Modified State Observer for Atmospheric Reentry Uncertainty Estimation

Adaptive Set-Theoretic Emulator Reference Architecture (ASTERA): Control of Uncertain Dynamical Systems with Performance Guarantees and Smooth Transients

“…We now introduce the state emulator dynamics, which is also called as the modified reference model by the authors of [10,11,16], the observer-like reference model by the author of [12], the modified state observer by the authors of [13,14], and the closed-loop reference model by the authors of [15]. In particular, consider the state emulator given byẋ…”

“…The contributions in [4][5][6][7][8][9][10][11][12][13][14][15][16][17] (see also references therein) present notable methods to address this challenge. In particular, the authors of [4] use a low-pass filter to reduce high-frequency oscillations due to high learning rates while achieving a desirable performance.…”

“…The authors of [10][11][12][13][14][15][16][17] propose state emulator-based or state emulator-like methods to adaptive control. Specifically, based on a given reference model, the state emulator alters the trajectories of this model with the system error (the difference between the uncertain dynamical system state and the state emulator state) for the purpose of achieving smooth transients -transients that do not necessarily exhibit high-frequency oscillations.…”

“…In fact, the common denominator of the contributions in [4][5][6][7][8][9][10][11][12][13][14][15][16][17] is that their respective worst-case system error bounds are conservative and not user-defined, since they are generally calculated using classical Lyapunov theory arguments that gives sufficient stability conditions only. To address this problem from a standard model reference adaptive control point, set-theoretic model reference adaptive control methods, which are predicated on a set-theoretic controller construction using generalized restricted potential functions (generalized barrier Lyapunov functions), are proposed in [18][19][20][21][22][23][24] (we refer to, for example, [ Section 1,19] for details on other adaptive control methods with strict performance guarantees such as [25][26][27][28][29][30][31][32]).…”

“…In particular, the key feature of [18][19][20][21][22][23][24] is to guarantee the weighted Euclidean norm between the uncertain dynamical system state and the given reference model state to be less than a-priori, user-defined scalar worst-case bound, where this implies that they achieve strict performance guarantees. However, unlike the contributions in [4][5][6][7][8][9][10][11][12][13][14][15][16][17], these approaches can suffer from high-frequency oscillations since their system error dependent learning rate can be high for specific time instants to enforce the aforementioned user-defined scalar worst-case bound. Thus, there is a practical need to develop a new adaptive control method to simultaneously achieve user-defined performance guarantees and smooth transients.…”