A Model Reference Adaptive Control Scheme Based on Dynamic Certainty Equivalence Principle and Its Stability

Abstract

A model reference adaptive control system (MRACS) based on dynamic certainty equivalence (DyCE) principle taking into consideration realization of high order tuner (HOT) is proposed. In conventional scheme using DyCE principle and HOT, the knowledge of upper bound of high frequency gain of controlled object was needed for stable MRACS. However, it is generally difficult to get exactly such a knowledge a priori and its conservative estimate often leads to numerical instability in realizing HOT. In this paper, the problem is solved by introducing a projection type of HOT and an adaptive control law with division. Stability proof of the proposed MRACS is given and its validity is verified by simple numerical simulations.

An Improvement of Transient Response of Dynamic Certainty Equivalent Model Reference Adaptive Control System Based on New Smooth Parameter Projection High Order Tuner

“…Therefore, this fact implies that (P1-3) from (24). The proof of (P1-4) can be shown in the same way as in [15], [20]. The proof of (P1-5) can be proven from (P1-1), (15), (24), (25) and mathematical induction.…”

“…The proof of (P1-5) can be proven from (P1-1), (15), (24), (25) and mathematical induction. The detailed proof can be shown in the same way as [15], [20]. Remark 5: The proof of the stability of MRACS and lim t→∞ỹ (t) = 0 can be shown in the same way as in [15], [20].…”

“…Therefore, a special adaptation law which can generateθ ( j) (t)( j = 1 ∼ n * ) without using y ( j) (t)( j = 1 ∼ n * − 1) is needed for synthesizing (3) since the realization of f (t) needsθ ( j) (t)( j = 1 ∼ n * ) and high order differential values of y(t) are not available from (A4). Such a special adaptation law is known as HOT and it is proposed by Morse [11] and the improved versions of the feasibility have been proposed in [20], [21].…”

Neural Adaptive PID and Neural Indirect Adaptive Control Switch Controller for Nonlinear MIMO Systems

“…Initialization of parameters w 0 , w 1 , w 2 , w 3 , w i , z i , k P i , k I i , and k D i of the neural network model, neural network indirect adaptive controller, adaptive neural network PID tuner, and PID controller, respectively, is based on expressions (3), (12), (31), and (34) using a reduced number of observations. (ii) If the condition e m i (k + 1) ≤ ε 1 , where ε 1 > 0 is a given small constant, is satisfied, then the neural network model, given by equation 3, approaches sufficiently the behavior of the system (iii) If the condition e c i (k + 1) ≤ ε 2 , where ε 2 > 0 is a given small constant, is satisfied, then the neural network adaptive PID controller provides sufficiently the control law u PIDi (k + 1) using expression (31) (iv) If the condition e c i (k + 1) ≤ ε 3 and 0 < ε…”

“…However, in [10], a PID-type fuzzy logic controller based on particle swarm optimization is proposed. e indirect adaptive control (IAC) is well used in [11][12][13]. is method is based on two parts: identification and control of the system.…”