Robust Adaptive Control for Constrained Dynamical Systems Following Unreliable Reference Signals

ABSTRACTIn this paper, we address the robust control design problem for nonlinear dynamical systems tracking unreliable reference signals. Specifically, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear plants that are affected by matched, unmatched, and parametric uncertainties, and are subject to constraints on the state space and the measured output. These control laws guarantee satisfactory results even in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example involving the attitude control of a spacecraft illustrates the feasibility of the theoretical results presented.

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control (MRAC) laws for systems represented by parabolic or hyperbolic partial differential equations (PDEs) with spatially varying parameters is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with known parameters or as a spatially-varying time-invariant signal.

This article presents an innovative control architecture for tilt-rotor quadcopters with H-configuration transporting unknown, sling payloads. This control architecture leverages on a thorough analysis of the aircraft's equation of motion, which reveals gyroscopic effects that were not fully characterized and were disregarded while synthesizing control algorithms in prior publications. Furthermore, the proposed control architecture employs barrier Lyapunov functions and a novel robust model reference adaptive control law to guarantee a priori user-defined constraints on both the trajectory tracking error and the control input, despite poor information on the aircraft's inertial properties and the presence of unknown, unsteady payloads. Flight tests involving a quadcopter pulling an unmodeled cart by means of a thin rope of unknown length, which is slack at the beginning of the mission, verify the effectiveness of the theoretical results.

This paper analyzes the dynamics of tilt-rotor quadcopters with H-configuration and synthesizes a control system for these vehicles. Our analysis is the first to show a nonlinear effect in the vehicle's rotational dynamics due to the fact that not all propellers of a tilt-rotor are aligned to one of the vehicle's principal axes. The proposed control system relies on an original robust model reference adaptive control law to guarantee user-defined constraints on both the trajectory tracking error and the adaptive gains at all despite parametric, matched, and unmatched uncertainties due to unknown external disturbances and dangling payloads.

A novel model-reference robust adaptive controller that does not require a priori knowledge of the high-frequency-gain sign is proposed. The scheme is applicable to minimum-phase plants of arbitrary relative degree and ensures that in the absence of unmodeled dynamics the tracking error converges to zero and all the signals remain bounded. The control law uses a particular projected parameter vector instead of the current estimates to avoid division by zero. >

This paper proposes the application of a combined adaptive controller for the current control loop of a Shunt Active Power Filter (Shunt APF). The proposed approach uses a Variable Structure Controller (VS) together with a Robust Model Reference Adaptive Controller (RMRAC), leading to a VS-RMRAC algorithm. The control law u = ¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> ¿ is comprised by two set of parameters. One set is related with the RMRAC while the other part is related with the VS controller. The VS parameters are used to improve the transient response, and its effect increases when the estimation error increases. The VS-RMRAC is experimentally tested and compared with a Dead Beat current controller in a three-phase four-wire Shunt APF.

In this paper, we investigate the trajectory tracking control problem of surface ships subject to unknown parameters, unknown time-varying disturbances, and input saturation. The input saturation is approximated using a Gaussian error function. The compounded uncertain term caused by the unknown parameters and disturbances is transformed into a linear parametric form with a single parameter called virtual parameter. Then, a novel robust adaptive ship trajectory tracking control law is designed using the adaptive vector-backstepping design method, where the adaptive law online provides the estimation of the virtual parameter. Further, a finite-time control scheme is developed injecting a power function vector of the position and velocity errors into the proposed control scheme such that the control performance is improved. Both our control schemes are simple to compute and easy to implement in engineering applications. Theoretical analysis indicates that the designed control laws can force the surface ship to track the desired trajectory while guaranteeing the global uniform ultimate boundedness of all the signals in the closed-loop trajectory tracking control system of surface ships. Simulation results and comparison verify the effectiveness of our novel robust adaptive trajectory tracking control schemes.

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

This work proposes a vector speed control scheme for Permanent Magnet Synchronous Motors (PMSM) which is robust against parameter uncertainties. It is based on a control law called VS-RMRAC (Variable Structure Robust Model Reference Adaptive Control). Such control law consists on a discrete time modification of the continuous control law presented in [1]. This paper main contribution is the proposal of a vector speed control scheme based on this controller for PMSM. Simulation and experimental results shows that the proposed scheme is robust against parameter uncertainties, which allows implementing this system without accurate plant knowledge. Obtained results show also system capability to compensate load disturbance applied to the motor axis.

This paper presents the development of direct adaptive control laws to enable an autonomous unmanned aerial vehicle (UAV) to track reference trajectories in the presence of external disturbances. A maneuver database of reference trajectories is computed offline from a linear UAV dynamic model using an optimization routine. Each maneuver in the database is therefore represented as a state trajectory, as well as the control input sequence that generates that trajectory. The trajectory tracking control laws are designed to enable a UAV to follow reference trajectories from this maneuver database. A disturbance accommodating control law is first developed and applied for the tracking of reference trajectories while the UAV is subjected to a persistent external disturbance. This control design requires a state-space disturbance generator model and the derivation of ideal trajectories from a reference model, which requires the solution of a set of matching conditions. A direct adaptive controller is then developed to enable the UAV to track reference trajectories while subject to modeling error and external disturbances. The adaptive controller also requires a disturbance model and the existence of ideal trajectories, but it does not require the explicit solution of the matching conditions. Simulation results for the disturbance accommodating controller and the adaptive controller are presented using a linear six-degree-of-freedom dynamic model that is representative of typical UAV dynamics. The results show that, although both controllers track reference trajectories and provide disturbance rejection, the adaptive controller is better suited for handling modeling errors or uncertainties.

This paper investigates the tracking control problem of underactuated surface vessels with non-diagonal inertia and damping matrices. Based on the inherent cascaded structure of vessel dynamics and the cascaded system theory, the tacking control problem of vessels is converted to the stabilization control problem of two cascaded subsystems. Two trajectory tracking control laws are designed respectively for known and unknown model parameters. The first feedback control law is derived with the aid of Lyapunov method, realizing the global $${\mathscr {K}}$$ -exponential trajectory tracking of vessels with accurate model parameters. As all the state variables in the first law are independent of model parameters, the sliding mode technique is applied to extend the first control scheme to the case of unknown model parameters, resulting into an another tracking control law, which ensures the global $${\mathscr {K}}$$ -exponential stability of the closed-loop error system despite unknown model parameters. Effectiveness of the proposed controllers is demonstrated by numerical simulations.

In this paper, a robust model reference adaptive controller is presented for robots based on neural network parametrization. The controller is based on applying direct adaptive techniques to a basic fixed controller for better control performance, while a sliding mode control is introduced to guarantee robust closed-loop stability. It is shown that if bounded basis function networks are used for the parallel NN, uniformly stable adaptation is assured and asymptotic tracking of the reference signal is achieved.

Differential games, partial-state stabilization, and model reference adaptive control

Recently, variable structure design (VSD) has been intensively researched in the literature of model reference adaptive control (MRAC) for its well-behaved transient response and appealing tracking performance. In the recent work by Hsu [6], parameter switching mechanism has been introduced in the design of model reference controller to obtain better transient behavior. By taking a different viewpoint, we apply VSD to the control channel, and develop a new robust model reference adaptive controller for a class of uncertain plants with arbitrary relative degree. It is shown that in the presence of additive, multiplicative unmodeled dynamics, and bounded disturbance, the output tracking error can still be guaranteed to converge to zero with an exponential rate. Since the parameter update law is introduced in the synthesis of this new adaptive control law, the magnitude of the switching control forces can be reduced to a more realistic level for implementation. To highlight the improved performance, simulation results are conducted with an uncertain plant with relative degree two.

This paper presents the development of an equilibrated three-phase power source, which is able to generate sinusoidal waveforms with adjustable amplitudes and frequencies, as well as several arbitrary waveforms. The setup is based on a computer-controlled three-phase PWM inverter system, whose model is rewritten using /spl alpha//spl beta/0 transformation. A robust model reference adaptive controller (RMRAC) is used to assure system robustness and performance. Simulation and experimental results are used to show the closed-loop system performance, when different waveforms are generated under several operation conditions.