We have developed novel nonlinear adaptive and neural adaptive control designs for high-performance air vehicles including the F-16, F-15 ? like aircraft and GHV models:

Robust Neural Adaptive and Adaptive Sliding Mode Control of a GHV
We have designed a multi-input multi-output (MIMO) adaptive sliding mode controller for the longitudinal dynamics of a generic hypersonic air vehicle. The longitudinal dynamics of the vehicle is nonlinear, unstable and include uncertainties in the aerodynamic parameters. The open-loop dynamics of the air vehicle exhibits unstable short-period, unstable height modes, as well as a lightly damped phugoid mode. Full state feedback is applied to linearize the dynamics of the air vehicle with respect to the controlled states; sliding mode and adaptive controllers are combined to improve performance in the presence of parametric uncertainty. In addition, a sliding mode observer is designed to estimate the angle of attack and the flight path angle, which are difficult to measure in a hypersonic flight.

Robust Neural Adaptive Control with Guaranteed Error Bounds
In an extension of the above work we have designed a robust MIMO neural adaptive controller for the longitudinal dynamics of a GHV. In this case, control design can proceed with little a priori knowledge of the dynamics of the vehicle. Neural networks designed approximate the unknown dynamics with the weights being estimated on-line. The control design is then proceeds based on the neural network approximated model rather than the actual system as shown in Figure 6. Even under such relax assumptions about system dynamics, the scheme guarantees closed loop system stability and convergence of the tracking errors at steady state inside a small residual set. The size of the residual set is determined a priori by using a step-by-step design procedure.

Figure 1
Block diagram of the overall closed loop system
  • Adaptive Linear Quadratic Design with Application to F-16 Fighter Model

    We have developed a complete Matlab/Simulink model for the F-16 fighter aircraft and investigated two control approaches to design flight control laws. These are the ALQ control design and the traditional gain-scheduling LQ design method. Through simulations we have benchmarked the new ALQ design against the traditional LQ with gain scheduling (Figure 7) in a number of steady state flight conditions. The ALQ control design combines a robust adaptive law combined with the same control law structure as the LQ with gain scheduling. The ALQ robust adaptive law estimates and updates the system model from measurements of the current flight condition. The estimated model information is used to adjust and tune the LQ controller. The ALQ method having the ability of glearning,h the controller exhibits superior performance when uncertainty is assumed in system dynamics. This study highlights the apparent deficiency of the traditional gain-scheduling method, where a large number of scenarios have to be stored in onboard computer in lieu of bestowing the controller with
    glearningh capability. Our simulation results (Fig 7), which uses the longitudinal trimmed dynamics of the vehicle in steady state flight, clearly exemplifies this conclusion.

Autonomous Soaring Applications

Autonomous Soaring: Soaring is the art of keeping a motorless aircraft airborne ? or sustained in flight beyond simply sinking in still air ? using only the air currents that occur in the atmosphere. Soaring is commonly classified as dynamic or static. Dynamic soaring makes use of irregularities in the natural wind. We focus our work on static soaring which is basically utilizing thermals - the air currents with an upward trend. Soaring has recently been investigated for Unmanned Aerial Vehicle (UAV) applications. Satisfactory experimental results have been obtained in terms of significant endurance, range and cross-country speed improvements. Substantial human intervention, however, is required to define the corresponding flight trajectory reducing the autonomy level of the UAV. Optimum Trajectory Generation: The vertical velocity of the thermal, which is referred to as its strength, is in general a slowly varying function of time. We assume it to be time-invariant, at least while the glider is soaring inside it. We assign the glider UAV to have a map of the flight region which stores position and vertical velocity data for the next thermal on the flight path, fairly accurately using sensor measurements from onboard and ground-based sources. This map will be referred to as the Cognitive Map since the glider receives environmental information through the map to form a basis for decisions. A one-step-look-ahead policy is applied so that the data is processed to evaluate gglide-and-thermalh or gglide-and-bypassh options and make a decision. Thermals that are too weak for soaring purposes are not utilized since it is not worth climbing a weak thermal rather than a stronger one. On the other hand, if the vertical velocity threshold for thermals used in the decision logic is increased too high, the glider will never switch into thermal soaring mode. When the decision made is in favor of thermal soaring, the same theory applied in the design of the speed ring for soaring pilots can be employed to determine the speed-to-fly for the glider UAV. If the decision is to bypass the thermal, the Cognitive Map updates the data for the next thermal in turn, and the decision process begins over again. As soaring at a thermal location is completed, it is checked whether the glider can switch safely to the maximum speed for the rest of the flight and reach its final destination in pure glide mode at the maximum allowed speed with no need for an early landing or crash landing. If the glider climbs inside a thermal, altitude gain is measured. We require that the altitude loss in inter-thermal glide is entirely gained back before leaving the thermal. As soon as this local constraint is satisfied, the glider resumes gliding at the speed the decision algorithm assigns based on the next thermal data. In our approach a decision is first made for each thermal in the flight direction on whether or not to enter the thermal for soaring. At each thermal being utilized the constraint to recover the altitude loss in inter-thermal glide after leaving the previous thermal is then applied. [3.1] Robust Adaptive Control Design for Gliders Subject to Actuator Saturation Nonlinearities: Recent advances in the area of static soaring assume known linear glider dynamics and no actuator saturation limits. In practice, the actuators moving the control surfaces have mechanical limits, and the dynamics of the glider change with flight and environmental conditions. We consider the optimization-based static soaring problem in the presence of actuator saturation nonlinearities and large parametric uncertainties in the dynamics of the vehicle. We use ideas from robust adaptive control and antiwindup design tools to develop an adaptive control scheme based on linear quadratic (LQ) control with disturbance rejection. The saturation-type nonlinearity problem is addressed by including an intuitive adaptive version of a linear matrix inequality (LMI) based antiwindup design. The resulting adaptive control scheme with adaptive antiwindup allows optimal soaring despite the presence of significant actuator saturation limits and unknown parameters. [3.2] The soaring performance of a glider UAV depends a great deal on the thermal characteristics including thermal strength and location. Onboard sensor measurements are typically corrupted by noise whereas gusts and turbulence effects can cause significant performance degradation during inter-thermal glide. We provide a stochastic approach to the optimal soaring problem. We quantify the performance losses due to incorrect thermal data, consider the effect of stochastic gust disturbances, and simulate the deterioration in the system response in the presence of additional sensor inaccuracies. Although the recovery of losses due to incorrect thermal data is possible only if data resources being used could be enhanced, an adaptive tracking control implied by a Linear Quadratic Regulator (LQR) design inherently provides the optimal control when the aircraft is subject to gust represented by a Gaussian white noise. In addition if stochastic noise is present at each sensor measurement channel, however, LQ control does not yield acceptable performance. By including an adaptive Kalman-Bucy filter and modifying the adaptive law and our optimum trajectory generation algorithm inputs accordingly, we generate an adaptive Linear Quadratic Gaussian (LQG) control design that filters the Gaussian white noise signals effectively. [3.3] Autonomous Soaring as a Vehicle Routing Problem: Variations in the climb rate of atmospheric air currents and the limited duration periods for which these currents are available for soaring flight pose extra constraints on static soaring. If these constraints are not properly addressed, the resultant performance of the vehicle can be quite far from optimal. We propose that the optimal static soaring problem can be efficiently adapted to a Vehicle Routing Problem (VRP), a generic combinatorial optimization problem well-known in academic literature. This problem formulation proves capable of being conveniently extended to the VRP with Time Windows (VRPTW) to consider duration constraints such as limited thermal lifespan whereas the variations in the air currents can possibly be modeled as a Dynamic Vehicle Routing Problem (DVRP). Based on our VRPTW formulation of static soaring problem, we develop an exact solution method including preprocessing, route optimization and route validation. As a result, the ability to effectively plan the flight path is improved, and considerable increase in the level of autonomy of a soaring UAV is attained. [3.4] We also discuss the maneuvering of a glider UAV across regions dense with thermals. The UAV is required to soar all the assigned thermals in the area of interest in minimum total time. Our solution methodology is based on dividing the maneuvering area into sectors, and applying a spanning tree algorithm in each sector independently to cover the set of thermals detected. A parallel savings based heuristic is then included in between these sectors to improve the decision process while some maximum distance constraint is also satisfied. The simulation results confirm the fact that the physical requirements and the flight constraints of soaring UAVs can be properly translated into mathematical language which results in significant performance improvements for the aircraft if efficient algorithms can be developed to define the flight path. [3.5] In order to conduct surveillance operations unmanned aircraft are equipped with downward pointing cameras monitoring the environment. Multiple aircraft can be assigned a cooperative mission providing a better surveillance platform in comparison to a single UAV in service. The automation of the vehicles in the formation, however, becomes a complicated task possibly demanding higher energy requirements. Soaring flight strategies thus appear to be effective for large area observation. We consider multiple glider UAVs and study the static soaring flight formulation in the form of a multiple-Vehicle Routing Problem (mVRP). The proposed guidance algorithm promises high level of autonomy for a UAV formation and guarantees energy efficient flight trajectories for the mission performance optimization. The flight path planning mechanism is demonstrated through a simulation scenario involving a team of unpowered UAVs being navigated along near-optimal flight trajectories and performing climb maneuvers to utilize rising air currents. [3.6] Thermal Soaring Flight with Reduced Models: Our research encourages using atmospheric currents to improve range and endurance for UAVs with higher order models which capture more of the aircraft performance and possibly involve uncertainties. In scenarios with more complicated performance demands, model reduction offers additional advantages in numerical computations. We propose an approximate implementation scheme for an adaptive linear quadratic control structure by employing a balanced truncation procedure in the loop prior to solving the associated Algebraic Riccati Equation (ARE). The control design combined with an adaptive law to compensate for uncertainties and possible changes in the dynamics is applied to the longitudinal model of a UAV in atmospheric flight. The tracking controllers based on the full and reduced order UAV models are constructed, and the resultant effect of the described model reduction on the flight performance of the vehicle is investigated through comparative simulations. [3.7] Future Work: The optimal flight paths have been generated for specific scenarios where the climb rates of the rising air currents in the region are assumed to be deterministic. In order to improve these algorithmic approaches some degree of uncertainty yet needs to be allowed in describing the thermals. In the next stage of the project we are planning to consider the recursive thermal streets which can be modeled through Gaussian distributions with uncertain standard deviations. The UAV can be assigned to climb several successive thermals characterizing these profiles and collect the required data which can then be used to estimate the location of the strongest thermals in the respective thermal streets. A more effective method for flight trajectory generation can hence be developed in comparison to the tools based merely on remote detection data. [3.8]

Control of Hypersonic Aircraft

The CSULA-GHV Model: Under an Air Force Office of Scientific Research Grant (AFOSR) (W911NF0710018) we have developed an integrated aero-propulsion elastic model of a full-scale generic airbreathing hypersonic flight vehicle, CSULA-GHV. The focus of that research was to investigate the challenges associated with the control of airbreathing hypersonic flight vehicles (AHFV.) Our goal is to develop a longitudinal high-fidelity model that will be used to quantify, by extensive CFD studies, the coupling between the aerodynamics, the propulsion system, the structure. The longitudinal model of the CSULA-GHV has been developed using extensive CFD simulations to generate the basic coefficients CL, CD, CM and CT. Because our CFD simulations include supersonic combustion and the thrust generated by the scramjet engine, these coefficients quantify the unique aero-propulsion coupling exhibited by aircrafts with a tightly integrated airframe-engine configuration. Additionally, aero-propulsion interactions with the vehiclefs structural dynamics are included analytically by considering the structural excitation induced by forces produced by the control surface (elevon) deflections. Structural modes are obtained from a finite element model using NASTRAN. The premise of our approach is that structural deformation manifest itself mainly through an effective change in the angle of attack and a perturbation in the control surface (elevon) effectiveness thereby interacting with the aerodynamics and propulsion ?[3.9]. Recently, we have developed multiple simulation models of CSULA-GHV suitable for control and validation. A control-orientated model is a simplified model of the CSULA-GHV dynamics suitable for control design. This model captures the salient features for control design, e.g., the strong aero-propulsion couplings, while neglected the less dominate feature, e.g., structural dynamics, to facilitate a tractable control design. A high-fidelity simulation model is used to validate the control design on the complete model obtained from the CFD simulations and structural analysis. The control-orientated model and high-fidelity simulation models are part of a simulation environment implemented in Simulink. The simulation environment allows seamless interoperability between the two models, a feature that facilitates rapid control design and validation. The Simulink model is open source and was distributed at the 2007 AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC. Controller Development for CSULA-GHV: The non-standard dynamic characteristics of air-breathing hypersonic flight vehicles together with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover the wide range of speed during operation and the lack of a broad flight dynamics database add significant plant parameter variations and uncertainties to the problem of controlling air-breathing hypersonic flight. Our past control designs have focused on investigating the merit of adaptive control schemes for improving the robustness and performance despite large parametric uncertainties associated with the AHFV models. For this purpose, we chose an adaptive linear quadratic control (ALQ) scheme because of the readily available software to synthesis linear quadratic (LQ) compensators. The results of ?[3.10] demonstrate that in the presence of parametric uncertainties and actuator failures the ALQ maintained stability, while the non-adaptive LQ scheme did not. The follow-up work ?[3.11] demonstrated similar results when the control scheme is applied to the elastic model. Despite the promising results of the ALQ scheme, it does have some practical concerns. First, an ALQ approach may require significant computational costs because the solution of an algebraic Riccati solution must be solve in real time. Another concern is that robust-stability and ?performance requirements are not straightforwardly specified in the control formulation. Our recent approach ?[3.12], called adaptive mixing control, combines mixed-mu synthesis and online parameter estimation. Because the CSULA-GHV model contains both unmodeled dynamics (e.g., structural dynamics) and parametric uncertainty (e.g., stability and control derivatives,) the mixed-mu approach is a natural way to formulate the control problem while incorporating robust-stability and ?performance requirements. The online parameter estimatorfs role is to reduce parametric uncertainty and, thereby, increasing the achievable level of performance. A conceptual schematic of the approach is shown in Figure 1. Each of the high performance controllers is a mixed-mu compensator, synthesized offline by the DGK-iteration algorithm, and is tuned to a small region of the uncertain parameter space. For any possible realization of the uncertain parameter, there exists at least one controller that is capable of achieving the desired closed-loop behavior. The stabilizing controllers are identified by the estimator, which processes the observed data to generate an estimate of the unknown parameter that drives controller mixing. The preliminary results of ?[3.12] show that the adaptive mixing control scheme provides improved altitude and velocity tracking performance when compared to a non-adaptive mixed-mu controller.

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Cal State University, Los Angeles