Adaptive Control of Piecewise Linear Systems with State Feedback for Output Tracking

Abstract

A piecewise linear system consists of a set of linear time-invariant (LTI) subsystems, with a switching sequence specifying an active subsystem at each time instant. This paper studies the adaptive control problem of single-input, single-output (SISO) piecewise linear systems. By employing the knowledge of the time instant indicator functions of system parameter switches, a new controller structure parametrization is proposed for the development of a stable adaptive control scheme with reduced modeling error in the estimation error signal used for parameter adaptive laws. This key feature is achieved by the new control scheme's ability to avoid a major parameter swapping term in the error model, with the help of indicator functions whose knowledge is available in many applications. A direct state feedback model reference adaptive control (MRAC) scheme is presented for such systems to achieve closed-loop signal boundedness and small output tracking error in the mean square sense, under the usual slow system parameter switching condition. Simulation results on linearized NASA GTM models are presented to demonstrate the effectiveness of the proposed scheme.

Model reference adaptive control of discrete‐time piecewise linear systems

“…Given the increasing interest in the analysis and control of switched and hybrid systems [2], it is natural to seek an extension of the MRAC approach to Piecewise Affine (PWA) plants. Examples of MRAC schemes for PWA systems can be found in [3,4,5].…”

Adaptive PID and Model Reference Adaptive Control Switch Controller for Nonlinear Hydraulic Actuator

“…And adaptive control for stochastic switched nonlinear triangular system is investigated in [5], different from the approaches investigated in [4,5]. The approach is to linearize the system by using standard linear estimation techniques at some operating points [6,7], within a neighborhood which can accurately describe the nonlinear system behavior, and a wealth of linearization-based design techniques can be applied to achieve the control objective [7]. So the nonlinear system consists of a set of linear timeinvariant subsystems [8,9].…”

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

“…Some works regarding the hybrid model reference adaptive control and the direct state feedback model reference adaptive control of switched systems have been reported. 25,26 In addition, Tan et al 27 presented a multiple-model reference adaptive design strategy for multivariable systems with matching uncertainties. In the work of Sang and Tao, 28 piecewise linear systems were used as reference model systems, and exponential tracking performance was also achieved under some persistency of excitation conditions.…”

“…25,26 In addition, Tan et al 27 presented a multiple-model reference adaptive design strategy for multivariable systems with matching uncertainties. In the work of Sang and Tao, 28 piecewise linear systems were used as reference model systems, and exponential tracking performance was also achieved under some persistency of excitation conditions. Since passivity is effective for addressing the stabilization problem, naturally, passivity is also expected to be useful in the study of tracking control.…”