RISE-Based Adaptive Control of a Control Affine Uncertain Nonlinear System With Unknown State Delays

Abstract

Abstract-A continuous robust adaptive control method is designed for a class of uncertain nonlinear systems with unknown constant time-delays in the states. Specifically, a robust adaptive control method and a delay-free gradient-based desired compensation adaptation law (DCAL) are utilized to compensate for unknown time-delays, linearly parameterizable uncertainties, and additive bounded disturbances for a general nonlinear system. Despite these disturbances, a Lyapunov Krasovskii-based analysis is used to conclude that the system output asymptotically tracks a desired time varying bounded trajectory.

Saturated RISE Feedback Control for a Class of Second-Order Nonlinear Systems

“…Let be a positive-definite, locally Lipschitz, regular function defined as (22) where and denote the -th element of the vector and , respectively. The Lyapunov function candidate in (22) satisfies the following inequalities: (23) Based on (4) and (22), the continuous, positive definite, strictly increasing functions in (23) are defined as , . Additionally, let denote a set defined as .…”

Online time delay identification and control for general classes of nonlinear systems

“…Model parameters were m = 1.16kg, τ = 60/Ω, Ω = 550rpm, k = mω 2 , c = 2mηω, η = 0.1, ω = 83π, k c /k = 0.5, b = 2mm, and f = 0.25mm per revolution [30]. The performance of the proposed technique was evaluated with and without additive noise.…”

Robust adaptive control of nonlinear systems with unknown state delay

“…In [11], Mirkin and Gutman proposed an output feedback model reference adaptive control scheme for a class of MIMO linear dynamic systems with unknown state delay and additive disturbance, and obtained semiglobal asymptotic tracking result. Recently, in [12] (and its preliminary version in [13]), Sharma et al presented a robust adaptive controller for the same class of systems in [6] where the robust integral of the sign of the error term in [14] was utilized in the controller design and obtained semi-global asymptotic tracking.…”

“…Review of the relevant literature highlights the fact that most of the proposed controllers for uncertain nonlinear systems with state delay fails to guarantee asymptotic stability result and additionally, almost all of the above papers (see [12] and [15]) considered the input gain matrix to be constant. Motivated by this fact, in this work we propose a continuous robust adaptive controller that can achieve asymptotic stability for a class of uncertain nonlinear systems i) subject to additive bounded input and output disturbances, ii) with a state-dependent input gain matrix, and iii) with an unknown state delay.…”

“…However, since the delay value is considered to be unknown, the delay dependent terms with structured uncertainties can not be utilized in the design of the regressor matrix. In [12], Sharma et al dealt with this challenging issue by segregating the appropriate terms when forming the linearly parameterizable function and a delayfree regressor matrix was obtained. Inspired by this, in our work, a similar segregation is utilized to obtain a delay-free regressor matrix.…”