Flight Validation of Metrics Driven L1 Adaptive Control

Recently, a class of adaptive control schemes called L1 Adaptive Control (L1-AC) has been proposed and widely advertised in aerospace control for achieving fast and robust adaptation and better performance than the existing Model Reference Adaptive Control (MRAC) Schemes. The L1-AC scheme is designed mainly for plants with full state measurement even though the name L1-AC has been used as an umbrella name for more general classes of plants. In this paper, we show that the L1-AC for plants with measured states is simply a standard MRAC with a low pass filter inserted in front of the control input. The analysis of the scheme is almost identical to that of MRAC as the same Lyapunov function is used to establish stability. The motivation for using the filter is the fact that for this class of adaptive schemes i.e. MRAC for plants with full state measurement the tracking error can be made arbitrarily small during transient by increasing the adaptive gain. A high adaptive gain however makes the differential equation of the adaptive law or estimator very stiff and leads to numerical problems that cause high oscillations in the estimated parameters leading to loss of adaptivity and deviations from what the theoretical properties dictate. The L1-AC approach mistook these numerical oscillations as properties of the adaptive scheme and inserted an input low pass filter in order to filter them out. While the filter helps reduce the frequency of these oscillations in the control law the price paid is high. First the numerical instability does not go away and the estimated parameters continue to oscillate without converging to the true parameters even in the presence of sufficiently rich signals. Second, due to the filter the tracking error is no longer guaranteed to converge to zero and the transient bounds for the tracking error also depend on the filter. As a result, the tracking properties of the L1-AC scheme are worse than what a simple MRAC scheme can generate with adaptive gains that could be high but away from the region of numerical instability. In addition, the presence of the filter reduces the robust stability margins in the presence of unmodeled dynamics and provides literally no advantage as simple robust MRAC techniques can solve the same problem achieving much better properties. The authors of L1-AC often compare the properties of a numerically unstable MRAC due to extremely high adaptive gains something that is prohibited by robust adaptive control with those of the filtered MRAC aka L1-AC to show that L1-AC performs better. Such comparisons are not only misleading but do not reveal what causes what giving the reader a false impression of a new theory that results to new performance and robustness improvements. The use of filters in adaptive control is not new and they are used to improve the performance and robustness of certain adaptive control schemes without destroying their ideal tracking properties. In this paper we present such a scheme that guarantees good transient performance and robustness and reveals the trade off between transient performance and robust stability.

SummaryIn this study, we present a reinforcement learning (RL)‐based flight control system design method to improve the transient response performance of a closed‐loop reference model (CRM) adaptive control system. The methodology, known as RL‐CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor‐critic RL agent is designed using the performance‐driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time‐varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high‐fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte‐Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM‐adaptive control system designs, the proposed RL‐CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.

Robust modification of nonlinear L1 adaptive flight control system via noise attenuation

Considered influence of nonlinear system and disturbance, a new adaptive fault-tolerant control method based on neural network model-following adaptive inversion control is introduced for flight control system in the presence of control surface damage. To restrain modeling uncertainties caused by fault system, neural network PID and inversion controllers are design for fault-tolerant flight control system. It is based on BP (back-propagation) neural network which is designed by applying improved algorithm of on-line training and parameter optimization. Moreover the output of fault aircraft can perfectly track the trajectory of the reference model. The scheme is demonstrated through simulations applying the flight control system of a fighter. The simulation results show fault-tolerant flight control system maintains stability and handling qualities.

L1 adaptive backstepping control for path-following of underactuated marine surface ships

This paper proposes an L1 adaptive backstepping control strategy integrated with a vector field-based guidance method to steer an underactuated autonomous marine vessel along a predefined trajectory, utilizing a nonlinear heading dynamics model. The controller is rigorously designed within a Lyapunov-based stability framework, ensuring convergence and system robustness. The L1 approach offers a promising balance between robustness and rapid adaptation to system uncertainties. To validate the proposed approach, numerical experiments are performed using a comprehensive nonlinear maneuvering model of an underactuated tanker subjected to random ocean current disturbances. This maneuvering model, developed based on free-running experimental data, serves as a reliable platform for assessing the controller’s practical viability. A simulation-based path following test demonstrates the performance and efficiency of the proposed control algorithm and guidance strategy.

Spacecraft formation flying is a fast improving technology for space missions, showcasing reduced cost, increased flexibility and efficiency and design redundancy over similar single satellite missions. Furthermore, it provides a viable solution for missions requiring high spacial and temporal resolutions. While a lot of work has been conducted on spacecraft formation flying control, very few of these algorithms have been validated on flight hardware or through hardware experiments. The L 1 adaptive control algorithm is a promising algorithm that can deal with various model uncertainties in real time. It's capability has been demonstrated through numerous aerospace simulations and also through real world experience on board NASA's AirSTAR aircraft. As such, this work focuses on the design, simulation, implementation and validation of the L 1 adaptive controller for spacecraft formation flying. More specifically, this thesis first introduces the L 1 adaptive control architecture using examples for simple linear systems, to gain an understanding of the controller implementation and behaviour. The desired controller design decisions are discussed I would like to begin by thanking my thesis supervisor, Steve Ulrich, for his support, guidance and motivation. His enthusiasm and mentorship always motivated me to put my best foot forward and I cannot imagine doing this with a better supervisor and mentor.

Nonlinear adaptive flight control system: Performance enhancement and validation

Flight control system design for two F/A- 18 aircraft flying in closed-coupled formation is the subject of this paper. Developed by Boeing - Phantom Works as an integral part of NASA revolutionary concept program called Autonomous Formation Flight (AFF), the Formation Flight Control System (FFCS) provides autonomous aircraft operation and flight testing capability. Using two specially instrumented Boeing-built F/A-18 Hornets research aircraft, AFF Phase I flight demonstrations are scheduled for the fall of 2002 at NASA's Dryden Flight Research Center, Edwards Air Force Base, in California. It is expected that the trailing aircraft equipped with FFCS would sustain 15-20% drag reduction if it is flown in the wake vortex created by the lead aircraft wingtips. This paper presents the baseline FFCS design, analysis, and evaluation using high fidelity 6-DoF nonlinear aircraft simulation environment. Aircraft vortex modeling is discussed. An alternative adaptive formation flight control system design is proposed. The adaptive system is shown to improve the formation tracking performance.

A New Approach to the Design of an Adaptive Control System

This paper presents an extension of the L1 adaptive controller to a class of nonlinear systems where the control effectiveness is time-varying and unknown, but with a known sign. Moreover, this class of nonlinear systems contains time-varying and unknown state-dependent nonlinearities. The proposed L1 adaptive controller consists of three components, a state predictor used to estimate real states, an adaptive law used to update the adaptive parameters in the state predictor, and a low-pass filtered control law. First, the stable closed-loop reference system is constructed. Then, the estimation errors between estimated states and real states are proved to be arbitrarily small by increasing the adaptation rate. After that, we further prove that the adaptive controller ensures uniformly bounded transient and asymptotical tracking of the reference system. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results on a single-link nonlinear robot arm verify the theoretical findings.

Important class of adaptive control systems with non-stochastic description of the uncertainty and disturbances is considered. New approach to the design of the non-stochastic adaptive dual control algorithms is suggested. The elaborated approach is based on the introducing of two new cost functions for optimisation of the control signal and exiting signal added to the control signal. The ellipsoid bounded estimation of the plant parameters is used for the plant parameter estimation and indirect adaptation. This estimation method was also named set-membership estimation. The approach is introduced and described comprehensive using simple controller of self-tuning type. The designed controller, which is used as an example to demonstrate the new suggested method, can be applied to control of nonminimumphase plants. The method can be extended to adaptive controllers of various other types. The violent contrast is attributed to the suggested design method as compared with other dual control approaches for non-stochastic systems with set-membership estimation. The method allows designing of non-stochastic dual adaptive controllers that are very simple computational and consist of the cautious controller with the optimal excitations. Non-stochastic adaptive dual controllers, which are designed using suggested approach, have superiorities over the similar controllers based on the certainty equivalence approach because of the properties of caution and optimal excitation.

The current development process especially of small unmanned aircraft systems from automatic to semi-autonomous or even fully autonomous behaviour demands reliable and precise navigation solutions as well as robust control strategies. For a truly autonomous system adequate as well as secure reactions towards nonlinearities arising for example from unknown environmental conditions or system damages are a prerequisite. An adaptive flight control system, which has to cancel the undesirable effects of such disturbances, depends on constantly available accurate navigation data. To satisfy these boundary conditions, it is sensible to stronger intertwine the development process of miniaturised navigation systems and adaptive flight controllers. As the controller design and its validation is based on nonlinear simulations, it is advisable to model the integrated navigation system and its low-cost components in a detailed way, so that its distinct dynamic properties can already be taken into account during the development process of the controller. In this context, a tightly coupled integrated navigation scheme is presented, where the characteristics of the sensor components are identified and modelled using the Allan variance analysis. This information can be used during the validation process of the proposed adaptive flight control system, which is based on the concept of nonlinear dynamic inversion combined with artificial neural networks. This paper gives an overview on how miniaturised navigation systems can be modelled and utilised for adaptive flight control schemes of small unmanned aircraft.

Robustly Stable, Discrete-time, Adaptive Flight Control using the Euler Operator

Robust Adaptive Control