Z. D. Wilcox

Lyapunov-Based Exponential Tracking Control of a Hypersonic Aircraft with Aerothermoelastic Effects

Hypersonic flightconditionsproducetemperaturevariationsthatcanalterboththestructuraldynamicsand flight dynamics. These aerothermoelastic effects are modeled bya nonlinear, temperature-dependent, parameter-varying state-space representation. The model includes an uncertain parameter-varying state matrix, an uncertain parameter-varying nonsquare (column-deficient) input matrix, and a nonlinear additive bounded disturbance. A Lyapunov-based continuous robust controller is developed that yields exponential tracking of a reference model, despite the presence of bounded nonvanishing disturbances. Simulation results for a hypersonic aircraft are provided to demonstrate the robustness and efficacy of the proposed controller.

Robust nonlinear control of a hypersonic aircraft in the presence of aerothermoelastic effects

Hypersonic flight conditions produce temperature variations that can alter the flight dynamics. A nonlinear temperature dependent, parameter varying state-space representation is proposed to capture the aerothermoelastic effects in a hypersonic vehicle. This model includes an uncertain parameter varying state matrix, an uncertain parameter varying non-square (column deficient) input matrix, and a nonlinear additive bounded disturbance. A Lyapunov-based continuous robust output feedback controller is developed that yields global exponential tracking of a reference model, despite the presence of disturbances that do not satisfy the linear-in-the parameters (LP) assumption.

Global Adaptive Output Feedback Tracking Control of an Unmanned Aerial Vehicle

An output feedback (OFB) dynamic inversion control strategy is developed for an unmanned aerial vehicle (UAV) that achieves global asymptotic tracking of a reference model. The UAV is modeled as an uncertain linear time-invariant (LTI) system with an additive bounded nonvanishing nonlinear disturbance. A continuous tracking controller is designed to mitigate the nonlinear disturbance and inversion error, and an adaptive law is utilized to compensate for the parametric uncertainty. Global asymptotic tracking of the measurable output states is proven via a Lyapunov-like stability analysis, and high-fidelity simulation results are provided to illustrate the applicability and performance of the developed control law.

Composite Adaptation for Neural Network-Based Controllers

This paper presents a novel approach to design a composite adaptation law for neural networks that uses both the system tracking errors and a prediction error containing parametric information by devising an innovative swapping procedure that uses the recently developed Robust Integral of the Sign of the Error (RISE) feedback method. Semi-global asymptotic tracking is proven for an Euler-Lagrange system.

Asymptotic optimal control of uncertain nonlinear Euler-Lagrange systems

A sufficient condition to solve an optimal control problem is to solve the Hamilton-Jacobi-Bellman (HJB) equation. However, finding a value function that satisfies the HJB equation for a nonlinear system is challenging. For an optimal control problem when a cost function is provided a priori, previous efforts have utilized feedback linearization methods which assume exact model knowledge, or have developed neural network (NN) approximations of the HJB value function. The result in this paper uses the implicit learning capabilities of the RISE control structure to learn the dynamics asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the RISE feedback term asymptotically identifies the unknown dynamics, yielding semi-global asymptotic tracking. In addition, it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element. An extension is included to illustrate how a NN can be combined with the previous results. Experimental results are given to demonstrate the proposed controllers.

Optimal control of uncertain nonlinear systems using RISE feedback

A Hamilton-Jacobi-Bellman optimization scheme is used along with a RISE feedback structure to minimize a quadratic performance index while the generalized coordinates of a nonlinear Euler-Lagrange system asymptotically track a desired time-varying trajectory despite general uncertainty in the dynamics, such as additive bounded disturbances and parametric uncertainty. Motivated by recent previous results that use a neural network structure to approximate the dynamics (i.e., the state space model is approximated with a residual function reconstruction error), the result in this paper uses the implicit learning capabilities of the RISE control structure to learn the dynamics asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the RISE feedback term asymptotically identifies the unknown dynamics, yielding semi-global asymptotic tracking. In addition, it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element. Simulation results are included to demonstrate the performance of the developed controller.

Adaptive control of a robotic system undergoing a non-contact to contact transition with a viscoelastic environment

Control of a robot interacting with a soft compliant environment is a practically important problem, with potential applications in areas involving human robot interaction (HRI) like rehabilitation, search and rescue, assistive robotics and haptics. The objective, in this paper, is to control a robot as it transitions from a non-contact to a contact state with an unactuated viscoelastic mass-spring system such that the mass-spring is regulated to a desired final position. Because of its simplicity and better physical consistency in explaining the behavior of viscoelastic materials, a Hunt-Crossley nonlinear model is used to represent the viscoelastic contact dynamics. An adaptive Lyapunov based controller is proposed, and shown to guarantee uniformly ultimately bounded (UUB) regulation of the system despite parametric uncertainty throughout the robot and mass-spring systems. The proposed controller only depends on the position and velocity terms, and hence, obviates the need for measuring the impact force and acceleration. Further, the resulting controller is continuous, and the same controller can be used for both non-contact and contact states of the robot with its environment.

Optimal control of uncertain nonlinear systems using a neural network and RISE feedback

A sufficient condition to solve an optimal control problem is to solve the Hamilton-Jacobi-Bellman (HJB) equation. However, finding a value function that satisfies the HJB equation for a nonlinear systems is challenging. Previous efforts have utilized feedback linearization methods which assume exact model knowledge, or have developed neural network (NN) approximations of the HJB value function. The current effort builds on our previous efforts to illustrate how a NN can be combined with a recent robust feedback method to asymptotically minimize a given quadratic performance index as the generalized coordinates of a nonlinear Euler-Lagrange system asymptotically track a desired time-varying trajectory despite general uncertainty in the dynamics. A Lyapunov analysis is provided to examine the stability of the developed optimal controller.

Composite adaptation for neural network-based controllers

With the motivation of using more information to update the parameter estimates to achieve improved tracking performance, composite adaptation that uses both the system tracking errors and a prediction error containing parametric information to drive the update laws, has become widespread in adaptive control literature. However, despite its obvious benefits, composite adaptation has not been widely implemented in neural network-based control, primarily due to the neural network (NN) reconstruction error that destroys a typical prediction error formulation required for the composite adaptation. This technical note presents a novel approach to design a composite adaptation law for NNs by devising an innovative swapping procedure that uses the recently developed robust integral of the sign of the error (RISE) feedback method. Semi-global asymptotic tracking is proven for a Euler-Lagrange system. Experimental results are provided to illustrate the concept.

Global adaptive output feedback MRAC

A robust adaptive output feedback (OFB) dynamic inversion control strategy is presented that achieves global asymptotic tracking of a reference model. The considered system contains linearly parameterizable uncertainty in the state and input matrices. The dynamic model also includes an unknown, nonlinear disturbance, which does not satisfy the linear-in-the-parameters assumption. A continuous tracking controller is designed to mitigate the nonlinear disturbance and inversion error, and a Lyapunov-based adaptive law is utilized to compensate for the parametric uncertainty. Global asymptotic tracking of the measurable output states is proven via Lyapunov stability analysis, and high-fidelity simulation results are provided to illustrate the applicability and performance of the developed control law for an unmanned air vehicle (UAV).