Koopman Predictor-Based Integrated Guidance and Control Under Multi-Force Compound Control System
Abstract
:1. Introduction
- (1)
- The mathematical model of the strapdown interceptor under the multi-force compound control is established, taking into account the physical limitations, working principles, and dynamic characteristics of the aerodynamic rudder, attitude control engine, and orbit control engine.
- (2)
- The high-order, strongly coupled, and strongly nonlinear interceptor kinematics/dynamics model under multi-force compound control is transformed into a linear IGC model using the Koopman predictor on the premise of satisfying the accuracy.
- (3)
- Based on the linear IGC model, the extended disturbance observer (EDO) and adaptive weight-based control allocation scheme are combined with the Koopman predictor-based sliding mode control (KPSMC) to form the IGC law for the interceptor under the multi-force compound control. The proposed Koopman predictor-based IGC method simplifies the complex model while retaining the dynamic characteristics, balancing the difficulty of the controller design and the control performance.
2. Problem Formulation
2.1. Multi-Force Compound Control System
- (1)
- The aerodynamic rudder and attitude control engine inevitably generate the force increments while generating the moment increments that affect the trajectory. Among them, the additional acceleration increment generated by the attitude control engine is particularly significant.
- (2)
- Due to the drift of the mass center caused by installation error and fuel consumption, the action point of the divert thrust is unavoidably deviated from the mass center, resulting in additional moment disturbance to the attitude.
- (3)
- The thrusts provided by the engines are fixedly connected to the interceptor.
2.2. Mathematical Model for Strapdown Interceptor Under Multi-Force Compound Control
2.3. Problem Analysis
- (1)
- Strong couplings. The effects of multiple control inputs are coupled, and the trajectory/attitude control systems are coupled.
- (2)
- High-order and strong nonlinearity. The relative order between the controlled outputs and the control inputs is high, and there are complex nonlinear relationships between states.
- (3)
- Overdriven control. The guidance and control system under the multi-force compound control is an overdriven control system, in which the number of control inputs exceeds the number of controlled outputs.
- (4)
- Dissimilar actuators compound control. Each actuator in the multi-force compound control system has different limitations and dynamic characteristics.
- (5)
- Unknown mismatched uncertainties. There are multiple disturbances in the controlled system that cannot be directly compensated for by the control inputs.
- (1)
- Reflecting the strongly coupled and nonlinear characteristics of the controlled system in the control law to improve the control performance.
- (2)
- Including the control allocation scheme that can simultaneously satisfy input constraints, save fuel and implement control commands.
- (3)
- Ensuring the stability and robustness of the control system.
3. IGC Model Under Multi-Force Compound Control Based on Koopman Operator
3.1. Koopman Operator-Based Linear Predictor
3.2. Linear IGC Model for Interceptor Under Multi-Force Compound Control
3.2.1. Data Collection
3.2.2. Determine Lifted States
3.2.3. Construct Linear IGC Model
4. Koopman Predictor-Based IGC Law
4.1. EDO for Koopman Predictor-Based IGC System
4.2. KPSMC-Based IGC Law Under Multi-Force Compound Control
4.3. Adaptive Weight-Based Control Allocation Scheme
- (1)
- Normalize the input range of actuators. Describing the control inputs in terms of a uniform standard, the control inputs are subjected to the following normalization transformation:Equation (33) transforms the absolute control input into the relative control input. Introducing the normalized control inputs into the adaptive weights is helpful for improving the fairness of the control allocation.
- (2)
- Coordinate the residual control capability. The control allocation scheme needs to avoid input saturation as much as possible. Additionally, considering that the fuel-consuming and non-fuel-consuming actuators simultaneously exist in the multi-force compound control system, the fuel margin should be considered in the control allocation scheme to avoid premature fuel exhaustion.Based on the above requirements, an adaptive weight based on a quadratic function with real-time control input as the benchmark is proposed as follows:
5. Simulation Studies
5.1. Accuracy of Koopman Predictor
5.2. Effectiveness of EDP-KPSMC
5.3. Effectiveness of Adaptive Weight-Based Control Allocation Scheme
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
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EDO-KPSMC | KPSMC | HOSMC | BCSMC | |
---|---|---|---|---|
Miss distance (m) | 0.37 | 0.25 | 0.12 | 0.10 |
Divert thrust impulse () | 5.87 | 5.83 | 7.54 | 8.99 |
Attitude thrust impulse () | 0.47 | 0.50 | 0.78 | 0.79 |
Adaptive Weight | Constant Weight | |
---|---|---|
Miss distance (m) | 0.62 | 0.62 |
Divert thrust impulse () | 8.31 | 8.47 |
Attitude thrust impulse () | 0.62 | 0.78 |
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Peng, Q.; Chen, G.; Guo, J.; Guo, Z. Koopman Predictor-Based Integrated Guidance and Control Under Multi-Force Compound Control System. Aerospace 2025, 12, 213. https://doi.org/10.3390/aerospace12030213
Peng Q, Chen G, Guo J, Guo Z. Koopman Predictor-Based Integrated Guidance and Control Under Multi-Force Compound Control System. Aerospace. 2025; 12(3):213. https://doi.org/10.3390/aerospace12030213
Chicago/Turabian StylePeng, Qian, Gang Chen, Jianguo Guo, and Zongyi Guo. 2025. "Koopman Predictor-Based Integrated Guidance and Control Under Multi-Force Compound Control System" Aerospace 12, no. 3: 213. https://doi.org/10.3390/aerospace12030213
APA StylePeng, Q., Chen, G., Guo, J., & Guo, Z. (2025). Koopman Predictor-Based Integrated Guidance and Control Under Multi-Force Compound Control System. Aerospace, 12(3), 213. https://doi.org/10.3390/aerospace12030213