SUMMARYIntegrated guidance and control of an elastic flight vehicle based on constrained robust model predictive control is proposed. The design is based on a partial state feedback control law that minimizes a cost function within the framework of linear matrix inequalities. It is shown that the solution of the defined optimization problem stabilizes the nonlinear plant. Nonlinear kinematics and dynamics are taken into account, and internal stability of the closed-loop nonlinear system is guaranteed. The performance and effectiveness of the proposed integrated guidance and control against non-maneuvering and weaving targets are evaluated using computer simulations.
This paper presents the design of a new robust model predictive control algorithm for nonlinear systems represented by a linear model with unstructured uncertainty. The linear model is obtained by linearizing the nonlinear system at an operating point and the difference between the nonlinear and linear model is considered as a Lipschitz nonlinear function. The controller is designed for the linear model, which fulfills the stabilization condition for the nonlinear term. Unlike previous studies that have not considered a valid Lipschitz matrix of nonlinear term in the design process, we propose an algorithm in this paper in which it is considered. Therefore, the closed loop stability of the nonlinear system is guaranteed. A novel SOS optimization problem to determine design parameters is introduced, which leads to improved closed‐loop performance in comparison to a trial and error tuning procedure. Furthermore, an algorithm is presented to enlarge the region of attraction for the nonlinear closed‐loop system. Stability is improved by checking some additional conditions if which the system may be unstable if not considered. The validity of the proposed algorithm is confirmed by examples.
Purpose
The purpose of this paper is to design an adaptive nonlinear controller for a nonlinear system of integrated guidance and control.
Design/methodology/approach
A nonlinear integrated guidance and control approach is applied to a homing, tail-controlled air vehicle. Adaptive backstepping controller technique is used to deal with the problem, and the Lyapanov theory is used in the stability analysis of the nonlinear system. A nonlinear model of normal force coefficient is obtained from an existing nonlinear model of lift coefficient which was validated by open loop response. The simulation was performed in the pitch plane to prove the benefits of the proposed scheme; however, it can be readily extended to all the three axes.
Findings
Monte Carlo simulations indicate that using nonlinear adaptive backstepping formulation meaningfully improves the performance of the system, while it ensures stability of a nonlinear system.
Practical implications
The proposed method could be used to obtain better performance of hit to kill accuracy without the expense of control effort.
Originality/value
A nonlinear adaptive backstepping controller for nonlinear aerodynamic air vehicle is designed and guaranteed to be stable which is a novel-based approach to the integrated guidance and control. This method makes noticeable performance improvement, and it can be used with hit to kill accuracy.
In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non-linear systems composed of a linear constant part followed by a non-linear term. We characterize the maximal admissible set for the non-linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state-feedback RMPC law is derived off-line for Lipschitz non-linear systems. The state-feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed-loop robust stability. Most of the computational burdens are moved off-line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on-line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.
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