Concurrent learning adaptive controllers, which use recorded and current data concurrently for adaptation, are developed for model reference adaptive control of uncertain linear dynamical systems. We show that a verifiable condition on the linear independence of the recorded data is sufficient to guarantee global exponential stability. We use this fact to develop exponentially decaying bounds on the tracking error and weight error, and estimate upper bounds on the control signal. These results allow the development of adaptive controllers that ensure good tracking without relying on high adaptation gains, and can be designed to avoid actuator saturation. Simulations and hardware experiments show improved performance. Copyright CONCURRENT LEARNING ADAPTIVE CONTROL OF LINEAR SYSTEMS 281 exponential weight convergence, and hence to guarantee exponential stability of the entire closed loop system, which consists of both the tracking error and weight error dynamics. Boyd and Sastry have shown that the condition on PE states can be directly related to a condition on the spectral properties of the exogenous reference input [11]. However, enforcing PE through exogenous excitation is not always feasible, particularly in applications that require high precision or smooth operation. Furthermore, since it is hard to predict the future behavior of systems such as aircraft, it can often be difficult to monitor online whether a signal will remain PE. Hence, exponential weight convergence, and therefore, exponential tracking error convergence, cannot be guaranteed in many adaptive control applications.In this paper, we describe a novel approach to guarantee exponential stability of MRAC of uncertain linear multivariable dynamical systems by utilizing the idea of concurrent learning [12,13]. Particularly, we show that a concurrent learning model reference adaptive controller, which uses both current and past data concurrently for adaptation, can guarantee global exponential stability of the zero solution of the closed loop dynamics subject to a verifiable condition on linear independence of the recorded data; without requiring PE states. That is, it can guarantee that the tracking error and the weight error dynamics simultaneously converge to zero exponentially fast as long as the system states are exciting over a finite period of time. Furthermore, we show that the guaranteed exponential stability results in guaranteed bound on how large the transient tracking error can be, and that this bound reduces exponentially fast in time. This bound can be used to design controllers that do not exceed pre-defined limits and do not saturate. Therefore, this result has significant importance in verification and validation of adaptive control systems. These results show that the inclusion of memory can significantly improve the performance and stability guarantees of adaptive controllers. Finally, these results compliment our previous work in concurrent learning (for example, [12][13][14]), and extend concurrent learning to adaptive control ...

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A concurrent learning adaptive-optimal control architecture is presented that combines learning-focused di rect adaptive controllers with model predictive control for guaranteeing safety during adaptation for nonlinear systems. Exponential parameter convergence properties of concurrent learning adaptive controllers are leveraged to learn a feedback linearization signal that reduces a nonlinear system to an approximation of a linear system for which an optimal solution is known or can be easily computed online. Stability of the overall architecture is analyzed, and numerical simulations on a wing-rock dynamics model are presented in presence of significant system uncertainty, parameter variation, and measurement noise.