Full State Constrained Stochastic Adaptive Integrated Guidance and Control for STT Missiles with Non-Affine Aerodynamic Characteristics

doi:10.1016/j.ins.2020.03.061

Information Sciences

Volume 529, August 2020, Pages 42-58

https://doi.org/10.1016/j.ins.2020.03.061 Get rights and content

Highlights

•
A novel stochastic adaptive IGC structure, which can guarantee all of the system states to be constrained and maintain desired guidance performance in the presence of the stochastic disturbances and aerodynamic uncertainties, is developed.
•
Different from the existing results, in this work the target is permitted to keep rapidly maneuvering with inaccessible and changing target accelerations.
•
As far as the authors know, it also the first IGC scheme for the STT missiles with the non-affine aerodynamic characteristics taken into consideration.

Abstract

Considering a class of skid-to-turn (STT) missiles with stochastic disturbances, non-affine aerodynamic characteristics and full state constraints, a novel full state constrained stochastic adaptive integrated guidance and control (IGC) scheme is proposed in this paper. By introducing several four-order Barrier Lyapunov functions (BLFs), the required state constraints of the stochastic closed-loop system are guaranteed to be never violated. With the aid of mean value theorem and neural network approximation, the non-affine aerodynamic characteristics can be handled. Moreover, by using several hyperbolic tangent functions and estimating the upper bounds of the uncertainties, the adverse effects caused by stochastic disturbances and unknown target maneuvers can be eliminated. The stochastic stability of the closed-loop system is proven based on Lyapunov theory. Numerical simulations results show the effectiveness and the advantages of the proposed algorithm.

Introduction

It is well-known that the practical plants are inevitable to suffer from the disturbances and the uncertainties. Motivated by practical and theoretical requirements and challenges, the controller design of uncertain systems has received much attention recently [1], [2]. The adaptive control methods [3], [4], [5], [6], the sliding mode controllers [7], [8], [9], the disturbance observer based control structures [10], [11], [12], have all been investigated for the systems with different kinds of uncertainties. Furthermore, the disturbances and uncertainties usually possess stochastic peculiarity in practical applications[13], [14], [15], [16], which make it difficult to design proper controllers [17], [18]. In the past years, fruitful results have been achieved for stochastic control and stochastic disturbances attenuation. In [19], a composite anti-disturbance method have been proposed for nonlinear systems with stochastic multiple disturbances. In [20], the stabilization problem of stochastic nonlinear systems suffering from noise with unknown covariance has been investigated. In [21], by using a augmented sliding mode observer, a fault-tolerant control structure has been established for Markovian jump stochastic systems. For a class of stochastic hybrid systems, a quadratic controller has been proposed in [22].

It should be noted that most of aforementioned results only concentrated on the stabilization of the plant’s states or the tracking errors [23]. However, a large amount of realistic applications are subjected to constraints and the violation of these constraints during operation may impose an adverse influence on the control quality [24], [25], [26], [27], [28], [29]. Recently, for the purpose of solving the control problem of nonlinear systems with output and state constraints, the Barrier Lyapunov functions have been employed in control design. For the nonlinear strict-feedback systems with the time-unvarying and time-varying constraints, two BLF-based adaptive controllers have been investigated in [30] and [31]. As a further development, to cope with the constrained nonlinear systems with completely unknown functions, a neural-network-based adaptive controllers has been presented using BLFs [32]. Moreover, aiming at a class of nonlinear pure-feedback systems in which the full state constraints are strictly required, an adaptive control structure is developed in [33] and only less adjustable parameters are used in the design. Most recently, to deals with the full state constrained tracking control problem of nonlinear systems with unknown time-varying delay, an effective BLF-based adaptive controller has been synthesized using Lyapunov - Krasovskii functions [34]. To just mention a few, a survey paper on constraint-handling ways of model predictive control has been well established in [35].

On the other hand, in the past decades, the integrated guidance and control (IGC) has received increasing attention. By viewing the guidance subsystem and control subsystem as a whole and directly generating the fin deflection commands, the IGC can overcome the problem of excessive design iterations and the high costs caused by designing the two subsystem separately [36]. In [37], an IGC structure has been constructed for the kinetic warheads using moving-mass actuators. For the ballistic-missile interceptors, an adaptive IGC approach has been proposed based on backstepping control technique [38]. In [39], a suboptimal θ-D control method has been employed in the design process of IGC system for missiles. In [40], by using the higher-order sliding mode control technique, an integrated autopilot and guidance algorithm has been developed for interceptors. Recently, the IGC methods for hypersonic vehicles and multiple missiles have been proposed in [41] and [42], respectively. By using the integrated design methods, the flight quality of the missiles can be improved for the synergistic relationships between the coupled subsystems can be fully exploited [43].

However, it has to be pointed out that the aforementioned IGC results only focused on the stabilization of the guidance variables, but the realistic constraints for the pitch rate and the normal acceleration were not taken into consideration. In fact, the states mentioned above are required to stay in proper intervals or the undesired system performance and system crash will be induced. Moreover, the disturbances in the flight process often possess stochastic features, and the conventional IGC methods are not capable of maintaining satisfactory guidance performance when the stochastic disturbances are taken into account. Besides, aerodynamic coefficients usually possess non-affine characteristics, but the corresponding IGC results have never been investigated. Therefore, in this paper, we focus on the full state constrained IGC design for the missiles subjected to stochastic disturbances and non-affine aerodynamic characteristics. The main challenge of this paper arise from how to establish the stochastic disturbed model for IGC systems and how to guarantee the state constraints under the stochastic uncertainties. By combining the four order Barrier Lyapunov functions and the adaptive control structure, the constraints on the pivotal states are guaranteed to be not violated. By making full use of the approximation ability of the neural networks and utilizing the bound adaptive control technique, the non-affine aerodynamic characteristics and the stochastic disturbances can be well coped with. In a word, the full state constrained stochastic adaptive IGC structure has been established and desired hit-to-kill interception can be maintained. Compared with the existing results, the proposed method in this paper possesses the following features:

•
A novel stochastic adaptive IGC structure, which can guarantee all of the system states to be constrained and maintain desired guidance performance in the presence of the stochastic disturbances and aerodynamic uncertainties, is developed.
•
Different from the existing results, in this work the target is permitted to keep rapidly maneuvering with inaccessible and changing target accelerations.
•
As far as the authors know, it also the first IGC scheme for the STT missiles with the non-affine aerodynamic characteristics taken into consideration.

Section snippets

System model

According to [44], the nonlinear longitudinal model of missile can be modeled as follows. $\begin{matrix} \dot{α} & = & q + \frac{- F_{x} \sin α + F_{z} \cos α}{m V} \\ \dot{V} & = & \frac{F_{x} \cos α + F_{z} \sin α}{m} \\ \dot{q} & = & \frac{M}{I_{y y}} \\ \dot{θ} & = & q \\ {\dot{n}}_{L} & = & \frac{- n_{L} + V q}{T_{α}} \\ γ_{M} & = & θ - α \end{matrix}$ where α, q, θ represent the angle of attack, the pitch rate and the pitch angle of the missile, respectively. V, n_L and γ_M denote the velocity, normal acceleration and flight-path angle of missile. m and I_yy denote the mass of the missile and moment of inertia around the pitch axis. The aerodynamic forces are represented by F_x, F_z, and the

Stochastic Adaptive Full State Constrained IGC Structure

In view of $σ = V_{λ} - c_{0} \sqrt{r},$ we can get the stochastic dynamics of σ as $d σ = [- \frac{V_{λ} V_{r}}{r} + A_{T λ} - \cos (λ - γ_{M}) n_{L} - \frac{c_{0} V_{r}}{2 \sqrt{r}}] d t + Δ_{r} d ζ_{r}$ Then, by considering the stochastic differential equation of n_L and q given in (7), we can obtain that $\begin{matrix} d σ & = & [F_{σ} + B_{σ} n_{L} + A_{T λ}] d t + Δ_{r} d ζ_{r} \\ d n_{L} & = & [F_{n_{L}} + B_{n_{L}} q] d t + Δ_{n_{L}} d ζ_{n_{L}} \\ d q & = & F_{q} c_{m} (α, M_{m}, b_{δ} δ_{c} + Δ_{δ}) d t + Δ_{q} d ζ_{q} \end{matrix}$ where $\begin{matrix} F_{σ} & = & - \frac{V_{λ} V_{r}}{r} - \frac{c_{0} V_{r}}{2 \sqrt{r}}, B_{σ} = - \cos (λ - γ_{M}) \\ F_{n_{L}} & = & \frac{- n_{L}}{T_{α}}, B_{n_{L}} = \frac{V}{T_{α}} \\ F_{q} & = & \frac{0.5 ρ V^{2} S l}{I_{y y}} \end{matrix}$ It should be noted that under the practical work condition, there often exist measurement uncertain-ties of B_σ and $B_{n_{L}}$ . To deal with this issue,

Stability analysis

The stability of the closed system by using the proposed method can be demonstrated by the following theorem.

Theorem 1

Consider the stochastic nonlinear system (15) with control laws (18), (24) , (32) and the updating laws (20), (26) (33). If the initial conditions satisfy $∥ σ (0) ∥ \leq ω_{σ}, ∥ z_{n_{L}} (0) ∥ \leq ω_{n_{L}}, ∥ z_{q} (0) ∥ \leq ω_{q}$ , then it can be guaranteed that all the signals are semi-globally uniformly ultimately bounded, and throughtout the convergence process, all the constraints are not violated.

Proof. Consider the

Simulations

In this section, we validate the effectiveness and performance of the proposed stochastic full state constrained IGC method. In the simulation, a skid-to-turn missile is required to intercept a maneuvering target. The parameters of the missile is given in Table 1.

The initial missile normal acceleration is $n_{L} (0) = 25 m / s^{2}$ . The line of sight angle is set as $λ (0) = 0.5 rad$ ; the range along the line of sight $r (0) = 6177 m$ . The admissible ranges of the system are set as $ω_{σ} = 25, ω_{n_{L}} = 100, ω_{q} = 5$ . The aerodynamic

Conclusions

In this paper, a full state constrained IGC design problem is addressed for the missiles suffering from stochastic disturbances and non-affine aerodynamic characteristics. A novel stochastic adaptive IGC structure, which can guarantee all of the system states to be constrained and maintain desired tracking performance in the presence of the time-varying target maneuvering, is developed. By combining the four-order Barrier Lyapunov functions and the adaptive control structure, the constraints

Author statement

I have made substantial contributions to the conception or the design of the work, or the acquisition, analysis, or the interpretation of data for the work, and I have drafted the work or revised it critically for important intellectual content, and I agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

All persons who have made substantial contributions to the work

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants no. 61473226 and no 61503302.

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Full State Constrained Stochastic Adaptive Integrated Guidance and Control for STT Missiles with Non-Affine Aerodynamic Characteristics

Highlights

Abstract

Introduction

Section snippets

System model

Stochastic Adaptive Full State Constrained IGC Structure

Stability analysis

Simulations

Conclusions

Author statement

Acknowledgements

Automatica

Automatica

International Journal of Robust and Nonlinear Control

Automatica

Automatica

Control Theory and Applications Iet

Systems Science and Control Engineering

Automatica

Journal of the Franklin Institute

Applied Thermal Engineering

International Journal of Electrical Power & Energy Systems

Energy

Applied Thermal Engineering

Solar Energy

Automatica

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IEEE Transactions on Neural Networks

IEEE Transactions on Cybernetics

Control Engineering Practice

Journal of Guidance, Control, and Dynamics

Aerospace Science and Technology

Journal of Guidance, Control, and Dynamics

Neurocomputing