LPVSTOCHSYN - LPV controller synthesis for stochastic LPV systems

Contents

Syntax

  [K,GAMMA,INFO] = lpvstochsyn(P,NMEAS,NCON)
  [K,GAMMA,INFO] = lpvstochsyn(P,NMEAS,NCON,XB,YB)
  [K,GAMMA,INFO] = lpvstochsyn(P,NMEAS,NCON,XB,YB,OPT)

Description

[K,GAMMA,INFO] = lpvstochsyn(P,NMEAS,NCON) computes a parameter-varying controller for the pss P. NCON specifies the number of available control inputs in P. NMEAS specifies the number of available measurements being output from P. K is the parameter-dependent controller for the stochastic plant P, which minimizes the stochastic LPV bound GAMMA. The stochastic LPV bound is defined as the expected value of the average instantaneous power of the output of P, assuming its inputs are zero mean, white-noise processes with unit intensity. INFO is a struct with additional data.

[K,GAMMA,INFO] = lpvstochsyn(P,NMEAS,NCON,XB,YB) performs a rate-bounded synthesis. Xb and Yb are basis objects which describe the assumed parameter dependence of the lyapunov matrices used in solving for K.

[K,GAMMA,INFO] = lpvstochsyn(P,NMEAS,NCON,XB,YB,OPT) allows the user to pass in a lpvsynoptions object.

The default algorithm for lpvstochsyn will solve the given synthesis problem twice. The first iteration attempts to find a solution that minimizes the stochastic LPV bound of lft(P,K). The second iteration will solve the optimization problem again, with the caveat that any solution that is found to lie within 15% of the optimal stochastic LPV bound of lft(P,K) from the first iteration, is satisfactory. This formulation has been found to yield controllers that are better numerically conditioned. The back-off factor of 15% can be reset to a different value in lpvsynoptions.