Reinforcement Learning Based Controller Synthesis for Flexible Aircraft Wings

Aeroelastic study of flight vehicles has been a subject of great interest and research in the last several years. Aileron reversal and flutter related problems are due in part to the elasticity of a typical airplane. Structural dynamics of an aircraft wing due to its aeroelastic nature are characterized by partial differential equations. Controller design for these systems is very complex as compared to lumped parameter systems defined by ordinary differential equations. In this paper, a stabilizing statefeedback controller design approach is presented for the heave dynamics of a wing-fuselage model. In this study, a continuous actuator in the spatial domain is assumed. A control methodology is developed by combining the technique of “proper orthogonal decomposition” and approximate dynamic programming. The proper orthogonal decomposition technique is used to obtain a low-order nonlinear lumped parameter model of the infinite dimensional system. Then a near optimal controller is designed using the single-network-adaptive-critic technique. Furthermore,to add robustness to the nominal single-network-adaptive-critic controller against matched uncertainties, an identifier based adaptive controller is proposed. Simulation results demonstrate the effectiveness of the single-network-adaptive-critic controller augmented with adaptive controller for infinite dimensional systems.

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and the predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and the predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

Robust Adaptive Model Tracking for Distributed Parameter Control of Linear Infinite-dimensional Systems in Hilbert Space

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model.Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase,we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness.The plant is described by a closed,densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states.The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinitedimensional Hilbert space.The result will not require the use of the standard Barbalat’s lemma which requires certain signals to be uniformly continuous.This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model.In particular,we examine conditions for a set of ideal trajectories to exist for the tracking problem.Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.