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Convergence off explicit LQG self-tuning controllers

Convergence off explicit LQG self-tuning controllers

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© The Institution of Electrical Engineers
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A global convergence and stability proof is presented for an indirect LQG self-tuning controller which employs a stochastic approximation type of identification algorithm. A discrete linear single-input/single-output time-invariant stochastic system with correlated noise inputs is considered. The plant model need not be stable or minimum phase. The usual assumption that unstable common factors do not occur in the estimated plant model is replaced by a weaker condition. The first set of stability and convergence results presented in the paper are independent of the control law employed. These are then applied to the specific case of the LQG self-tuner. The control and tracking error signals are shown to be sample mean square bounded, prediction error convergence is demonstrated and optimal pole locations are shown to be achieved asymptotically. A persistency of excitation condition is not assumed.

Inspec keywords: adaptive control; poles and zeros; identification; discrete systems; optimal control; stability; self-adjusting systems; linear systems; convergence; stochastic systems

Other keywords: stochastic system; time-invariant system; discrete systems; linears system; stochastic approximation; self-adjusting systems; adaptive control; identification algorithm; optimal control; indirect control; explicit LQG self-tuning controllers; global convergence; optimal pole locations; stability; single input single output system

Subjects: Time-varying control systems; Stability in control theory; Simulation, modelling and identification; Self-adjusting control systems; Discrete control systems; Optimal control

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