i1 (y i ) is defined as follows:

[0051] ζ i1 (y i )=o i1 (y i )q i1 (y i )+o i2 (y i )q i2 (y i )

[0052] in, s i1 and i2 is a positive constant and satisfies s i1 ≤m i1 (0),s i2 ≤m i2 (0).q i1 (y i ), q i2(y i ) is defined as follows:

[0053]

[0054] When e i1 When (t) is bounded, the system output y i (t) will be strictly constrained to n i1( -m i1 (t)) <y i <n i2 (m i2 (t)). Among them,

[0055] Step 3: Perform the following coordinate transformation:

[0056] z i1 =e i1

[0057]

[0058] Among them, α ij -1 is a dummy control input.

[0059] Designing a virtual controller α ij , the actual controller u if (t) and the corresponding adaptive parameter update law The details are as follows:

[0060] Virtual Controller α i1 for:

[0061]

[0062] Virtual Controller α ij for:

[0063]

[0064] Actual controller u if (t) Designed to:

[0065]

[0066] Corresponding adaptive parameter update law for:

[0067]

[0068] in, c∈(0, 1) is a constant; sgn(*) represents a sign function. and d ij is a positive design parameter.

[0069] In this example, the above method is used to perform simulation verification using MatlabR2023b software. The verification process and results are as follows: Consider two inverted pendulums connected by springs, such as Figure 1 As shown. The i-th inverted pendulum can be modeled as follows:

[0070]

[0071] Among them, x i1 represents the angular displacement of the inverted pendulum relative to the vertical direction, x i,2 Indicates angular velocity; M1 = M2 = 1 kg·m 2 represents the moment of inertia; k = 5 N / m represents the spring constant; l = 1 m represents the height of the pendulum; g = 9.8 m / s 2 represents the acceleration due to gravity; m1 = 0.5 kg, m2 = 1 kg represents the mass of the ball at the end of the rod; r = ψ = 0.5 m; is the interconnection function.

[0072] For subsystem 1, the functions related to faults and constraints are designed as follows:

[0073] p 11 =0.5+0.4sin(t), p 12 =0.3+0.1cos(2t);m 11 =0.5e -t cos 2 (t)+0.1,m 12 =0.8e - t cos 2 (t)+0.1:s 11 =0.6,s 12 =0.9.

[0074] For subsystem 2, the functions related to faults and constraints are designed as follows:

[0075] p 21 =0.6+0.2sin(t), p 22 =0.4+0.3sin(2t);m 21 =e -t +0.1,m 22 =1.2e -t +0.1;s 21 =1.1,s 22 =1.3.

[0076] The initial state of the system and the design parameters are set as follows through repeated debugging:

[0077] d 11=3,d 12 =10; d 21 =1,d 22 =2; x 11 (0) = 1.8, x 12 (0) = 0, x 21 (0) = 1.5, x 22 (0) = 0;

[0078] Figure 1 is the simplified model diagram of the selected interconnected nonlinear system, Figure 2 It can be seen that the output of the subsystem can be quickly stabilized and strictly meets the given constraint requirements; Figure 3 This is the control input waveform of the subsystem. It can be seen that the control input of the subsystem undergoes a rapid adjustment process and finally stabilizes near 0; Figure 4 This is the change diagram of the adaptive parameter update law of the subsystem. It can be seen that the adaptive parameter update law of the subsystem is bounded and convergent.

[0079] The parts of the present invention that are not described in detail are common knowledge to those skilled in the art. The above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A distributed fault-tolerant stabilization control method for interconnected nonlinear systems with unknown sensor faults and output signal constraints, including the identification of unknown nonlinear functions, fault-tolerant control of unknown sensor faults, constraints on the output signals of the controlled system and experimental simulation verification, characterized by The following steps are involved: Step 1: A mathematical model of the interconnected nonlinear system with unknown sensor faults and output signal constraints is established; Step 2: In order to solve the output signal constraint problem, an improved barrier function is proposed; Step 3: In order to solve the fault-tolerant stabilization control problem of sensor failure, a virtual controller, actual controller and adaptive parameter update law with novel structures are designed.

2. According to step 1 of claim 1, consider a type of mechanical system and establish the following mathematical model: in, x ij (t)(i=1,2,...,N,j=1,2,...,n i ) represents the state of the system, u if (t) represents the control input of the system, y i (t) represents the output of the system, where N is the subsystem number, n i is the order of the subsystem; is the state variable measured by the sensor; is an unknown nonlinear function, is the unknown interconnection function; p ij (t) is the unknown failure factor; n i1 and n i2 is the preset constraint boundary.

3. According to step 1 of claim 1, for the sensor failure factor p ij (t) The following assumptions are made: 0<p ij，0 ≤p ij (t)≤1 in, p ij，0 is a constant; p ij (t) itself and its first-order derivative are bounded.

4. According to step 2 in claim 1, the barrier function construction method is as follows: in, m ij (t) is a second-order continuously differentiable positive time-varying function and satisfies m ij (0)>m ij (t), t∈(0,+∞). i1 (y i ) is defined as follows: ζ i1 (and i )=or i1 (and i )q i1 (and i )+o i2 (and i )q i2 (and i ) in, s i1 and i2 is a positive constant and satisfies s i1 ≤m i1 (0),s i2 ≤m i2 (0).q i1 (y i ), q i2 (y i ) is defined as follows: When e i1 When (t) is bounded, the system output y i (t) will be strictly constrained to n i1 (-m i1 (t))<y i <n i2 (m i2 (t)). Among them, 5. According to step 3 of claim 1, firstly perform the following coordinate transformation based on the backstepping method: with i1 =e i1 in, z i1 and z ij is the tracking error, α ij-1 is the virtual control input. Designing a virtual controller α ij And the corresponding adaptive parameter update law The details are as follows: Virtual Controller α i1 for: Virtual Controller α ij for: Actual controller u if (t) Designed to: Corresponding adaptive parameter update law for: in, c∈(0,1) is a constant; sgn(*) represents the sign function; and d ij is a positive design parameter. The main control objective of the present invention is to design a distributed fault-tolerant control method for interconnected nonlinear systems in the presence of sensor failures and output constraints, ensuring that all signals of the closed-loop system are bounded and that the system output signals meet the given constraint requirements.

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