Large Adaptive Gain Research Articles

L1 adaptive control design for the rigid body launch vehicle

This paper investigates the use of an L1-adaptive controller to improve the performance of the Vega launch vehicle because the classical controller does not guarantee stability and tracking of the system in the transient. The L1-AC ensures uniformly bounded transient and steady-state tracking for both systems’ signals, input, and output. In this paper, we used the equations of the adaptation and the L1-norm with two filters, the first one is first-order order and the second filter is third-order, we used the large adaptive gain with the first filter, also used the low adaptive gain with the second filter, and after the analysis the result numerically we found the lambda with the first filter less than 1 and the lambda with second filter larger than lambda with the first filter. The L1 adaptive controller can generate a stable system response to track the control input and the system output, both in transient and steady-state because we selected the adaptive gain large with minimize lambda. It is noted that the system response for the L1 adaptive control configuration with the first filter, as compared with the system response with the second filter, has much better performances, both from the point of view of the overshoot and rise time.

Distributed adaptive formation control for underactuated quadrotors with guaranteed performances

This paper investigates a distributed adaptive formation control problem for underactuated quadrotors with guaranteed performances. To ensure a robust and stable formation pattern with predefined behavior bounds, by transforming the original constrained formation synchronization error dynamics into an equivalent unconstrained one, a prescribed performance mechanism is introduced in the translational loop to render the formation regulation as a prior. An adaptive consensus strategy is developed according to undirected graph theory and Lyapunov stability rules for follower quadrotors to achieve a distributed cooperative formation with prescribed tracking abilities via exchanging local information with neighbors. The presented control scheme has the following salient merits: (1) the formation synchronization errors can be guaranteed within pre-assigned bounds with desired transient behaviors despite of uncertain disturbances; (2) by using a state estimation error to update neural network (NN) parameters, rather than the tracking error that widely applied in traditional NN approximators, and with the help of MLP technique, the proposed SE-MLP observer capable of decreasing the computational complexity can achieve a fast identification of lumped disturbances without causing high-frequency oscillations even using a large adaptive gain, and the transient solutions of L2 norm of the differential of neural weights are established to illustrate the mechanism of SE-MLP observer in reducing chattering behaviors. The merits of presented algorithm are confirmed by sufficient simulations.

Prescribed chattering reduction control for quadrotors using aperiodic signal updating

In the paper, a prescribed chattering reduction control using aperiodic signal updating is presented for quadrotors subject to parameter uncertainties and external disturbances. Using estimation errors instead of tracking errors to update adaptive laws, estimator-based minimum learning parameter (EMLP) observers capable of relaxing computational complexity are respectively explored in translational and rotational loops to reject fast time-varying disturbances, such that transient oscillations can be efficiently mitigated even with a large adaptive gain. Meanwhile, quantitative analysis for transient learning performance is characterized by means of L2 norms of time differential of neural network weights. With the aid of disturbance estimates, a relative event-triggered robust control law is derived by inserting a compensation term to guarantee a favorable trajectory tracking with Zeno free behaviors and decreased sampling cost. Besides, an appointed-time prescribed performance control (APPC) is established, enforcing trajectory tracking errors to evolve within pre-given regions even in face of triggering errors, where a piecewise and continuous finite-time behavior function, rather than an exponential decaying function, is applied to enable a preassigned fast convergence time without retuning controller parameters. Finally, the stability of closed-loop system is proved via Lyapunov synthesis, while comparative studies are provided to validate the effectiveness of presented control method.

Neurodynamic Approximation-Based Quantized Control With Improved Transient Performances for Microelectromechanical System Gyroscopes: Theory and Experimental Results

This article investigates a neurodynamic quantized control problem with improved transient performances for microelectromechanical system (MEMS) gyroscopes subject to lumped disturbances induced by parameter uncertainties, dynamic coupling, and external disturbances. First, a modified prescribed performance control mechanism based on a hyperbolic cosecant performance function is proposed to specify the transient behavior of tracking errors with an arbitrarily small overshoot. Then, to eliminate the lumped disturbances with a better identification property, a novel echo state network approximator that uses the estimation error to learn neural weights is designed with the aid of a minimal learning parameter technique, which not only can exclude the poor transient behaviors occurring extensively in the existing neural control with a large adaptive gain, but also dramatically reduce the number of parameters to be updated online. Furthermore, contrasting to the available tracking results assuming a continuous control updating, a hysteresis quantizer is introduced to provide discrete values of control signals, supporting the use of digital devices in MEMS gyroscope implementations to realize a closed-loop error stabilization. Finally, ultimately uniformly bounded stability of closed-loop system is proved with the aid of Lyapunov function and nonsmooth analysis technique, while not only simulations but also experimental results are performed to validate the effectiveness of the proposed scheme.

Neural Adaptive Control for MEMS Gyroscope with Full-State Constraints and Quantized Input

In this article, we investigate the neural adaptive quantized control problem for microelectromechanical system (MEMS) gyroscope with full-state constraints and lumped disturbances. With two different kinds of one-to-one nonlinear mappings, the traditional gyroscope model with matched disturbances is transformed into an unconstrained one with both unmatched and matched disturbances, thus the predefined time-varying state constraints imposed on MEMS gyroscope can be achieved. To compensate for the lumped disturbances, a state estimator-based minimal learning parameter neural network is proposed to obtain fast and smooth disturbance estimates for both position and velocity control loops, which not only can eliminate the poor transient behaviors that widely appear in the available neural adaptive control with a large adaptive gain, but also greatly reduce the number of leaning parameters updated online. Furthermore, by employing a hysteresis logarithmic quantizer, the neglected difficulty, named as constrained data bandwidth of actuator can be overcome with less chattering in control signal, which is more convenient to implement. Finally, the neural adaptive control for MEMS gyroscope is developed such that satisfactory tracking performance is achieved despite of large disturbances, full-state constraints as well as quantized input. The effectiveness and advantages of the proposed control method are demonstrated through extensive simulations.

Robust adaptive estimation of nonlinear system with time‐varying parameters

SummaryThe vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time‐varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high‐frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time‐varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time‐varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite‐time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time‐varying parameters. Copyright © 2014 John Wiley & Sons, Ltd.

Adaptive Loop Transfer Recovery

DAPTIVE control is an attractive approach in nonlinear systems theory due to its ability to cope with system uncertainties and failures. Adaptive controllers can be classified as either indirect or direct. This paper focuses on improving the robustness of a direct adaptive control design. The method is arrived at by examining the loop transfer properties of an adaptive system when linearized about an equilibrium condition. The design approach modifiesanadaptivelawwiththegoalofpreservingthelooptransfer propertiesofareferencemodelassociatedwithanonadaptivecontrol design. The aim is to achieve an adaptive system that preserves the stability margins of a nonadaptive design, while at the same time providing the benefits of adaptation to modeling error. Many modification terms are reported in the literature [1–11]. Included among these, � modification [1] adds a pure damping term to the adaptive law, whereas e modification [2] adds a variable damping term that depends on the error signal. These terms are introduced to ensure that the adapted weights remain bounded. Backgroundlearning[3–5]usescurrentandpastdataconcurrentlyin the adaptation process. It allows the adaptation law to continually train in the background based on past data, while still being responsivetodynamicchangesbasedonthecurrentdata.Inthisway, background learning incorporates long-term learning. Q modification [6–8] is similar in spirit to background learning in its intent to improve adaptation performance by using a moving window of the integrated system uncertainty. There is an optimal control theory based modification term that improves adaptation in the presence of large adaptive gain [9]. More recently, a Kalman filter modification approach[10]hasbeenintroducedasamodificationterminadaptive control.Kalman filtermodificationleadstoalternativeformsforwell

Optimal control modification for robust adaptive control with large adaptive gain

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain so as to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness. A new adaptive law, called optimal control modification, is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations. The modification is based on a minimization of the L2 norm of the tracking error bounded away from some lower bound, formulated as an optimal control problem. The optimality condition is used to derive the modification based on the Pontryagin’s Minimum Principle. The optimal control modification is shown to improve robustness of the standard MRAC without significantly compromising the tracking performance. Flight control simulations demonstrate the effectiveness of the new adaptive law. A series of recent, successful flight tests of this adaptive law on a NASA F/A-18A aircraft at NASA Dryden Flight Research Center further demonstrate the effectiveness of the optimal control modification adaptive law.

Rate of convergence in model reference adaptive control

A new adaptive scheme for continuous-time model reference adaptive control systems is proposed. It is shown that this scheme allows us to increase the exponential rate of parameter convergence to an arbitrary, desired level subject to a sufficiently rich reference input and a sufficiently large adaptive gain, while retaining global stability of the overall system. For simplicity and brevity the results are presented for plants with known high-frequency gain k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> .