skip to main content

Title: Adaptive NN-Based Boundary Control for Output Tracking of A Wave Equation with Matched and Unmatched Boundary Uncertainties
This paper is focused on the output tracking control problem of a wave equation with both matched and unmatched boundary uncertainties. An adaptive boundary feedback control scheme is proposed by utilizing radial basis function neural networks (RBF NNs) to deal with the effect of system uncertainties. Specifically, two RBF NN models are first developed to approximate the matched and unmatched system uncertain dynamics respectively. Based on this, an adaptive NN control scheme is derived, which consists of: (i) an adaptive boundary feedback controller embedded by the NN model approximating the matched uncertainty, for rendering stable and accurate tracking control; and (ii) a reference model embedded by the NN model approximating the unmatched uncertainty, for generating a prescribed reference trajectory. Rigorous analysis is performed using the Lyapunov theory and the C0-semigroup theory to prove that our proposed control scheme can guarantee closed-loop stability and wellposedness. Simulation study has been conducted to demonstrate effectiveness of the proposed approach.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of the American Control Conference
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. In this paper, we propose a novel control architecture, inspired from neuroscience, for adaptive control of continuous time systems. The objective here is to design control architectures and algorithms that can learn and adapt quickly to changes that are even abrupt. The proposed architecture, in the setting of standard neural network (NN) based adaptive control, augments an external working memory to the NN. The learning system stores, in its external working memory, recently observed feature vectors from the hidden layer of the NN that are relevant and forgets the older irrelevant values. It retrieves relevant vectors from the working memory to modify the final control signal generated by the controller. The use of external working memory improves the context inducing the learning system to search in a particular direction. This directed learning allows the learning system to find a good approximation of the unknown function even after abrupt changes quickly. We consider two classes of controllers for illustration of our ideas (i) a model reference NN adaptive controller for linear systems with matched uncertainty (ii) backstepping NN controller for strict feedback systems. Through extensive simulations and specific metrics we show that memory augmentation improves learning significantly even when the system undergoes sudden changes. Importantly, we also provide evidence for the proposed mechanism by which this specific memory augmentation improves learning. 
    more » « less
  2. Summary

    A new robust adaptive control scheme is developed for nonlinearly parametrized multivariable systems in the presence of parameter uncertainties and unmatched disturbances. The developed control scheme employs a new integrated framework of a functional bounding technique for handling nonlinearly parametrized system dynamics, an adaptive parameter estimation algorithm for dealing with parameter uncertainties, a nonlinear feedback controller structure for stabilization of interconnected system states, and a robust adaptive control design for accommodating unmatched disturbances. It is proved that such a new robust adaptive control scheme is capable of ensuring the global boundedness and mean convergence of all closed‐loop system signals. A complete simulation study on an air vehicle system with nonlinear parametrization in the presence of an unmatched wind disturbance is conducted, and its results verify the effectiveness of the proposed robust adaptive control scheme.

    more » « less
  3. Allowing for a “virtual” full actuation of a rotary inverted pendulum (RIP) system with only a single physical actuator has been a challenging problem. In this paper, a hybrid control scheme that involves a pole-placement feedback controller and an optimal proportional–integral–derivative (PID) or fractional-order PID (FOPID) controller is proposed to simultaneously enable the tracking control of the rotary arm and the stabilization of the pendulum arm in an input–output feedback linearized RIP system. The PID controller is optimized first with the particle swarm optimization (PSO) to obtain three optimal gains, and then the other two parameters of the FOPID controller are optimized with the PSO. Compared to the optimized PID controller, the optimized FOPID controller improves the tracking and stabilizing accuracy by 53% and 29%, respectively, and demonstrates better adaptability for tracking different reference signals. Moreover, the hybrid FOPID controller exhibits 74.8% and 53% higher tracking accuracy than previous optimized model reference adaptive control PID (MRAC-PID) and linear–quadratic regulator (LQR) controllers, respectively. The proposed hybrid controllers are also digitized with different rules and sampling times, showing a closer performance between the discrete-time and continuous-time hybrid controllers under smaller sampling times.

    more » « less
  4. The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations. 
    more » « less
  5. Summary

    This paper addresses a new adaptive output tracking problem in the presence of uncertain plant dynamics and uncertain sensor failures. A new unified nominal state‐feedback control law is developed to deal with various sensor failures, which is directly constructed by state sensor outputs. Such a new state‐feedback compensation control law is able to ensure the desired plant‐model matching properties under different failure patterns. Based on the nominal compensation control design, a new adaptive compensation control scheme is proposed, which guarantees closed‐loop signal boundedness and asymptotic output tracking. The new adaptive compensation scheme not only expands the sensor failures types that the system could tolerate but also avoids some signal processing procedures that the traditional fault‐tolerant control techniques are forced to encounter. A complete stability analysis and a representative simulation study are conducted to evaluate the effectiveness of the proposed adaptive compensation control scheme.

    more » « less