Indirect Adaptive Control for Systems with Unknown or Varying Dynamics

Abstract

An indirect adaptive control algorithm is presented that combines a Modified-Gain Extended Kalman Filter (MGEKF) and an Extended Linear Quadratic Gaussian (ELQG) controller to synthesize feedback control laws that are robust to large uncertainties in the system model. The MGEKF estimates the system dynamical parameters and their associated variances, which are used to synthesize the control gains. The gains are determined from the solution of the stochastic optimal control problem where the cost criterion to be minimized is the expected value of a quadratic function of the state and control variables, subject to linear dynamics, with White Gaussian stateand control-dependent noise. The ELQG finds the feedback control laws by solving a nonlinear matrix differential equation that takes in account both the mean and variance of the estimated parameters. This matrix equation reduces to a Riccati equation when the uncertainties go to zero. The controller gains are obtained by solving the algebraic form of this nonlinear matrix equation. Since the covariance of the estimated system parameters from the MGEKF dictate the controller gains, the resulting controller does not obey the Certainty Equivalence Principle. This indirect adaptive controller appears to be robust to large changes in system parameters. In comparison to a standard linear-quadratic-regulator, this controller demonstrates the ability to handle large changes in the system dynamics. The tracking performance of the controller is evaluated through a numerical example.