Spacecraft Formation Flying Using L1 Adaptive Control Techniques

The paper addresses initial steps involved in the development and flight implementation of new metrics driven L1 adaptive flight control system. The work concentrates on (i) definition of appropriate control driven metrics that account for the control surface failures; (ii) tailoring recently developed L1 adaptive controller to the design of adaptive flight control systems that explicitly address these metrics in the presence of control surface failures and dynamic changes under adverse flight conditions; (iii) development of a flight control system for implementation of the resulting algorithms onboard of small UAV; and (iv) conducting a comprehensive flight test program that demonstrates performance of the developed adaptive control algorithms in the presence of failures. As the initial milestone the paper concentrates on the adaptive flight system setup and initial efforts addressing the ability of a commercial off-the-shelf autopilot with and without adaptive augmentation to recover from control surface failures.

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.

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.

Developing closed-loop brain stimulation systems can benefit the treatment of neurological and neuropsychiatric disorders and facilitate brain functions. Current designs of closed-loop controllers have used time-invariant linear models of brain activity to devise non-adaptive controllers. However, unmodeled nonlinear dynamics can happen during real-time closed-loop control, leading to nonlinear uncertainty in the brain activity model. Current non-adaptive controllers cannot track the nonlinear model uncertainty and are not robust to noise, both of which can compromise their control performance. Here, within an ℒ1 adaptive control framework, we develop a new discrete-time robust and adaptive closed-loop control algorithm that addresses a general form of nonlinear model uncertainty. We conduct Monte Carlo simulations to validate the robust and adaptive control algorithm and show that it significantly outperforms existing closed-loop control algorithms. Our results can facilitate future designs of precise and safe closed-loop brain stimulation systems to treat neurological and neuropsychiatric disorders and modulate brain functions.

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.

6-DOF fixed-time adaptive tracking control for spacecraft formation flying with input quantization

Reduction of hydrocarbon emissions during the engine cold start process is a major design and control goal in the automotive industry in recent years, with considerable impact on not only the vehicle's fuel economy, but the environment as well. The key to producing the most emission efficient powertrain system is the ability to drive the engine variables to operate under certain behavioral parameters, that is, to drive the engine states to follow ideal desired trajectories. Therefore, the control target of driving down tracking error to produce ideal engine behavior is an important consideration in the control design process. Due to the highly nonlinear and transient nature of the engine cold start process, the choice was made in this work to employ a scalar sliding control technique. Additionally, in order to mitigate possible model uncertainty in real time, an adaptation update algorithm was incorporated. The combined algorithm was implemented on an engine test cell and experimentally validated. The work was inspired by the Verification & Validation procedure used in standard industry practice to reduce errors and uncertainties early on in the control design phase so as to produce desired engine behavior as soon as possible.

The extreme aeroheating at hypersonic regime and the insufficient dynamic pressure in the near space limit the achievable performance of the hypersonic vehicles using aerosurfaces alone. In this paper, an integrated pneumatic and thrust vectoring control strategy is employed to design a control scheme for the longitudinal dynamics of a hypersonic vehicle model. The methodology reposes upon a division of the model dynamics, and an L1 adaptive control architecture is applied to the design of the inner-loop and outer-loop controllers. Further, a control allocation algorithm is developed to coordinate pneumatic and thrust vectoring control. Simulation results demonstrate that the allocation algorithm is effective in control coordination, and the proposed control scheme achieves excellent tracking performance in spite of aerodynamic uncertainties.

This paper presents an extension of the L1 adaptive output feedback controller to systems of unknown dimension in the presence of unmodeled dynamics and time- varying uncertainties. The adaptive output feedback controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation rate. Simulations of an unstable non-minimum phase system verify the theoretical findings.

The model-free adaptive control (MFAC) which is based on compact from format dynamic linearization (CFDL) is applied in the speed control system of automatic door. The design of the adaptive controller is model free. It is directly based on the estimation and prediction of pseudo partial derivative (PPD). It analyzed and compared the effects of speed control which displayed by model free adaptive control and PID algorithm. And it also adaptive analyzed adaptive the effects when changing the parameters adaptive of pseudo partial derivative. The results of the adaptive experiments showed that the model-free adaptive control algorithm in the control of Auto-Door servo system is better than that of PID control. And the results also highlight the model free adaptive control algorithm for fast motion system stability and robustness.

The purpose of this work is to design a new layout for a quadrotor unmanned aerial vehicle (UAV) for experimental customized control-system validation. Geometrical and structural properties have been computed, and commercial off-the-shelf equipment has been selected. The flight control system, both hardware and software, has been custom developed; the same applies for the mathematical model describing the flight dynamics. Two proportional-derivative (PD) controllers have been designed and experimentally tested. A different control strategy with a state feedback controller has been implemented, assigning a robust eigenstructure and the desired dynamic specifications. An adaptive algorithm, which guarantees a uniformly bounded response for both the inputs and the outputs, has been presented. An L1 adaptive controller has been studied and implemented, including the state predictor and the adaptive and control laws. Tests with the PD controller have shown slowly stable response even in the event of nu...

An adaptive backstepping controller is proposed to control the mover position of a linear-induction-motor (LIM) drive to compensate the uncertainties including the friction force. First, the dynamic model of an indirect field-oriented LIM drive is derived. Next, a backstepping approach is designed to compensate the uncertainties occurred in the motion-control system. Moreover, the uncertainties are lumped and the upper bound of the lumped uncertainty is necessary in the design of the backstepping controller. However, the upper bound of the lumped uncertainty is difficult to obtain in advance in practical applications. Therefore, an adaptive law is derived to adapt the value of the lumped uncertainty in real time, and an adaptive backstepping control law is resulted. Then, a field-programmable-gate-array (FPGA) chip is adopted to implement the indirect field-oriented mechanism and the developed control algorithms for possible low-cost and high-performance industrial applications. The effectiveness of the proposed control scheme is verified by some experimental results. With the adaptive backstepping controller, the mover position of the FPGA-based LIM drive possesses the advantages of good transient-control performance and robustness to uncertainties in the tracking of periodic reference trajectories.

The paper details the application and handling qualities evaluation through computer-based simulation of an adaptive model reference controller acting on the longitudinal modes of a fighter-type aircraft. Whereas classical control designs depend largely on a priori knowledge of the system dynamics, adaptive control algorithms do not require the same degree of a priori sophistication, or alternately the same controller can be applied on a plant with varying dynamics such as experienced by an aircraft over a wide range of flight conditions. Although the applications of an adaptive controller are well understood, much of the existing research focuses on an adaptive controllers' ability to track a basic input (such as step, ramp, or sinusoid) over a range of time-varying plants. In this research the adaptive controller is evaluated through a series of pilot-in-the-loop tracking tasks utilizing the boundary avoidance tracking technique designed to highlight potential control difficulties which may lead to pilot-in-the-loop oscillations, task abandonment or loss of control. The results presented will serve as a precursor to flight tests of adaptive controllers on-board next generation fighter aircraft.

Nonlinear adaptive flight control system: Performance enhancement and validation