Search

The use of a neural network (NN) as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade. Typical NN-based controllers yield uniformly ultimately bounded (UU-B) stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances. Several researchers have proposed discontinuous feedback controllers (e.g., variable structure or sliding mode controllers) to reject the residual errors and yield asymptotic results. The research in this paper describes how a recently developed continuous robust integral of the sign of the error (RISE) feedback term can be incorporated with a NN-based feedforward term to achieve semi-global asymptotic tracking. To achieve this result, the typical stability analysis for the RISE method is modified to enable the incorporation of the NN-based feedforward terms, and a projection algorithm is developed to guarantee bounded NN weight estimates. Index Terms--Adaptive control, asymptotic stability, Lyapunov methods, neural network, nonlinear systems, RISE feedback, robust control.

A sliding mode observer (SMO) design and convergence analysis are presented in this paper, which includes a rigorous treatment to address multiple discontinuities in the resulting estimation error dynamics. In an extension of our previous SMO results, the current work provides a non-trivial reworking of the SMO estimation error system development and stability analysis that incorporates differential inclusions. The specific contributions presented in this paper beyond the previous work include: (1) A differential inclusions-based analysis of the SMO, which incorporates the set-valued definition of the discontinuous signum function; (2) An expanded derivation of the estimation error dynamics, which emphasises advantageous properties particular to our SMO structure; (3) A Lyapunov-based stability analysis of the SMO, that rigorously incorporates the multiple discontinuities in the estimation error dynamics. The Lyapunov-based stability analysis proves that the SMO achieves finite-time estimation of the complete state vector, where the output equation is in a nonstandard mathematical form. To test the performance of the SMO, numerical simulation results are also provided, which demonstrate the capability of the SMO to estimate the state of a fluid flow dynamic system using only a single sensor measurement of the flow field velocity. [ABSTRACT FROM AUTHOR]

Summary: This article presents a nonlinear closed‐loop active flow control (AFC) method, which achieves asymptotic regulation of a fluid flow velocity field in the presence of actuator uncertainty and sensor measurement limitations. To achieve the result, a reduced‐order model of the flow dynamics is derived, which utilizes proper orthogonal decomposition (POD) to express the Navier‐Stokes equations as a set of nonlinear ordinary differential equations. The reduced‐order model formally incorporates the actuation effects of synthetic jet actuators (SJA). Challenges inherent in the resulting POD‐based reduced‐order model include (1) the states are not directly measurable, (2) the measurement equation is in a nonstandard mathematical form, and (3) the SJA model contains parametric uncertainty. To address these challenges, a sliding mode observer (SMO) is designed to estimate the unmeasurable states in the reduced‐order model of the actuated flow field dynamics. A salient feature of the proposed SMO is that it formally compensates for the parametric uncertainty inherent in the SJA model. The SMO is rigorously proven to achieve local finite‐time estimation of the unmeasurable state in the presence of the parametric uncertainty in the SJA. The state estimates are then utilized in a nonlinear control law, which regulates the flow field velocity to a desired state. A Lyapunov‐based stability analysis is provided to prove local asymptotic regulation of the flow field velocity. To illustrate the performance of the proposed estimation and AFC method, comparative numerical simulation results are provided, which demonstrate the improved performance that is achieved by incorporating the uncertainty compensator. [ABSTRACT FROM AUTHOR]

Summary: Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO. [ABSTRACT FROM AUTHOR]

Observer-based sliding mode control of combustion instability in a Rijke-type thermoacoustic system is considered. A commonly used thermoacoustic model with sensors and monopole-like actuators is linearized and formulated in a state-space form. It is assumed that the velocity or pressure sensor locations are chosen to assure the observability of the system. An observer-based sliding mode controller is then implemented to tune the actuators so that the system is asymptotically stable. The effectiveness of the controller is illustrated through a simulation example involving two modes and one sensor. The successful demonstration indicates that the observer-based feedback controller can be applied to a real combustion system with multiple modes. [ABSTRACT FROM AUTHOR]

The flight trajectory of unmanned aerial vehicles (UAVs) can be significantly affected by external disturbances such as turbulence, upstream wake vortices, or wind gusts. These effects present challenges for UAV flight safety. Hence, addressing these challenges is of critical importance for the integration of unmanned aerial systems (UAS) into the National Airspace System (NAS), especially in terminal zones. This work presents a robust nonlinear control method that has been designed to achieve roll/yaw regulation in the presence of unmodeled external disturbances and system nonlinearities. The data from NASA-conducted airport experimental measurements as well as high-fidelity Large Eddy Simulations of the wake vortex are used in the study. Side-by-side simulation comparisons between the robust nonlinear control law and both linear H ∞ and PID control laws are provided for completeness. These simulations are focused on applications involving small UAV affected by the wake vortex disturbance in the vicinity of the ground (which models the take-off or landing phase) as well as in the out-of-ground zone. The results demonstrate the capability of the proposed nonlinear controller to asymptotically reject wake vortex disturbance in the presence of the nonlinearities in the system (i.e., parametric variations, unmodeled, time-varying disturbances). Further, the nonlinear controller is designed with a computationally efficient structure without the need for the complex calculations or function approximators in the control loop. Such a structure is motivated by UAV applications where onboard computational resources are limited. [ABSTRACT FROM AUTHOR]

The occlusion of feature points and/or feature points leaving the field of view of a camera is a significant practical problem that can lead to degraded performance or instability of visual servo control and vision-based estimation algorithms. By assuming that one known Euclidean distance between two feature points in an initial view is available, homography relationships and image geometry are used in this paper to determine the Euclidean coordinates of feature points in the field of view. A new daisy-chaining method is then used to relate the position and orientation of a plane defined by the feature points to other feature-point planes that are rigidly connected. Through these relationships, the Euclidean coordinates of the original feature points can be tracked even as they leave the field of view. This objective is motivated by the desire to track the Euclidean coordinates of feature points on one face of a satellite as it continually rotates and feature points become self-occluded. A numerical simulation is included to demonstrate that the Euclidean coordinates can be tracked even when they leave the field of view. However, the results indicate the need for a method to reconcile any accumulated error when the feature points return to the field of view. [ABSTRACT FROM AUTHOR]

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control. [ABSTRACT FROM AUTHOR]