Skid-to-turn Research Articles

Reinforcement learning-adaptive fault-tolerant IGC method for a class of aircraft with non-affine characteristics and multiple uncertainties

Abstract In this paper, a brand-new adaptive fault-tolerant non-affine integrated guidance and control method based on reinforcement learning is proposed for a class of skid-to-turn (STT) missile. Firstly, considering the non-affine characteristics of the missile, a new non-affine integrated guidance and control (NAIGC) design model is constructed. For the NAIGC system, an adaptive expansion integral system is introduced to address the issue of challenging control brought on by the non-affine form of the control signal. Subsequently, the hyperbolic tangent function and adaptive boundary estimation are utilised to lessen the jitter due to disturbances in the control system and the deviation caused by actuator failures while taking into account the uncertainty in the NAIGC system. Importantly, actor-critic is introduced into the control framework, where the actor network aims to deal with the multiple uncertainties of the subsystem and generate the control input based on the critic results. Eventually, not only is the stability of the NAIGC closed-loop system demonstrated using Lyapunov theory, but also the validity and superiority of the method are verified by numerical simulations.

Nonlinear transformed function-based adaptive finite-time integrated guidance and control design with full state constraints

This paper proposes a novel finite-time integrated guidance and control (IGC) design for skid-to-turn (STT) missiles, taking full state constraints into account. Firstly, the actuator saturation is converted into a state constraint. Secondly, to handle full state constraints effectively, the “non-constrained” IGC (NCIGC) model is constructed by combining the IGC model with a permissible set of states and applying a nonlinear transformed function. Thirdly, a finite-time full state constraints IGC scheme based on the NCIGC model is presented. According to Lyapunov stability theory, the proposed IGC method is verified to ensure that all states of the IGC model converge to a small neighborhood near zero within a finite time while satisfying the predefined state constraints. Finally, numerical simulations are performed to demonstrate the effectiveness and robustness of the proposed IGC scheme.

Three-dimensional approximate cooperative integrated guidance and control with fixed-impact time and azimuth constraints

A novel three-dimensional (3D) approximate cooperative integrated guidance and control (ACIGC) scheme based on backstepping control (BC), sliding mode control (SMC), dynamic surface control (DSC), and a 3D reduced-order extended state observer (ESO) for multiple hypersonic skid-to-turn (STT) missiles simultaneously attacking ground-maneuver targets is proposed in this study, which considers a fixed-impact azimuth and time constraints. First, we established a novel integrated guidance and control (IGC) model that includes the missile-target relative distance and azimuth based on the missile-target engagement dynamics, attitude dynamics, and first-order delay dynamics of the rudder. It is a 3D fifth-order strict-feedback time-varying nonlinear model with mismatched uncertainties. Second, a 3D ACIGC scheme was designed, where a cooperative strategy was designed by transforming a fixed-impact time constraint into a nominal range-to-go constraint. The IGC model consists of seeker, guidance, angle-of-attack, attitude, and rudder subsystems based on the BC, and the SMC designs each subsystem. The DSC obtains the derivatives of virtual control commands, which solves the “differential explosion” caused by the BC. The unknown target acceleration, unmodeled parts of the system states, perturbations caused by time-varying parameters, and external disturbances are regarded as lumped disturbances, which are estimated and compensated for by the 3D reduced-order ESO to improve the robustness. Subsequently, the closed-loop system was proven to be stable, and the system states were ultimately uniformly bounded using Lyapunov theory. Finally, the simulation results of three missiles attacking a simultaneously ground-maneuvering target and Monte Carlo simulations demonstrated the effectiveness and robustness of the proposed ACIGC scheme.

Three-dimensional low-order fixed-time integrated guidance and control for STT missile with strap-down seeker

Strap-down seeker is rigidly fixed onto the missile body, which results in detection information being coupled to the missile’s attitude and having a narrow field-of-view (FOV). During the terminal guidance flight, attitude adjustment of the missile may lose the target’s lock and reduce interception accuracy. Therefore, this paper investigates three-dimensional integrated guidance and control (IGC) under the constraints of the FOV and roll angle for skid-to-turn (STT) missile with strap-down seeker. A new low-order IGC model is constructed by establishing a second-order model of body line-of-sight (BLOS) angle based on strap-down decoupling theory and combining it with the second-order roll angle equation. Furthermore, a low-order fixed-time IGC scheme is developed using the integral barrier Lyapunov function (iBLF) to limit BLOS and roll angles. Fixed-time filter, which avoids the “complexity explosion” caused by conventional back-stepping technique, is utilized for obtaining virtual control command and its derivative. A fixed-time disturbance observer is introduced to compensate for the lumped disturbance. According to Lyapunov stability theory, it is proven that the proposed IGC scheme can make the closed-loop system converge within a fixed time. Finally, the effectiveness and robustness of the IGC scheme are verified by various numerical simulations.

Robust Adaptive Composite Learning Integrated Guidance and Control for Skid-to-Turn Interceptors Subjected to Multiple Uncertainties and Constraints

This paper investigates a novel robust adaptive dynamic surface control scheme based on the barrier Lyapunov function (BLF), online composite learning, disturbance observer, and improved saturation function. It is mainly designed for a class of skid-to-turn (STT) interceptor integrated guidance and control (IGC) design problems under multi-source uncertainties, state constraints, and input saturation. The serial-parallel estimation model used in this study estimates the system states and provides “critic” information for the neural network and disturbance observer; then, these three are combined to realize online composite learning of the multiple uncertainties of the system and improve the interception accuracy. In addition, the state and input constraints are resolved by adopting the BLF and the improved saturation function, while the design of the auxiliary system ensures stability. Finally, a series of simulation results show that the proposed IGC scheme with a direct-hit intercept strategy achieves a satisfactory effect, demonstrating the validity and robustness of the scheme.

Field-to-View Constrained Integrated Guidance and Control for Hypersonic Homing Missiles Intercepting Supersonic Maneuvering Targets

An integrated guidance and control (IGC) scheme considering the field-of-view (FOV) constraint is proposed in this paper for hypersonic skid-to-turn (STT) missiles with a strapdown seeker intercepting a high-speed maneuvering target, which is based on the backstepping control (BC), barrier Lyapunov function (BLF), sliding mode control (SMC), dynamic surface control (DSC), and reduced-order extended state observer (ESO). First, a fifth-order strict feedback IGC model considering the rudder delay dynamics is derived, which also considers the drag effect on the axial velocity. Second, the missile guidance control system based on the BC consists of seeker, guidance, angle-of-attack, attitude, and rudder subsystems. The seeker subsystem was designed based on the BLF, and the other four subsystems were designed based on the SMC. The system-lumped disturbances, including unknown target maneuvers, unmodeled parts, perturbations caused by aerodynamic parameter variations, and external disturbances, were estimated and compensated for using the reduced-order ESO. The DSC prevented the “differential explosion” caused by virtual control commands introduced by the BC. Subsequently, the stability of the closed-loop system was strictly proven using the Lyapunov theory, and the boundedness of the FOV angle was strictly derived. Finally, the simulation results demonstrated the effectiveness and robustness of the proposed IGC scheme.

Three-dimensional integrated guidance and control with input saturation and impact angle constraints

Considering the problem of a skid-to-turn (STT) interceptor attacking maneuvering targets in the three-dimensional space, a new integrated guidance and control (IGC) law with the constraints of impact angles and input saturation is developed. To achieve the finite-time convergence and satisfactory input characteristics, a time-varying sliding mode control (TVSMC) method is presented based on a time base generator function. To this end, the IGC scheme is developed based on the TVSMC and the back-stepping. At each step, the derivative of the virtual signal is approximated by a tracking differentiator. Meanwhile, an auxiliary compensation system is designed to reduce the adverse effect raised from the saturation error. Moreover, the modeling uncertainties and disturbances are attenuated effectively by using fractional power extended state observers to estimate them. The closed-loop system states are proved to be uniformly ultimately bounded and the controlled states are proved to converge into small neighborhoods of the origin at the interception time. Finally, the performance of the presented IGC law is verified through numerical simulations.

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

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.

Three-dimensional integrated guidance and control for strap-down missiles considering seeker’s field-of-view angle constraint

This paper investigates a novel three-dimensional (3D) integrated guidance and control (IGC) method for skid-to-turn (STT) missiles with strap-down seeker. Firstly, a nonlinear IGC model considering seeker’s field-of-view (FOV) constraint is built by employing the strap-down decoupling model, based on which the strict feedback state equation with matched and unmatched uncertainties is derived. Secondly, to handle the FOV angle and the roll angle constraints, an IGC law is proposed by combining dynamic surface control (DSC) approach with integral barrier Lyapunov function (iBLF), by which an adaptive law is employed to estimate the square of the disturbance bound. Finally, the uniform ultimately boundedness of the closed-loop system is proved strictly based on the Lyapunov stability theory, and the effectiveness and robustness of the proposed IGC scheme are illustrated with numerical simulations.

Fuzzy adaptive fault tolerant IGC method for STT missiles with time-varying actuator faults and multisource uncertainties

This paper studies the integrated guidance and control (IGC) problem for a class of skid-to-turn (STT) missiles subjected to rapidly changing actuator failures and coupled multisource uncertainties. Meanwhile, during interception, the target is allowed to possess unknown and changeable maneuver accelerations. By analyzing the dominating factors in the IGC system, a nonlinear uncertain strict-feedback system suffering from matched and mismatched uncertainties is utilized to describe the IGC dynamics. Furthermore, for each subsystem, the control gain functions and their boundaries are assumed unknown, which make it difficult to design the controllers. By using a hyperbolic tangent function and estimating the bounds of the lumped disturbances, the time-varying multisource uncertainties can be handled. To compensate the unknown nonlinearities existing in the IGC system, several fuzzy logic systems are established. Furthermore, a number of reciprocal adaptive laws are developed such that unwanted effects caused by the unknown control gain functions and changing actuator gain faults can be surmounted. As a result, a novel fault tolerant IGC structure is constructed and satisfactory hit-to-kill interception performance can be obtained. Finally, the numerical simulations are provided to verify the validity and advantage of the proposed method.

Integrated guidance and control with partial state constraints and actuator faults

In this paper, a novel adaptive integrated guidance and control (IGC) scheme is proposed for skid-to-turn (STT) missile with partial state constraints and actuator faults. Considering the strict-feedback form of the IGC model, the dynamic surface control (DSC) approach is adopted to design the IGC scheme. To prevent the attack angle, sideslip angle and velocity deflection angle from violating the constraints, the barrier Lyapunov function (BLF) and modified saturation function are employed in the IGC design procedure. Moreover, an auxiliary system is constructed to remove the adverse effects that caused by the modified saturation function. The adaptive laws are constructed to estimate the actuation effectiveness of actuators and the upper bounds of lumped uncertainties in the IGC model. It is theoretically shown that all signals in the closed-loop system are bounded while the state constraints are not violated in presence of actuator faults and uncertainties. Numerical simulation results are presented to verify the effectiveness and robustness of the proposed IGC scheme.

Impact Angle Constrained Three-Dimensional Integrated Guidance and Control Based on Fractional Integral Terminal Sliding Mode Control

In this paper, considering a class of skid-to-turn (STT) missile with impact angle constraint to intercept the maneuvering target, a three-dimensional integrated guidance and control law based on the fractional integral terminal sliding mode control (FITSMC) scheme is proposed. Firstly, a three-dimensional integrated guidance and control model is established for missile-target relative motion and nonlinear missile dynamics with multiple system uncertainties and unknown disturbances. Secondly, in order to achieve the desired impact angle in finite-time without singularity, a novel nonsingular FITSMC scheme is employed to construct the sliding surface, and a modified filter is applied to dynamic surface control design. Also, an extended state observer is introduced to estimate and compensate the system uncertainties and unknown disturbances. Then, a robust integrated guidance and control scheme with impact angle constraint is developed using aforementioned techniques. Furthermore, the finite-time stability of the closed-loop system is proven based on Lyapunov theory. Finally, the effectiveness and robustness of the proposed integrated guidance and control algorithm are verified through numerical simulations.

Adaptive sliding mode autopilot design for skid-to-turn missile model with uncertainties

This paper presents an adaptive sliding mode controller for a skid-to-turn missile model with uncertainties. It is assumed that missile velocity, aerodynamic parameters and dynamics are non-constant or fast-varying. Although a general sliding mode controller inherently robust in this situation, the performance of a general sliding mode control scheme is not good if the aerodynamics parameter and the center of gravity position are not exactly known whereas the adaptive controller estimates some uncertainties, such as the aerodynamics parameter and the center of gravity. Therefore, the sliding mode control scheme and the adaptive control scheme are combined to ensure the performance. To verify the proposed nonlinear controller, numerical simulations are performed for a missile which is maneuvered widely in various scenarios. The proposed adaptive sliding mode control scheme has comparatively better performance than other control scheme. This claim is substantiated through the simulation of the Skid-To-Turn (STT) missile model whose aerodynamic parameters and dynamics are suddenly changed during the boost phase.

Hybrid BTT/STT missile autopilot design

PurposeTraditional skid-to-turn (STT) missile control mode is adopted mostly, but with the improvement of requirements for mobility and the emergence of new aerodynamic layout, a bank-to-turn (BTT) control mode gradually shows a greater advantage. However, the BTT missile also has certain defects, for example, when attacking against a maneuvering target and at the last section of guidance, the maximum lifting surface position of the missile needs to be adjusted frequently, thereby increasing the difficulty of control as well as introducing high-frequency noise.Design/methodology/approachBased on respective characteristics of the two control modes, this paper puts forward a hybrid autopilot design method based on nonlinear dynamic inversion. Firstly, the method converts overload instructions into corresponding angle instructions through the design of hybrid control guidance logic; secondly, based on the nonlinear dynamic inversion algorithm and combined with the fast-changing circuit/slowly changing circuit, a hybrid controller is designed; finally, combined with the missile mathematical model and actuator, it forms a autopilot design closed loop.FindingsThe simulation result shows that the non-linear dynamic inverse-based BTT/STT hybrid controller can input a track command well, normal overload and roll angle tracking performance have more advantages than the hybrid controller designed on the basis of classical control method in terms of overshooting and hysteretic characteristics.Originality/valueThe paper puts forward a new BTT/STT hybrid control method which has both the high mobile ability of the BTT missile and the precise control ability of the STT missile, which can adapt to the more complicated fighting environment. And, the method can effectively weaken the impact of the transformation of the control mode on the system.

Robust autopilot design for STT missiles with multiple disturbances using twisting control

In this paper, a novel second-order sliding mode control (NSOSMC) scheme with finite time convergence is proposed for the autopilot design of skid-to-turn (STT) missiles considering coupling effects to track the desired maneuver commands. Firstly, the control system formulation is developed based on the mathematical model for nonlinear missile dynamics with system uncertainties and unknown multiple disturbances. Secondly, the NSOSMC scheme is developed by using a PID sliding mode surface with twisting control algorithm, which is to suppress the system uncertainties and unknown external disturbances, and to eliminate the chattering phenomenon. Then, the proposed NSOSMC law is proved to be finite time convergent to the origin. Finally, the effectiveness and robustness of the proposed NSOSMC scheme is verified through the numerical simulations with comparisons.

Roll-pitch-yaw autopilot design for nonlinear time-varying missile using partial state observer based global fast terminal sliding mode control

The acceleration autopilot design for skid-to-turn (STT) missile faces a great challenge owing to coupling effect among planes, variation of missile velocity and its parameters, inexistence of a complete state vector, and nonlinear aerodynamics. Moreover, the autopilot should be designed for the entire flight envelope where fast variations exist. In this paper, a design of integrated roll-pitch-yaw autopilot based on global fast terminal sliding mode control (GFTSMC) with a partial state nonlinear observer (PSNLO) for STT nonlinear time-varying missile model, is employed to address these issues. GFTSMC with a novel sliding surface is proposed to nullify the integral error and the singularity problem without application of the sign function. The proposed autopilot consisting of two-loop structure, controls STT maneuver and stabilizes the rolling with a PSNLO in order to estimate the immeasurable states as an output while its inputs are missile measurable states and control signals. The missile model considers the velocity variation, gravity effect and parameters’ variation. Furthermore, the environmental conditions’ dynamics are modeled. PSNLO stability and the closed loop system stability are studied. Finally, numerical simulation is established to evaluate the proposed autopilot performance and to compare it with existing approaches in the literature.

Impact angle constrained three-dimensional integrated guidance and control for STT missile in the presence of input saturation

Considering a class of skid-to-turn (STT) missile with fixed target and constrained terminal impact angles, a novel three-dimensional (3D) integrated guidance and control (IGC) scheme is proposed in this paper. Based on coriolis theorem, the fully nonlinear IGC model without the assumption that the missile flies heading to the target at initial time is established in the three-dimensional space. For this strict-feedback form of multi-variable system, dynamic surface control algorithm is implemented combining with extended observer (ESO) to complete the preliminary design. Then, in order to deal with the problems of the input constraints, a hyperbolic tangent function is introduced to approximate the saturation function and auxiliary system including a Nussbaum function established to compensate for the approximation error. The stability of the closed-loop system is proven based on Lyapunov theory. Numerical simulations results show that the proposed integrated guidance and control algorithm can ensure the accuracy of target interception with initial alignment angle deviation and the input saturation is suppressed with smooth deflection curves.

Fuzzy adaptive disturbance observer-based robust adaptive control for skid-to-turn missiles

This paper proposes a robust adaptive control method for the acceleration control of tail-controlled STT (skid-to-turn) missiles, using a fuzzy adaptive disturbance observer. The dynamics with disturbances are analyzed in the general form, as well as aerodynamic uncertainties. A fuzzy adaptive disturbance observer and a robust adaptive controller are then designed. Stability analysis and simulation results demonstrate the effectiveness of the proposed method for the STT missile systems, against both aerodynamic uncertainties, and disturbances.

Three-dimensional nonlinear coupling guidance for hypersonic vehicle in dive phase

Three-dimensional (3D) nonlinear diving guidance strategy considering the coupling between longitudinal and lateral motions for hypersonic vehicle is investigated in this paper. It constructs the complete nonlinear coupling motion equation without any approximations based on diving relative motion relationship directly, and converts it into linear state space equation with the same relative degree by feedback linearization. With the linear equation, slide mode control with strong robustness is employed to design the guidance law, and 3D diving guidance law which can satisfy terminal impact point and falling angle constraints with high precision is obtained by substituting the previous control law into the origin nonlinear guidance system. Besides, regarding lateral overload as the standard, hybrid control strategy which can take full advantage of the excellent characters of both bank-to-turn (BTT) and skid-to-turn (STT) controls is designed to improve the guidance accuracy further. Finally, the results of CAV-H vehicle guidance test show that the algorithm can realize high accuracy guidance even if serious motion coupling exists, and has strong robustness to the path disturbances and navigation errors as well.

New Structure for an Aerodynamic Fin Control System for Tail Fin-Controlled STT Missiles

This paper presents a new design method for an aerodynamic fin-control system for tail-fin controlled skid to turn (STT) missiles. The performance of the actuation system plays a decisive role in determining the performance of the flight control system for a highly maneuverable missile. To control the missiles by aerodynamics, control surfaces, sometimes called fins, are used. Deflection angles of these fins are the control variables of aerodynamics, but aerodynamicists prefer to use analytic variables called aileron, elevator, and rudder instead of these physical variables because these three analytic variables dominantly influence the roll, pitch, and yaw motion of the missile, respectively; and each can be considered a linear combination of four fin deflection angles. On that basis, roll, pitch, and yaw autopilots for controlling the attitudes or lateral acceleration of the missile are designed, and aileron, elevator, and rudder commands, respectively, are generated as consequence outputs of each autopilot. In the existing fin-actuation control scheme for the typical tail-fin controlled cruciform missiles, these outputs are distributed to four fin defection commands. After that, the four fins are actuated by fin controllers so that their deflections follow the commands. This paper shows that such control schemes can cause a significant deterioration in flight control system performance when fin-actuators have certain physical constraints such as slew rate, voltage, or current limit, or have an uncertainty of actuator dynamics, and proposes a new control scheme that alleviates such problems. This scheme can be widely applied to various fin-actuation control systems. But in this paper, for convenience, a tail-fin controlled cruciform missile is used as the example, and the proposed control scheme is shown to give better performance than the existing one.