Output Feedback Adaptive Control with Low-Frequency Learning and Fast Adaptation

Abstract

Although adaptive control has been used in numerous applications to achieve system performance without excessive reliance on system models, the necessity of high-gain learning rates for achieving fast adaptation can be a serious limitation of adaptive controllers. Specifically, in safety-critical systems involving large system uncertainties and abrupt changes in system dynamics, fast adaptation is required to achieve stringent tracking performance specifications. However, fast adaptation using high-gain learning rates can cause high-frequency oscillations in the control response, resulting in system instability. This paper develops an output feedback adaptive control framework for continuous-time minimum-phase multivariable dynamical systems for output stabilization and command following to address the problem of achieving fast adaptation using high-gain learning rates for systems with partial state information. The proposed framework uses a controller architecture involving a modification term in the update law that filters out the high-frequency content in the control response while preserving uniform boundedness of the system error dynamics. The approach is based on a nonminimal state-space realization that generates an expanded set of states using the filtered inputs and filtered outputs, as well as their derivatives, of the original system, and requires knowledge of only the open-loop system's relative degree and a bound on the system's order.

Performance enhancement of model reference adaptive control through normalized Lyapunov design

“…21,22 This architecture filtered out the high-frequency oscillations contained in the updating law and allows for robust, fast adaptation with high-gain adaptive learning rate. An output feedback version of this control architecture for a multivariable system is also proposed by Rajpurohit et al 23 These methods successfully converge fast and stay in the low-frequency range, but they usually use high adaptation gain for fast convergence that may lead to a large control signal, which is undesirable practical.…”

Parameter‐dependent Riccati equation–based output feedback adaptive control

“…Consequently, either |x| > Ψ 1 or ||W|| > Ψ 2 (37) rendersV(x,W) < 0, where Ψ 1 = e∕ √ c + d 1 ∕c and Ψ 2 = e∕ √ σ + d 2 ∕σ, and it follows thatx andW are UUB.…”

“…This issue has more recently been given attention in the adaptive control literature. 21,[32][33][34][35][36][37][38][39] This section adopts a simple approach to address this problem and provides a theoretical justification based on the singular perturbation theory. 32 An advantage to this approach is that it does not require modification of the observer portion of the nominal control law, which is used in place of the usual reference model to generate an error signal for the adaptive law.…”

Tracking and parameter identification for model reference adaptive control

“…While usually dependent on some structural properties of the system, adaptive control is valuable because of its ability to solve tracking problems for a wide range of possible values of the unknown model parameters including higher‐order systems. One area where adaptive control is important is in aerospace problems . In basic adaptive control for some classes of control systems (such as linear systems), one can often use nonstrict (or weak) Lyapunov functions to ensure that tracking objectives are realized, and then achieve parameter identification (ie, convergence of the parameter estimates to the true parameter values) provided that a persistency of excitation (PE) condition is also satisfied.…”

“…One area where adaptive control is important is in aerospace problems. [5][6][7][8][9][10][11][12][13][14][15][16] In basic adaptive control for some classes of control systems (such as linear systems), one can often use nonstrict (or weak) Lyapunov functions to ensure that tracking objectives are realized, and then achieve parameter identification (ie, convergence of the parameter estimates to the true parameter values) provided that a persistency of excitation (PE) condition is also satisfied.…”