Design Of Robust LQR Control For Nonlinear System Using Adaptive Dynamic Programming

Document Type : Primary Research paper


1 Associate Professor, Dept of I&CE, PSG College of Technology, Coimbatore.

2 PG Scholar,Department of Instrumentation and Control systems Engineering, PSG College of Technology, Coimbator


One of the important challenges in the design of LQR for real time applications
is the optimal choice state and input weighting matrices (Q and R), which play a vital role
in determining the performance and optimality of the controller. Commonly, trial and
error approach is employed for selecting the weighting matrices, which not only burdens
the design but also results in non-optimal response. Hence, to choose the elements of Q
and R matrices optimally, Adaptive Dynamic Programming (ADP) algorithm is used for
selecting the most suitable Q and R matrices by iteration which reduces the performance
index of the system to be considered. However, stability is only a bare minimum
requirement in a system design. Ensuring optimality guarantees the stability of the
nonlinear system. Dynamic programming is a very useful tool in solving optimization and
optimal control problems by employing the principle of optimality. There are several
spectrums about the dynamic programming. One can consider discrete-time systems or
continuous-time systems, linear systems or nonlinear systems, time-invariant systems or
time-varying systems, deterministic systems or stochastic systems. The inverted pendulum
is a standard benchmark control problem and for the control of which numerous control
algorithms have evolved over the ages. The main objective of this project is to design a
robust linear quadratic regulator (RLQR) for nonlinear system using adaptive dynamic
programming and to propose an optimal tracking control approach based on adaptive
dynamic programming (ADP) algorithm in order to solve the linear quadratic regulation
problems for nonlinear systems in an online fashion.