Scientia Iranica

Scientia Iranica

Guaranteed Cost Control of Uncertain Discrete Time Systems Subjected to Actuator Saturation via Homogenous Polynomial Lyapunov Function

Authors
S. M. Nashit Arshad 1
Kamal Mazhar 1
M. Umer Khan 1
S.M. Usman Hashmi 2
1 Air University, Islamabad, Pakistan
2 Iqra University, Islamabad, Pakistan
10.24200/sci.2016.3898
Abstract
Estimation of an optimal controller is a fundamental problem in control engineering and is widely known as Optimization. Numerous computation and numerical techniques have been evolved during the past years for the estimation of the optimal solution. Optimal control of a discrete-time system is concerned with optimizing a given objective function using “Homogenous Polynomial Lyapunov Function (HPLF)”. This research focuses upon the design of optimal guaranteed cost controller (GCC) for discrete-time uncertain system using HPLF. The uncertainties are assumed to be norm bounded uncertainties. The effect of actuator saturation is also incorporated in the system. Sufficient conditions for the existence of HPLF are derived in term of Linear Matrix Inequalities (LMI). The LMI approach has the advantage that it can be solved efficiently using Convex Optimization. LMI’s combined with HPLF helps to design the guaranteed cost controller which minimizes the cost by minimizing cost function. Furthermore, the state trajectories and the invariant set is also shown to observe the overall performance.
Keywords
convex optimization
lyapunov function
uncertainty
discreet time control
Scientia Iranica
Volume 23, Issue 3 - Serial Number 3
Transactions on Computer Science & Engineering and Electrical Engineering (D)
June 2016
Pages 1301-1309

  • Receive Date 13 February 2016
  • Accept Date 27 July 2017