Parag M. Patre

Asymptotic Tracking for Systems With Structured and Unstructured Uncertainties

The control of systems with uncertain nonlinear dynamics has been a decades-long mainstream area of focus. The general trend for previous control strategies developed for uncertain nonlinear systems is that the more unstructured the system uncertainty, the more control effort (i.e., high gain or high-frequency feedback) is required to cope with the uncertainty, and the resulting stability and performance of the system is diminished (e.g., uniformly ultimately bounded stability). This brief illustrates how the amalgamation of an adaptive model-based feedforward term (for linearly parameterized uncertainty) with a robust integral of the sign of the error (RISE) feedback term (for additive bounded disturbances) can be used to yield an asymptotic tracking result for Euler-Lagrange systems that have mixed unstructured and structured uncertainty. Experimental results are provided that illustrate a reduced root-mean-squared tracking error with reduced control effort.

Asymptotic Tracking for Uncertain Dynamic Systems Via a Multilayer Neural Network Feedforward and RISE Feedback Control Structure

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 (UUB) 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.

Asymptotic Tracking for Systems with Structured and Unstructured Uncertainties

The control of systems with uncertain nonlinear dynamics has been a decades long mainstream area of focus. The general trend for previous control strategies developed for uncertain nonlinear systems is that the more unstructured the system uncertainty, the more control effort (i.e., high gain or high frequency feedback) is required to reject the uncertainty, and the resulting stability and performance of the system is diminished (e.g., uniformly ultimately bounded stability). This paper is the first result that illustrates how the amalgamation of an adaptive model-based feedforward term with a high gain integral feedback term can be used to yield an asymptotic tracking result for systems that have mixed unstructured and structured uncertainties.

Asymptotic Tracking for Aircraft via Robust and Adaptive Dynamic Inversion Methods

Two asymptotic tracking controllers are designed in this paper, which combine model reference adaptive control and dynamic inversion methodologies in conjunction with the robust integral of the signum of the error (RISE) technique for output tracking of an aircraft system in the presence of parametric uncertainty and unknown, nonlinear disturbances, which are not linearly parameterizable (non-LP). The control designs are complicated by the fact that the control input is multiplied by an uncertain, non-square matrix. A robust control design is presented first, in which partial knowledge of the aircraft model along with constant feedforward estimates of the unknown input parameters are used with a robust control term to stabilize the system. Motivated by the desire to reduce the need for high-gain feedback, an adaptive extension is then presented, in which feedforward adaptive estimates of the input uncertainty are used. These results show how asymptotic tracking control can be achieved for a nonlinear system in the presence of a non-square input matrix containing parametric uncertainty and nonlinear, non-LP disturbances. Asymptotic output tracking is proven via Lyapunov stability analysis, and high-fidelity simulation results are provided to verify the efficacy of the proposed controllers.

Asymptotic Tracking for Uncertain Dynamic Systems via a Multilayer NN Feedforward and RISE Feedback Control Structure

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 (UUB) 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.

Brief paper: Composite adaptive control for Euler-Lagrange systems with additive disturbances

In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error. Ideally, the adaptive update law would also include some feedback of the parameter estimation error. The desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a prediction error and the state feedback. In all previous composite adaptive controllers, the formulation of the prediction error is predicated on the critical assumption that the system uncertainty is linear in the uncertain parameters (LP uncertainty). The presence of additive disturbances that are not LP would destroy the prediction error formulation and stability analysis arguments in previous results. In this paper, a new prediction error formulation is constructed through the use of a recently developed Robust Integral of the Sign of the Error (RISE) technique. The contribution of this design and associated stability analysis is that the prediction error can be developed even with disturbances that do not satisfy the LP assumption (e.g., additive bounded disturbances). A composite adaptive controller is developed for a general MIMO Euler-Lagrange system with mixed structured (i.e., LP) and unstructured uncertainties. A Lyapunov-based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi-global asymptotic tracking. Experimental results are presented to illustrate the approach.

Modular Adaptive Control of Uncertain Euler–Lagrange Systems With Additive Disturbances

A novel adaptive nonlinear control design is developed which achieves modularity between the controller and the adaptive update law. Modularity between the controller/update law design provides flexibility in the selection of different update laws that could potentially be easier to implement or used to obtain faster parameter convergence and/or better tracking performance. For a general class of linear-in-the-parameters (LP) uncertain Euler-Lagrange systems subject to additive bounded non-LP disturbances, the developed controller uses a model-based feedforward adaptive term in conjunction with the recently developed robust integral of the sign of the error (RISE) feedback term. Modularity in the adaptive feedforward term is made possible by considering a generic form of the adaptive update law and its corresponding parameter estimate. This generic form of the update law is used to develop a new closed-loop error system and stability analysis that does not depend on nonlinear damping to yield the modular adaptive control result.

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.

Nonlinear Control of NMES: Incorporating Fatigue and Calcium Dynamics

Neuromuscular electrical stimulation (NMES) is a promising technique that has the potential to restore functional tasks in persons with movement disorders. Clinical and commercial NMES products exist for this purpose, but a pervasive problem with current technology is that overstimulation of the muscle (among other factors) leads to muscle fatigue. The objective of the current effort is to develop a NMES controller that incorporates the effects of muscle fatigue through an uncertain function of the calcium dynamics. A neural network-based estimate of the fatigue model mismatch is incorporated in a nonlinear controller through a backstepping based method to control the human quadriceps femoris muscle undergoing non-isometric contractions. The developed controller is proven to yield uniformly ultimately bounded stability for an uncertain nonlinear muscle model in the presence of bounded nonlinear disturbances (e.g., spasticity, delays, changing load dynamics).© 2009 ASME