Software Enabled Flight Control Using Receding Horizon Techniques

Transcription

1 Software Enabled Flight Control Using Receding Horizon Techniques Tamás Keviczy and Gary J Balas University of Minnesota, Minneapolis, Minnesota An adaptive Receding Horizon Control (RHC) approach is presented for aircraft control to achieve aggressive maneuvering while enforcing flight condition and mission-state dependent operational limits Results suggest that the modelling flexibility provided by an adaptive RHC scheme based on flight condition dependent linear prediction models is a necessary requirement for achieving good performance as opposed to a single LTI model based method The adaptive scheme allows real-time implementation by retaining the modest computational complexity of the optimization problem (QP) that arises when linear prediction models are used The performance of the RHC controller is evaluated on a nonlinear fighter aircraft model Introduction RECEDING horizon control (RHC) techniques, also nown as model based predictive control methods, have been the focus of significant research efforts, motivated by several successful industrial applications 1 3 The process industry provided a perfect fit for these algorithms that respected critical processconstraints to achieve safer and more efficient operation of industrial plants These applications were not only well-suited for RHC methods but due to their relatively slow dynamics (large time constants), the significant computational effort of repetitive optimization, which is inherently involved in receding horizon approaches, could be accommodated by the relatively infrequent updates of the control signal In the past few decades it became apparent that predictive control methods possess qualities that could be utilized in more complex, nonlinear applications, possibly with much faster dynamics 4 As more and more of these cutting edge systems (eg active suspension, 5 gas turbine engine, 6 civil aircraft, 7 etc) emerge as applications, for which RHC methods could provide a candidate solution, it is left to the system engineer to choose the particular approach that best fits the problem at hand A main consideration of RHC schemes is real-time implementation, ie whether sufficient computational resources are available to accommodate repetitive solution of the optimization problem within each sampling time interval This paper intends to highlight these issues in the application of a receding horizon control scheme to a nonlinear aircraft and propose an approach that achieves a reasonable trade-off between computational time and performance for this specific application The Graduate Research Assistant, Control Science and Dynamical Systems Center, eviczy@aemumnedu Professor, Department of Aerospace Engineering and Mechanics, balas@aemumnedu generic nature of the RHC framewor used in the problem formulation suggests that similar results can be anticipated on other aircraft platforms such as the Boeing T-33/UCAV, which is designated as the final demonstration testbed for the DARPA Software Enabled Control (SEC) program 8 This program motivated the wor presented in this paper by indicating a clear incentive for online optimization based algorithms that can be implemented in real-time, based on the Open Control Platform (OCP) middleware 9 In order to highlight the advantages of the proposed methodology, simulation results of a single LTI model based algorithm are also presented as a benchmar Nonlinear receding horizon control approaches 1 provide an alternative to the method described in this paper with a potential to achieve increased performance, however the limited computational power currently available on aircraft hinders real-time application of these algorithms The compromise between performance and computational time is studied in Ref 11, where a comparison is presented between the adaptive RHC approach proposed in this paper and a nonlinear RHC method using the same cost function Aircraft modelling The nonlinear model of a fighter aircraft used in simulations and the problem formulation was obtained from Ref 12 and is available on the web 13 as a low fidelity model The dynamics of the continuous time aircraft model is represented as ẋ NL = f (x NL, δ) (1) The mathematical model uses simplified high-fidelity data from NASA Langley wind-tunnel tests conducted on a scale model of an F-16 aircraft 14 For our investigations, only the longitudinal motion of the aircraft is considered and the states x NL R 5 and controls δ R 2 in the model are defined as x NL = [h, θ, V t, α, q] T, δ = [δ th, δ e ] T 1 of 8

2 where h stands for altitude [ft], θ for pitch angle [rad], V t for total airspeed [ft/s], α for angle of attac [rad], q for pitch rate [rad/s], δ th for thrust [lb] and δ e for elevator deflection [deg] Actuators for the control surface and engine are modelled as first-order systems, details of which are discussed in a subsequent tion The aerodynamic data are valid up to Mach 9 and angle of attac range of 1 deg α 45 deg Inner-loop control The nonlinear aircraft model in (1) was augmented with an inner-loop controller based on pitch rate feedbac A benefit of the augmented system is stability of the closed-loop vehicle Output predictions of an unstable system can be numerically very inaccurate and cause numerical problems in optimization software 3 Hence, an unstable prediction model should be avoided whenever possible This underscores the practical importance of having a stabilizing controller augment the unstable plant before RHC methods are applied (this of course is not a theoretical necessity) Another practical reason for employing an inner-loop in the receding horizon framewor is that the RHC sampling rate can be reduced since the inner-loop is handling the high bandwidth disturbance and tracing requirements This allows more computational time for the outer-loop RHC algorithm (even though the horizon lengths are expected to be longer), whereas the inner-loop controller provides the necessary control authority at higher frequencies with its smaller sampling time implementation Another reason is that actual aircraft (either commercial or experimental), often come equipped with an inner-loop flight control system (most commonly stability or control augmentation systems SAS/CAS) Even in case of an experimental aircraft, which serves as a controller testbed, flight control engineers are very reluctant to implement and test control algorithms without the existing, stabilizing inner-loop control system, which has been flight certified Therefore, it is reasonable to assume that an inner-loop controller will augment the actual aircraft due to safety, certification or other implementation requirements In this paper, a pitch rate tracing inner-loop controller was chosen to provide a similar level of performance throughout a sufficiently large flight envelope This inner-loop controller is a linear H -controller designed with parameter space techniques 15, 16 and implemented in a two-degree-of-freedom structure as two ond order transfer functions with a first order command prefilter The two inputs to the controller are the commanded and measured pitch rate, the output is elevator deflection change from the trim value: [ ] qdem δ e = K (s) (2) q meas It is important to note, that the choice of the stabilizing inner-loop controller could be arbitrary It is assumed to be developed and implemented independently of the outer-loop RHC scheme under consideration This means that a grey-box inner-loop philosophy is adopted, namely only a certain number of linearized models are assumed to be nown about the inner-loop at certain flight conditions This philosophy is sometimes motivated by the restrictions on the availability of nonlinear models that represent proprietary or otherwise sensitive material In our opinion however, with the proposed adaptive RHC algorithm described in the next tion, this approach serves as a viable alternative to a full nonlinear model-based technique The nonlinear model in (1) is augmented with the inner-loop controller to form the inner closed-loop and used as the actual aircraft model that the RHC scheme is implemented on This inner closed-loop was linearized and discretized at several trim flight conditions (cref tion about Simulation details) The obtained set of linearized models is used for interpolation in the adaptive RHC scheme described in the next tion Each linearized inner-loop model has the inner-loop command signals (thrust, pitch rate) as inputs, and aircraft altitude, velocity, vertical acceleration (nz), and actuator positions and rates as outputs to be able to enforce actuator constraints, maneuvering limits and tracing performance The output signals are assigned to these three objective groups denoted by u, z and y, respectively The commanded input signals are denoted by r [ ] h y =, z = nz, u = V t δ th dδ th dt δ e dδ e dt, [ ] r = δth dem q dem Each trim flight condition was characterized by the corresponding dynamic pressure ( q) and Mach number (M) Denoting this vector of parameters with ϱ () = [ q () M ()] T, the linearized discrete-time inner-loop models have the form x( + 1) = A x() + B r() (3) y() z() = C x() + D r() u() where the flight condition dependency of the prediction models is indicated by the subscript, meaning A = A (ϱ ()), B = B (ϱ ()), C = C (ϱ ()), D = D (ϱ ()) Adaptive RHC problem formulation The optimization problem setup is based on the linear MPC formulation of Ref 3 with some modifications In most linear predictive controllers, the performance is specified by the following quadratic cost 2 of 8

3 ŵ ( + 1 ) C A C B D ŵ ( + 2 ) C A 2 C A B C B D r ( ) ŵ ( + H c ) = C A Hc ˆξ() + C A Hc 1 B C A Hc 2 B C B ŵ ( + H c + 1 ) C A Hc+1 C A Hc B C A Hc 1 B C A B r ( + H c 1 ) }{{} R() ŵ ( + H p ) C A Hp C A Hp 1 B C A Hp 2 B C A Hp Hc B }{{}}{{}}{{} W() Ψ Θ (6) function to be minimized, which will also be adopted in this paper: H p J() = ŷ ( + i ) y ref ( + i ) 2 Q + i=1 + H c 1 i=(δh c) r ( + i ) 2 R + ρε (4) where ŷ ( + i ) is the i-step ahead prediction of the outputs based on data up to time H p denotes the number of steps in the output prediction horizon These predictions of the outputs are functions of future control increments r ( + i ) for i =, δh c, 2δH c,, H c 1 The integer number of samples H c is called the control horizon, the control signal is allowed to change only at integer multiples of δh c samples and is set to be constant for all i H c This means that the future control signal has the form of a stairstep function with steps occuring at δh c intervals The reference signal y ref represents the desired outputs, Q and R are suitably chosen weighting matrices The slac variable ε and its weight ρ is used for softening constraints The exact purpose of the slac variable and weight in the problem formulation will be clarified shortly In order to obtain the predictions for the signals of interest, a model of the process is needed By using a linear model, the resulting optimization problem of minimizing J() will be a quadratic programming (QP) problem, for which fast and numerically reliable algorithms are available The linearized inner-loop model, developed in the previous tion, is augmented with extra states to fit the formulation in this RHC scheme Two integrators are added to convert the control changes r into actual controls r, one associated with thrust command and the other with pitch rate command A simple disturbance model is incorporated to the state space description of the inner-loop model in equation (5), which assumes constant disturbances are acting on outputs The constant disturbance estimates are obtained by observing the difference between measured and predicted outputs The disturbance model also serves to mitigate the effect of model mismatch The augmented linear inner-loop model has the following form ˆξ(+1) A ˆξ() { }} { {}} {{ }} { {}} { ˆx( + 1) A B ˆx() B ˆd( + 1) = I ˆd() + r() r() I r( 1) I ŷ() ẑ() = û() }{{} ŵ() I C I } {{ } C B ˆx() D ˆd() + D }{{} r( 1) D }{{} ˆξ() (5) r() By using successive substitution, it is straightforward to derive that the prediction model of inner-loop outputs (signals of interest) over the prediction horizon is given by equation (6) Denote parts of the state matrices C and D in equation (6) that correspond to the predicted ŷ() outputs in ŵ(), with an additional y subscript Consider only those predicted outputs that appear in the performance index ŷ() = C y ˆξ() + Dy r(), Y() = [ŷ ( + 1 ),, ŷ ( + H p )] T using only the corresponding C y and D y matrices in expression (6) The prediction for these outputs has the form Y() = Ψ y ˆξ() + Θy R() (7) Substituting the predicted output in (7) into the cost function of (4), we get a quadratic expression in terms of the control changes R(): J() = R() T H R() R() T G + const + ρε (8) 3 of 8

4 where H = Θ T yq e Θ y + R e, const = E T ()Q e E() G = 2Θ T yq e E(), and E() is defined as a tracing error between the future target trajectory and the free response of the system, ie E() = Y ref () Ψ y ˆξ() Qe and R e are bloc diagonal matrices of appropriate dimensions with Q and R on the main diagonal, respectively (These could be chosen parameter-dependent also) As in most applications, there are level and rate limits on actuators These are enforced as hard constraints posed as linear constraints on the optimization variables R and ε Finally, the QP to be solved at each time step has the following form min R T H R + R T G + const + ρε R, ε [ ] [ ] [ ] Ω,hard ω,hard s t R + Ω,soft ω,soft ε ε (11) Figure 1 illustrates the general receding horizon control setup presented in this tion u û ( + 1 ),, û ( + H p ) u (9) since the RHC algorithm has almost direct control over some of them (thrust level and rate) and the effect of the RHC command signal on the others is also nown with high accuracy (effect of pitch rate demand on elevator deflection and rate) Actuator level and rate constraints are also implemented in the nonlinear aircraft model, which reduces the chance of these hard constraints causing infeasibility to a practically negligible level However, another type of constraint is also considered in this specific application example represented by certain maneuvering limits on the aircraft The controller has to be versatile enough to handle these limits that might be system-state dependent or change according to different stages of a mission We assume the existence of such limitations on the vertical acceleration (nz) of the aircraft in certain simulation scenarios that play an important role in the operation of an unmanned aerial vehicle, such as the Boeing T-33/UCAV A simulation example that illustrates the handling of such constraints is discussed in the following two tions It is vital that these limits are treated as soft constraints, since disturbances and model mismatch can easily lead to infeasibility problems if hard constraints are put on these type of output signals Constraint softening is accomplished by introducing an additional slac variable that allows some level of constraint violation if no feasible solution exists z ε ẑ ( + 1 ),, ẑ ( + H p ) z + ε (1) ε It is beneficial to use an -norm (maximum violation) penalty on constraint violations (as shown in (4) and (1)), because it gives an exact penalty method if the weight ρ is large enough This means that constraint violations will not occur unless no feasible solution exists to the original hard problem If a feasible solution exists, the same solution will be obtained as with the hard formulation Using the linear prediction model in (6), all of the constraints in (9) and (1) can be Fig 1 General RHC framewor for aircraft control Remars The problem formulation in the preceding tion is a natural extension of a fixed LTI model based RHC The prediction at a certain time step is based on a linear model that best describes the plant (inner-loop) at the actual flight condition, assuming that flight condition dependent linear models are available for prediction A fixed LTI model is used over the entire prediction horizon but it is updated according to the values of the scheduling parameters ϱ () every time the horizon is propagated and the optimization is resolved based on new measurement data This approach leads to the QP problem in (11), and the state matrices describing the internal model change in each implementation cycle according to their current values: A, B, C, D This flight condition dependent description of the inner-loop dynamics could be obtained either by freezing the scheduling parameters of a quasi-lpv model, 17 or interpolating over a database of linearized models The latter approach is used in this paper to illustrate the general applicability of this approach motivated by the remars made earlier on restricted model availability We note if an accurate prediction of the parameters that the linear models depend on is available, this would allow for the prediction model to vary over the prediction horizon The optimization problem could still be formulated as a quadratic program using different state matrices of the internal model at each time step Obtaining a reasonable prediction of the scheduling parameters is not always easy, one could experiment with solving the problem first with the fixed 4 of 8

5 LTI model based RHC method and use the solution as the prediction for the scheduling parameters Our investigations indicate, that this extra effort doesn t lead to significant improvement for the specific application example and horizon lengths considered Moreover, even though the optimization problem complexity is retained, the additional computational overhead from the large number of interpolations was significant enough to undermine real-time implementation of these ideas Simulation details As it was mentioned in the previous tions, a database of linearized inner-loop models was created to be used by the interpolation routine in the adaptive RHC scheme Based on the validity range of the aerodynamic coefficients in the aircraft model, the operating flight envelope was chosen to be between 5 to 4 ft in altitude and 3 to 9 ft/s in true airspeed Dynamic pressure ( q) and Mach number (M) are selected as flight condition dependent scheduling parameters that determine which linear model to use for prediction The flight envelope is shown in Fig 2 in terms of dynamic pressure and Mach The nonlinear aircraft dynamics was linearized at steady level flight trim condition, at 38 different points of the flight envelope Given a q M value pair, triangular interpolation is performed over the coefficients of the inner-loop state matrices based on the grid depicted in Fig 2 Mach F 16 flight envelope: h = 5 4 ft V = 3 9 ft/s dynamic pressure [psf] Fig 2 F-16 model flight envelope with the interpolation grid of linearized models Level and rate limits, as well as time constants of the actuators used in the nonlinear aircraft model are shown in Table 1 The augmented linear models in equation (5) of the inner-loop had 17 states and were discretized at 2 Hz Five states were associated with the aircraft dynamics, an additional five states represented the H inner-loop controller Engine and elevator actuators Engine (throttle) Elevator Upper level limit 19 lb +25 deg Lower level limit 1 lb 25 deg Upper rate limit +1 lb/s +6 deg/s Lower rate limit 1 lb/s 6 deg/s Time constant 1 s 495 s Table 1 Engine and elevator actuator description together contributed two more states The five remaining states were introduced by the augmentation of the inner-loop state-space description with integrators in equation (5) Three of these extra states were associated with the simple disturbance predictor and two integrators were used to convert control changes r into actual controls r The proposed RHC scheme was implemented with a 5 ms sampling time, 4 ond prediction horizon (H p = 8) and 15 ond control horizon with future control changes at every 5 ond (H c = 31, δh c = 1) The values of the weighting matrices Q and R in the cost formulation were tuned based on the linear MPC scheme in Ref 3 and had constant values of Q = diag{4, 1} and R = diag{1, 1} Two simulation scenarios are presented to illustrate the behavior of the proposed adaptive RHC scheme: 1 The first example is a disturbance rejection scenario, in which the objective is to eep steady level flight at trim altitude and velocity in the presence of vertical wind gusts that occur in the form of a 5 ft/s step disturbance on velocity at 5 onds and a 1 ft step disturbance on altitude at 5 onds into the simulation The nonzero trim states and controls at this flight condition are h 1 ft V t α = θ δ th = ft/s 2315 deg lb δ e 1945 deg The results of using a single fixed LTI model based RHC scheme are also given to provide a basis for evaluating the performance of the adaptive scheme The fixed LTI prediction model corresponds to a flight condition of (h = 6 ft, V t = 8 ft/s) to better illustrate the inherent problems with this approach 2 The ond example aims at pointing out the aggressive maneuvering capabilities enabled by the adaptive RHC approach, as well as system-state dependent constraint enforcement represented by 5 of 8

6 ft deg 1 x 1 4 Altitude Angle of attac ft/s Velocity Thrust and elevator 9 thrust 6 deg 3 3 elevator lb Fig 3 Simulation results of example scenario 1 (reference: dotted magenta, single model RHC: dash red, adaptive RHC: solid blue) vertical acceleration limits that vary with true airspeed This is a characteristic constraint that technology developers have to respect in the T-33/UCAV fixed-wing flight demonstration of the DARPA Software Enabled Control program The simulation demonstrates two cases First, a relatively aggressive reference altitude and velocity trajectory is flown without any maneuvering constraints on vertical acceleration Then soft constraints are enforced during the same maneuver on vertical acceleration to eep the aircraft within velocity dependent upper and lower acceleration limits, which might be motivated by the stall characteristics of the aircraft The trim conditions are the same as in example 1 In both of these examples, the general goal of the outer-loop RHC controllers is to accomplish higher level control objectives, by exploiting a priori reference information The controllers have to ensure that the aircraft s inputs are held within saturation limits even in the presence of wind gusts and respect flight envelope constraints and system-state dependent maneuver limits by acting as a system/mission-state dependent variable inner-loop command prefilter The next tion presents the simulation results for the two described scenarios 6 of 8 Results All RHC simulations were run on a 12 GHz Pentium III machine running RedHat Linux Using the specific parameters described in the previous tion to formulate the optimization problem, the resulting QP had 8 decision variables (9 with the slac variable in example 2) The number of linear constraints were 664 (826 with the soft constraints) Example 1 The results of the disturbance rejection scenario are shown in Fig 3 for the proposed adaptive RHC approach as well as the single LTI model based one The different performances of the single model and adaptive RHC methods are apparent from the results: the single model RHC approach introduced some steady state errors, whereas the adaptive RHC based controller provides a more acceptable performance In contrast to this example, which intends to investigate local behavior of the RHC methods, errors introduced by the single model RHC scheme get much bigger as larger excursions are made in the flight envelope The main underlying reason for this is the absence of a trim map in the single model approach, however mismatch in plant dynamics is also a strong contributor to these errors, especially in the low dynamic pressure and Mach region of the flight envelope

7 16 x 14 Altitude 6 Velocity ft ft/s 55 5 g Vertical acceleration 5 nz constraints upper nz limit lower nz limit deg Thrust and elevator thrust elevator lb Fig 4 Simulation results of example scenario 2 (reference: dotted magenta, adaptive RHC w/o constraints: dash red, adaptive RHC with soft constraints: solid blue) Naturally, the single model RHC scheme requires less amount of computational time, the QP problem involved in calculations can be solved analytically, if no constraints are active In this case, calculation of the next control signal value at each 5 ond taes approximately 3 ond to complete on the platform used for computations If constraints are active, Matlab s QP solver is used, which provided a solution in 5 ond on average These numbers indicate that this approach is readily implementable in real time, even using the Matlab environment Our previous experience shows that by implementing the algorithm in C code, execution gets approximately ten times faster The optimization problem complexity is exactly the same in the adaptive RHC scheme as in the single model one, i e the QP can be solved in approximately real-time, even in the Matlab environment, if constraints are active Calculating the analytical solution if constraints are inactive is of course much faster in this case also However, a potentially significant computational overhead comes from the need for interpolation over the linearized inner-loop models The amount of time this prediction model looup requires depends heavily on the implementation of the interpolation routine and the size of the linear model database The Matlab-based interpolation algorithm (griddata) performs this tas in approximately 1 ond, which renders this RHC algorithm about 2 times slower than real time in the Matlab environment Considering our previous experience with the amount of speed-up gained from C implementation of the single model RHC scheme, and the other possible avenues of decreasing computation time (using different interpolation routines, less number of linear models, variable time interval formulation 7 or a number of other options), real-time implementation of this scheme is also deemed achievable Example 2 The ond example shown in Fig 4, was performed only using the adaptive RHC approach and demonstrates that aggressive maneuvers, as well as systemstate dependent maneuvering limits can be enforced by the flexibility offered in this methodology (The flight path angle peas near 25 degrees during the maneuver and angle of attac approaches 15 degrees in the unconstrained case, and 8 degrees in the constrained case) It is interesting to note, that in the case of soft constraints on vertical acceleration, the aircraft violates the lower limit to a small extent between 15 and 2 onds, which indicates that the actual maneuver would have been infeasible if hard constraints were imposed on vertical acceleration This has been verified by running the algorithm with this modification 7 of 8

8 The simulation also demonstrates how the controller enforces smaller upper limits, as the total airspeed is reduced Conclusions As simulation results demonstrate for the F-16 longitudinal axis control example, computationally efficient receding horizon schemes can be developed for highly nonlinear, complex systems based on linear prediction models to eep the optimization problem manageable Using flight condition dependent linearized models or a quasi-lpv system for prediction, the modest complexity of the predictive control problem can still be retained (QP) with improved accuracy and extended operation limits Even though additional computational overhead is introduced by interpolating over linearized models, our experience suggests that real-time implementation is plausible The proposed adaptive RHC scheme has the desired flexibility that these type of applications, such as the versatile mission objectives of the Boeing T-33/UCAV testbed often require On-line constraint modification allows straightforward incorporation of system-state dependent, and time-varying constraints 1 Bhattacharya, R, Balas, G J, Kaya, M A, and Pacard, A, Nonlinear Receding Horizon Control of an F-16 Aircraft, Journal of Guidance, Control, and Dynamics, Vol 25, No 5, 22, pp Keviczy, T and Balas, G J, Receding Horizon Control of an F-16 Aircraft: a Comparative Study, European Control Conference, Stevens, B and Lewis, F, Aircraft Control and Simulation, Wiley, New Yor, /darpa_/secsoftwarehtml 14 Nguyen, L, Ogburn, M, Gilbert, W, Kibler, K, Brown, P, and Deal, P, Simulator Study of Stall/Post-Stall Characteristics of a Fighter Airplane with Relaxed Longitudinal Static Stability, NASA Technical Report 1538, Dec Blue, P, Güvenç, L, and Odenthal, D, Large Envelope Flight Control Satisfying H Robustness and Performance Specifications, American Control Conference, Blue, P, Odenthal, D, and Muhler, M, Designing Robust Large Envelope Flight Controllers for High-Performance Aircraft, AIAA Guidance, Navigation, and Control Conference, Huzmezan, M and Maciejowsi, J M, Reconfiguration and Scheduling in Flight Using Quasi-LPV High-Fidelity Models and MBPC Control, American Control Conference, 1998 Acnowledgements This wor was funded by the Defense Advanced Research Projects Agency under the Software Enabled Control program, Dr John Bay Program Manager The contract number is USAF/AFMC F C-1497, Dale Van Cleave is the Technical Contract Monitor References 1 Camacho, E F and Bordons, C, Model Predictive Control in the Process Industry, Advances in Industrial Control, Springer, London, Bemporad, A and Morari, M, Robust Model Predictive Control: A Survey, Robustness in Identification and Control, Lecture Notes in Control and Information Sciences, Springer- Verlag, Berlin, 1999, pp Maciejowsi, J M, Predictive Control with Constraints, Prentice Hall, 22 4 Papageorgiou, G, Glover, K, Huzmezan, M, and Maciejowsi, J M, A Combined MBPC /H Automatic Pilot for a Civil Aircraft, American Control Conference, 1997, pp Donahue, M D, Implementation of an Active Suspension, Preview Controller for Improved Ride Comfort, MS thesis, University of California at Bereley, 21 6 Fuller, J and Meisner, R, Optimization-based Control for Flight Vehicles, AIAA Guidance, Navigation, and Control Conference, 2 7 Schram, G, de Vries, R A J, Cevaal, E, and van den Boom, T J J, Predictive Control Applied to a Civil Aircraft Benchmar Problem, European Control Conference, Bay, J S, Hec, B S, et al, Special Section: Software- Enabled Control, IEEE Control Systems Magazine, Vol 23, No 1, Feb 23 9 Paunica, J, Mendel, B, and Corman, D, The OCP An open middleware solution for embedded systems, Proc American Control Conference, Arlington, VA, 21, pp of 8