Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

Minimum eigenvalue based adaptive fault compensation for hypersonic vehicles

The attitude tracking control problem is addressed for hypersonic vehicles under actuator faults that may cause an uncertain time-varying control gain matrix.An adaptive compensation scheme is developed to ensure system stability and asymptotic tracking properties,including a kinematic control signal and a dynamic control signal.To deal with the uncertainties of the control gain matrix,a new positive definite one is constructed.The minimum eigenvalue of such a new control gain matrix is estimated.Simulation results of application to an X-33 vehicle model verify the effectiveness of the proposed minimum eigenvalue based adaptive fault compensation scheme.

Continuous Sliding Mode Controller with Disturbance Observer for Hypersonic Vehicles

In this paper, a continuous sliding mode controller with disturbance observer is proposed for the tracking control of hypersonic vehicles to suppress the chattering. The finite time disturbance observer is involved to make that the continuous sliding mode controller has the property of disturbance rejection. Due to continuous terms replacing the discontinuous term of traditional sliding mode control, switching modes of velocity and altitude firstly arrive at small regions with respect to disturbance observation errors. Switching modes keep zero and velocity and altitude asymptotically converge to their reference commands after disturbance observation errors disappear. Simulation results have proved the proposed method can guarantee the tracking of velocity and altitude with continuous sliding mode control laws, and also has the fast convergence rate and robustness. © 2014 Chinese Association of Automation.

Experimental demonstration of a new concept of drag reduction and thermal protection for hypersonic vehicles

A new idea of drag reduction and thermal protection for hypersonic vehicles is proposed based on the combination of a physical spike and lateral jets for shockreconstruction. The spike recasts the bow shock in front of a blunt body into a conical shock, and the lateral jets work to protect the spike tip from overheating and to push the conical shock away from the blunt body when a pitching angle exists during flight. Experiments are conducted in a hypersonic wind tunnel at a nominal Mach number of 6. It is demonstrated that the shock/shock interaction on the blunt body is avoided due to injection and the peak pressure at the reattachment point is reduced by 70% under a 4° attack angle.

Research progress on thermal protection materials and structures of hypersonic vehicles

Hypersonic vehicles represent future trends of military equipments and play an important role in future war. Thermal protection materials and structures, Which relate to the safety of hypersonic vehicles, are one of the most key techniques in design and manufacture of hypersonic vehicles. Among these materials and Structures, such as metallic temperature protection structure, the temperature ceramics and carbon/carbon composites are usually adopted in design. The recent progresses of research and applica- tion of ultra-high temperature materials in preparation, oxidation resistance, mechanical and physical characterization are summarized.

Back-Stepping Control for Flexible Air-Breathing Hypersonic Vehicles Based on Uncertainty and Disturbance Estimator

A theoretical framework of nonlinear flight control for a flexible air-breathing hypersonic vehicle(FAHV)is proposed in this paper.In order to suppress the system uncertainty and external disturbance,an uncertainty and disturbance estimator(UDE)based back-stepping control strategy is designed for a dynamic state-feedback controller to provide stable velocity and altitude tracking.Firstly,the longitudinal dynamics of FAHV is simplified into a closure loop form with lumped uncertainty and disturbance.Then the UDE is applied to estimate the lumped uncertainty and disturbance for the purpose of control input compensation.While a nonlinear tracking differentiator is introduced to solve the problem of“explosion of term”in the back-stepping control.The stability of the UDE-based control strategy is proved by using Lyapunov stability theorem.Finally,simulation results are presented to demonstrate the capacity of the proposed control strategy.

Multi-objective reentry trajectory optimization method via GVD for hypersonic vehicles

In the constrained reentry trajectory design of hypersonic vehicles, multiple objectives with priorities bring about more difficulties to find the optimal solution. Therefore, a multi-objective reentry trajectory optimization (MORTO) approach via generalized varying domain (GVD) is proposed. Using the direct collocation approach, the trajectory optimization problem involving multiple objectives is discretized into a nonlinear multi-objective programming with priorities. In terms of fuzzy sets, the objectives are fuzzified into three types of fuzzy goals, and their constant tolerances are substituted by the varying domains. According to the principle that the objective with higher priority has higher satisfactory degree, the priority requirement is modeled as the order constraints of the varying domains. The corresponding two-side, single-side, and hybrid-side varying domain models are formulated for three fuzzy relations respectively. By regulating the parameter, the optimal reentry trajectory satisfying priorities can be achieved. Moreover, the performance about the parameter is analyzed, and the algorithm to find its specific value for maximum priority difference is proposed. The simulations demonstrate the effectiveness of the proposed method for hypersonic vehicles, and the comparisons with the traditional methods and sensitivity analysis are presented.

Calculation of Aerodynamic Characteristics of Hypersonic Vehicles Based on the Surface Element Method

A program for calculating the aerodynamic properties of hypersonic vehicles based on the surface element method was developed using the general-purpose programming language C++. The calculated values of lift coefficients, drag coefficients, and surface pressure coefficients are discussed with the results of wind tunnel experiments using the HL-20 lift body and the NASA hypersonic aircraft STS Columbia OV-102 as research subjects. Finally, the results of the experimental and wind tunnel studies of the aerodynamic characteristics of the HL-20 lift body at an altitude of 65 km and Mach numbers of 6 and 10 Ma are discussed. The maximum error in the aerodynamic characteristics at 6 Ma does not exceed 3%, consistent with the results. The maximum error at 10 Ma occurs in the 11° - 14° angle of attack and does not exceed 10%, which is still within the error tolerance. The STS results for NASA’s hypersonic aircraft were also tested using this procedure. Experimental aerodynamic data for the Colombian OV-102 aircraft. The results show that the program takes only 10 minutes to calculate the results, with no more than 2% error from the wind tunnel experimental results.

Review on heat-to-power conversion technologies for hypersonic vehicles

Hypersonic vehicles have enormous military and economic value,while their power and thermal protection demands will increase substantially with the rise in Mach number and duration.Converting the tremendous high-quality heat on the vehicle surface and engine wall into electrical energy through heat-to-power technologies will not only play a role in thermal protection,but also supply power for the vehicle.This paper provides a comprehensive review of heat-to-power conversion technologies on hypersonic vehicles,including the indirect conversion of Brayton and Rankine cycles,direct conversion of thermoelectric materials,and combined conversion.For the open Brayton cycle with hydrocarbon fuel as the working fluid,the Power-to-Weight Ratio(PWR)can achieve the highest,at around 1.8,due to the high PWR of the hydrocarbon fuel turbine and the few components of the system.However,its work capacity is limited by the flow rate of the supplied fuel.The closed Brayton cycle can maintain a relatively high PWR,ranging from 0.2 to 0.8,while achieving relatively high output power and conversion efficiency.The Rankine cycle has a higher PWR,its range is close to that of the closed Brayton cycle,peaking at about 0.88.The thermoelectric materials technology has a small power generation level,making it more suitable for scenarios with low power demand.This review provides a basis for selecting and developing heat-to-power conversion technologies on hypersonic vehicles.

Cooperative game penetration guidance for multiple hypersonic vehicles under safety critical framework

The rapid development of the anti-missile weapon technology brings new challenges to the cooperative penetration strategy solution and the guidance law design for Hypersonic Vehicles(HVs).This paper studies the coordinated game penetration guidance problem for multiple hypersonic vehicles faced with space threat areas.A scheme for seeking cooperative game penetration guidance strategy under safety critical control framework is presented.In this scheme,a multiHV cooperative game model is proposed in a minimum optimization form which can simplify the solving process and accelerate the computing speed.Then,a second-order control barrier function is developed to transform the implicit nonlinear constraints of the proposed model into linear ones.In order to obtain better performance of guidance strategy,a composite guidance law under the safety critical control framework is presented to allocate guidance strategies appropriately in the whole process.It is shown that the proposed scheme can guarantee successful penetration while avoiding threat areas.Finally,a comparative simulation with a two-on-three game is conducted to verify the effectiveness of the proposed method.

Resilient control of flexible hypersonic vehicles against unmatched distributed faults

This paper studies a robust fault compensation and vibration suppression problem of flexible hypersonic vehicles.The controlled plant is represented by a cascade system composed of a nonlinear Ordinary Differential Equation(ODE)and an Euler-Bernoulli Beam Equation(EBBE),in which the vibration dynamics is coupled with the rigid dynamics and suffers from distributed faults.A state differential transformation is introduced to transfer distributed faults to an EBBE boundary and a longitudinal dynamics is refined by utilizing T-S fuzzy IF-THEN rules.A novel T-S fuzzy based fault-tolerant control algorithm is developed and related stability conditions are established.The robust exponential stability and well-posedness are proved by using the modified l_(0)-semigroup based Lyapunov direct approach.A simulation study on the longitudinal dynamics of flexible hypersonic vehicles effectively verifies the validity of the developed theoretical results.

Adaptive fault-tolerant control for non-minimum phase hypersonic vehicles based on adaptive dynamic programming

In this paper,a novel adaptive Fault-Tolerant Control(FTC)strategy is proposed for non-minimum phase Hypersonic Vehicles(HSVs)that are affected by actuator faults and parameter uncertainties.The strategy is based on the output redefinition method and Adaptive Dynamic Programming(ADP).The intelligent FTC scheme consists of two main parts:a basic fault-tolerant and stable controller and an ADP-based supplementary controller.In the basic FTC part,an output redefinition approach is designed to make zero-dynamics stable with respect to the new output.Then,Ideal Internal Dynamic(IID)is obtained using an optimal bounded inversion approach,and a tracking controller is designed for the new output to realize output tracking of the nonminimum phase HSV system.For the ADP-based compensation control part,an ActionDependent Heuristic Dynamic Programming(ADHDP)adopting an actor-critic learning structure is utilized to further optimize the tracking performance of the HSV control system.Finally,simulation results are provided to verify the effectiveness and efficiency of the proposed FTC algorithm.

Accurately tracking hypersonic gliding vehicles via an LEO mega-constellation in relay tracking mode

In order to effectively defend against the threats of the hypersonic gliding vehicles(HGVs),HGVs should be tracked as early as possible,which is beyond the capability of the ground-based radars.Being benefited by the developing megaconstellations in low-Earth orbit,this paper proposes a relay tracking mode to track HGVs to overcome the above problem.The whole tracking mission is composed of several tracking intervals with the same duration.Within each tracking interval,several appropriate satellites are dispatched to track the HGV.Satellites that are planned to take part in the tracking mission are selected by a new derived observability criterion.The tracking performances of the proposed tracking mode and the other two traditional tracking modes,including the stare and track-rate modes,are compared by simulation.The results show that the relay tracking mode can track the whole trajectory of a HGV,while the stare mode can only provide a very short tracking arc.Moreover,the relay tracking mode achieve higher tracking accuracy with fewer attitude controls than the track-rate mode.

Current status and prospects of terminal guidance laws for intercepting hypersonic vehicles in near space:a review

The unique performance advantages of hypersonic vehicles represent a critical challenge for existing defense systems.To facilitate defensive operations against hypersonic vehicles in near space,this paper systematically discusses both the advantages of these vehicles and the difficulties in intercepting them.Focusing on the state-of-the-art terminal guidance laws for intercepting hypersonic vehicles in near space,we examine research progress in the area of single-and multi-interceptor cooperative guidance laws and summarize their advantages and disadvantages.We also highlight future research directions for developing an effective terminal guidance law for multi-interceptor cooperative interception of hypersonic vehicles,based on four aspects:the information domain,space domain,physical domain,and effect-cost ratio.The findings provide a reference for further research into near-space interceptor terminal guidance technologies.

Quasi-equilibrium glide adaptive guidance for hypersonic vehicles

The entry-glide guidance strategy for hypersonic vehicles that can satisfy both terminal and path constraints is investigated in this paper.We propose a quasi-equilibrium glide adaptive guidance methodology based on the quasi-equilibrium glide condition(QEGC),which innovatively utilizes the quasi-equilibrium glide phenomenon in lifting entry.With the aid of QEGC,both range and terminal velocity can be predicted analytically with high precision.The path constraints are converted into angle of attack constraints,which has been difficult to realize by using traditional predictive guidance methods.The algorithm is independent of the standard trajectory.All the guidance commands,including the bank angle and the angle of attack,are calculated analytically in real time,which endows the algorithm with sufficient adapbility.The results of a CAV-H vehicle guidance test show that the algorithm leads the vehicle along a quasi-equilibrium glide trajectory satisfying both the terminal and path constraints and has sufficient flexibility for occasional mission changes.Furthermore,the robustness of the guidance algorithm under disturbances is validated through a Monte Carlo simulation.

A reduced order aerothermodynamic modeling framework for hypersonic vehicles based on surrogate and POD

Aerothermoelasticity is one of the key technologies for hypersonic vehicles. Accurate and efficient computation of the aerothermodynamics is one of the primary challenges for hypersonic aerothermoelastic analysis. Aimed at solving the shortcomings of engineering calculation, compu- tation fluid dynamics （CFD） and experimental investigation, a reduced order modeling （ROM） framework for aerothermodynamics based on CFD predictions using an enhanced algorithm of fast maximin Latin hypercube design is developed. Both proper orthogonal decomposition （POD） and surrogate are considered and compared to construct ROMs. Two surrogate approaches named Kriging and optimized radial basis function （ORBF） are utilized to construct ROMs. Furthermore, an enhanced algorithm of fast maximin Latin hypercube design is proposed, which proves to be helpful to improve the precisions of ROMs. Test results for the three-dimensional aerothermody- namic over a hypersonic surface indicate that： the ROMs precision based on Kriging is better than that by ORBF, ROMs based on Kriging are marginally more accurate than ROMs based on POD- Kriging. In a word, the ROM framework for hypersonic aerothermodynamics has good precision and efficiency.

Evasion guidance algorithms for air-breathing hypersonic vehicles in three-player pursuit-evasion games

In practical combat scenario,the cooperative intercept strategies are often carefully designed,and it is challenging for the hypersonic vehicles to achieve successful evasion.Based on the analysis,it can be found that if several Successive Pursuers come from the Same Direction(SPSD)and flight with a proper spacing,the evasion difficulty may increase greatly.To address this problem,we focus on the evasion guidance strategy design for the Air-breathing Hypersonic Vehicles(AHVs)under the SPSD combat scenario.In order to avoid the induced influence on the scramjet,altitude and speed of the vehicle,the lateral maneuver and evasion are employed.To guarantee the remnant maneuver ability,the concept of specified miss distance is introduced and utilized to generate the guidance command for the AHV.In the framework of constrained optimal control,the analytical expression of the evasion command is derived,and the constraints of the overload can be ensured to be never violated.In fact,by analyzing the spacing of the pursers,it can be classified whether the cooperative pursuit is formed.For the coordination-unformed multiple pursers,the evasion can be achieved lightly by the proposed strategy.If the coordination is formed,the proposed method will generate a large reverse direction maneuver,and the successful evasion can be maintained as a result.The performance of the proposed algorithms is tested in numerical simulations.

Flight control for air-breathing hypersonic vehicles using linear quadratic regulator design based on stochastic robustness analysis

The flight dynamics model of air-breathing hypersonic vehicles （AHVs） is highly nonlinear and multivariable cou- pling, and includes inertial uncertainties and external disturbances that require strong, robust, and high-accuracy controllers. In this paper, we propose a linear-quadratic regulator （LQR） design method based on stochastic robustness analysis for the longitudinal dynamics of AHVs. First, input/output feedback linearization is used to design LQRs. Second, subject to various system parameter uncertainties, system robustness is characterized by the probability of stability and desired performance. Then, the mapping rela- tionship between system robustness and LQR parameters is established. Particularly, to maximize system robustness, a novel hybrid particle swarm optimization algorithm is proposed to search for the optimal LQR parameters. During the search iteration, a Chernoff bound algorithm is applied to determine the finite sample size of Monte Carlo evaluation with the given prohabilily levels. Finally, simulation results show that the optimization algorithm can effectively find the optimal solution to the LQR parameters.

Aeroservoelastic modeling and analysis of a canard-configured air-breathing hypersonic vehicles

Air-breathing hypersonic vehicles （HSVs） are typically characterized by interactions of elasticity, propulsion and rigid-body flight dynamics, which may result in intractable aeroservoelastic problem. When canard is added, this problem would be even intensified by the introduction of low-frequency canard pivot mode. This paper concerns how the aeroservoelastic stability of a canard-configured HSV is affected by the pivot stiffnesses of all-moveable horizontal tail （HT） and canard. A wing/pivot system model is developed by considering the pivot torsional flexibility, fuselage vibration, and control input. The governing equations of the aeroservoelastic system are established by combining the equations of rigid-body motion, elastic fuselage model, wing/pivot system models and actuator dynamics. An unsteady aerodynamic model is developed by steady Shock-Expansion theory with an unsteady correction using local piston theory. A baseline controller is given to provide approximate inflight characteristics of rigid-body modes. The vehicle is trimmed for equilibrium state, around which the linearized equations are derived for stability analysis. A comparative study of damping ratios, closed-loop poles and responses are conducted with varying controller gains and pivot stiffnesses. Available bandwidth for control design is discussed and feasible region for pivot stiffnesses of HT and canard is given.

Overview of control-centric integrated design for hypersonic vehicles

Hypersonic vehicles(HSVs)exhibit significant advantages over other vehicles,including the wide range of velocity and large airspace types,and these features have contributed to the rapid development of HSVs in the last 20 years.Moreover,hypersonic technologies have become a multidisciplinary research topic in the fields of aerodynamics,propulsion,structure,material,and control.Different types of re-entry gliding,air-breathing cruise,and aerospace vehicles have been designed to realize ambitious tasks,which in turn influenced the technological advancements and process change in the military.This paper summarizes the control-oriented integrated design of HSVs.First,the status of current research on the distinct characteristics and technique issues of HSVs is introduced.Then,the progresses made on complex modeling,guidance and control,and trajectory optimization are elaborated to exhibit the significant research interest in hypersonic technologies.The control-integrated design of HSVs is emphasized to solve the multidisciplinary design problems associated with the model and its control and trajectory.Various strategies regarding the multidisciplinary optimization design are also proposed to solve the integrated design problem.Finally,suggestions are provided for the control-oriented integrated design of HSVs.