Nonlinear Unfalsified Adaptive Control with Bumpless Transfer and Reset

Robustness of Uncertain Switching Nonlinear Feedback Systems against Large Time-Variation

“…If {t i } = Z then H is said to be σpe -stable which we denote as ∞e -stability for σ = 1 and p = ∞. Given a system H, the supremum of the set of σ for which (1) holds is called the degree σ 0 of stability of H. Remark 1: By [11] and [12], if a linear and time-invariant system H has finite σ2e -semi norm with degree σ ≥ 1, then H has all its poles within the circle of radius 1 σ . Remark 2: If σ 1 > σ 2 , where σ 1 arg sup σ≥1 H 1 σp < ∞ and σ 2 arg sup σ≥1 H 2 σp < ∞, then system H 1 is comparatively more stable than system H 2 by [12].…”

“…Remark 3: The adaptive switching control with reset mechanism, proposed in [11] and [12] adaptively generates an infinite time sequence {t k :…”

“…A HL based switched system with an additional reset feature which safely discards past evaluated controller performances is developed by Battistelli, Hesphana, Mosca, and Tesi in [11]. The results of [11] are generalized in [12] by (i) considering non-linear plants and controllers and (ii) adding a bumpless switching feature. A switching system that considers real-time and data-driven controller performance based on loop-shape specifications is developed in [13].…”

Data‐driven loop‐shaping controller design

“…We implement Algorithm 1 in the adaptive switching system with the controller selection criterion C1. Upon each switch, the state of the new controller is re‐initialized to maintain continuity and smoothness of the control signal u by using the bumpless transfer method .…”

“…Let the constant D 0:01 in the cost functions V .K; W; ; t/; 8K 2 K. We implement Algorithm 1 in the adaptive switching system with the controller selection criterion C1. Upon each switch, the state of the new controller is re-initialized to maintain continuity and smoothness of the control signal u by using the bumpless transfer method [20,21]. Figure 9 shows that the initially active and destabilizing controller K 980 is switched off, and the controller K 1 with the parameters .c p ; c i ; c d / D .60; 100; 2/ is switched on at the first switching time ST 1 D 0:09 s. At the second switching time ST 2 D 15:58 s, the active controller K 1 is switched off, and the controller K 85 with the parameters .c p ; c i ; c d / D .60; 100; 0:1/ is switched on and remained active for the rest of the experiment.…”