Huyen T. Dinh

Approximate optimal trajectory tracking for continuous-time nonlinear systems

Adaptive dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous-time nonlinear systems has remained a non-trivial open problem. The control development in this paper guarantees ultimately bounded tracking of a desired trajectory, while also ensuring that the enacted controller approximates the optimal controller.

Robust Identification-Based State Derivative Estimation for Nonlinear Systems

A robust identification-based state derivative estimation method for uncertain nonlinear systems is developed. The identifier architecture consists of a recurrent multilayer dynamic neural network which approximates the system dynamics online, and a continuous robust feedback Robust Integral of the Sign of the Error (RISE) term which accounts for modeling errors and exogenous disturbances. Numerical simulations provide comparisons with existing robust derivative estimation methods including: a high gain observer, a 2-sliding mode robust exact differentiator, and numerical differentiation methods, such as backward difference and central difference.

Dynamic neural network-based robust observers for uncertain nonlinear systems

A dynamic neural network (DNN) based robust observer for uncertain nonlinear systems is developed. The observer structure consists of a DNN to estimate the system dynamics on-line, a dynamic filter to estimate the unmeasurable state and a sliding mode feedback term to account for modeling errors and exogenous disturbances. The observed states are proven to asymptotically converge to the system states of high-order uncertain nonlinear systems through Lyapunov-based analysis. Simulations and experiments on a two-link robot manipulator are performed to show the effectiveness of the proposed method in comparison to several other state estimation methods.

Output feedback control for uncertain nonlinear systems with slowly varying input delay

Output Feedback (OFB) control of a nonlinear system with time-varying actuator delay is a challenging problem because of both the the lack of full state information and the need to develop prediction of the nonlinear dynamics. In this paper, an OFB tracking controller is developed for a general second-order system with time-varying input delay, uncertainties, and additive bounded disturbances. The developed controller is a modified PD controller working in association with a predictor-like feedback term to compensate for the input delay. The PD components are formulated using the difference between a desired trajectory and an estimate of the unknown state, acquired from a dynamic neural network-based observer, to compensate for the unavailability of the true system state. A stability analysis using Lyapunov-Krasovskii functionals is provided to for uniformly ultimately bounded (UUB) tracking and UUB estimation of the unavailable state. A numerical simulation is provided to illustrate the performance of the control design and illustrate its robustness to delay variations.

Dynamic neural network-based robust identification and control of a class of nonlinear systems

A methodology for dynamic neural network (DNN) identification-based control of nonlinear systems is proposed. The multi-layer DNN structure is modified by the addition of a sliding mode term in order to robustly account for exogenous disturbances and DNN reconstruction errors. New weight update laws for the DNN are proposed which guarantee asymptotic regulation of the identification error to zero. The DNN identifier is used in conjunction with a continuous RISE feedback term for asymptotic tracking of a desired trajectory. Both the identifier and the controller operate simultaneously in real time.

Dynamic neural network-based global output feedback tracking control for uncertain second-order nonlinear systems

A methodology for dynamic neural network (DNN) observer-based output feedback control of uncertain nonlinear systems with bounded disturbances is developed. The DNN-based observer works in conjunction with a dynamic filter for state estimation using only output measurements during on-line operation. A sliding mode term is added to the DNN structure to robustly account for exogenous disturbances and reconstruction errors. Weight update laws for the DNN, based on estimation, tracking errors, and filter output are proposed which guarantee global asymptotic regulation of the estimation error. A combination of a neural network feedforward term, along with estimated state feedback and sliding mode terms yields a global asymptotic tracking result. The developed method yields the first output feedback technique simultaneously achieving global asymptotic tracking and global asymptotic estimation of unmeasurable states for the class of uncertain nonlinear systems with bounded disturbances.

Lyapunov-Based Tracking of Store-Induced Limit Cycle Oscillations in an Aeroelastic System

Store-induced limit cycle oscillations (LCOs) are a common issue on current fighter aircraft and are expected to be present on next generation fighter aircraft. Current efforts in control systems designed to suppress LCO behavior have been either linear and restricted to specific flight regimes or nonlinear but require uncertainties in the system dynamics to be linear-in-the-parameters and only present in the torsional stiffness. Furthermore, the aerodynamic model used in prior research efforts neglects any nonlinear effects. This paper presents the development of a controller consisting of a continuous RISE feedback term with a neural network feedforward term to achieve semiglobal asymptotic tracking of the wing angle of attack in the presence of structural and aerodynamic uncertainties that do not satisfy the linear-in-the-parameter assumption.© 2012 ASME

Dynamic neural network-based robust observers for second-order uncertain nonlinear systems

A dynamic neural network (DNN) based robust observer for second-order uncertain nonlinear systems is developed. The observer structure consists of a DNN to estimate the system dynamics on-line, a dynamic filter to estimate the unmeasurable state and a sliding mode feedback term to account for modeling errors and exogenous disturbances. The observed states are proven to asymptotically converge to the system states though Lyapunov-based stability analysis.

Identification-Based Closed-Loop NMES Limb Tracking With Amplitude-Modulated Control Input

An upper motor neuron lesion (UMNL) can be caused by various neurological disorders or trauma and leads to disabilities. Neuromuscular electrical stimulation (NMES) is a technique that is widely used for rehabilitation and restoration of motor function for people suffering from UMNL. Typically, stability analysis for closed-loop NMES ignores the modulated implementation of NMES. However, electrical stimulation must be applied to muscle as a modulated series of pulses. In this paper, a muscle activation model with an amplitude modulated control input is developed to capture the discontinuous nature of muscle activation, and an identification-based closed-loop NMES controller is designed and analyzed for the uncertain amplitude modulated muscle activation model. Semi-global uniformly ultimately bounded tracking is guaranteed. The stability of the closed-loop system is analyzed with Lyapunov-based methods, and a pulse frequency related gain condition is obtained. Experiments are performed with five able-bodied subjects to demonstrate the interplay between the control gains and the pulse frequency, and results are provided which indicate that control gains should be increased to maintain stability if the stimulation pulse frequency is decreased to mitigate muscle fatigue. For the first time, this paper brings together an analysis of the controller and modulation scheme.

Dynamic Neural Network-Based Output Feedback Tracking Control for Uncertain Nonlinear Systems

A dynamic neural network (DNN) observer-based output feedback controller for uncertain nonlinear systems with bounded disturbances is developed. The DNN-based observer works in conjunction with a dynamic filter for state estimation using only output measurements during online operation. A sliding mode term is included in the DNN structure to robustly account for exogenous disturbances and reconstruction errors. Weight update laws for the DNN, based on estimation errors, tracking errors, and the filter output are developed, which guarantee asymptotic regulation of the state estimation error. A combination of a DNN feedforward term, along with the estimated state feedback and sliding mode terms yield an asymptotic tracking result. The developed output feedback (OFB) method yields asymptotic tracking and asymptotic estimation of unmeasurable states for a class of uncertain nonlinear systems with bounded disturbances. A twolink robot manipulator is used to investigate the performance of the proposed control approach. [DOI: 10.1115/1.4035871]