Page 16 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

Introduction 5

(PPF) is incorporated into DSC design to guarantee prescribed transient
error bound.
Chapter 4 proposes an adaptive control for non-linear servo systems,
where a PPF characterizing the convergence rate, maximum overshoot,
and steady-state error is used. A continuously differentiable friction model
is incorporated into the high-order neural network (HONN) to account
for the friction dynamics, where only a scalar weight needs to be online
updated.
Chapter 5 proposes and experimentally validates an alternative robust
adaptive control for servo systems with frictions, which guarantees asymp-
totic tracking error convergence in the steady-state, while the transient
response can also be prescribed by using a prescribed performance func-
tion (PPF). A robust integral of sign of the error (RISE) term is used to
accommodate the residual NN approximation error to achieve asymptotic
convergence.
Chapter 6 introduces a novel friction modeling method based on
the discontinuous piecewise parametric representation (DPPR), which
captures the main characteristics of frictions including Stribeck effect,
Coulomb, and viscous dynamics. The identified friction is then used as
a feedforward compensator for manipulator systems.
Part 3 consisting of Chapter 7 to Chapter 11 focuses on the modeling
and control of non-linear uncertain systems with dead-zone input.
In Chapter 7, the dynamics of dead-zone and two classical dead-zone
models are briefly introduced, e.g., linear dead-zone model and non-linear
dead-zone model. Several typical systems with dead-zone dynamics are also
provided.
In Chapter 8, an adaptive robust finite-time neural control is proposed
for uncertain permanent magnet synchronous motor (PMSM) system with
non-linear dead-zone input. After representing the dead-zone as a linear
time-varying system, an adaptive control is designed by modifying a fast
terminal sliding mode surface to remedy singularity problem.
In Chapter 9, an adaptive neural control is proposed for non-linear
strict-feedback systems with a non-linear dead-zone and time-delays. The
“explosion of complexity” in the backstepping synthesis is eliminated in
terms of the DSC technique, and the online learning parameters (e.g., NN
weight) are reduced. Simulations are provided to verify the efficacy.
In Chapter 10, an adaptive control with prescribed performance is pro-
posed for non-linear strict-feedback systems with a dead-zone input. A PPF