Adaptive continuous-time linear quadratic Gaussian control

©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.The adaptive linear quadratic Gaussian control problem, where the linear transformation of the state A and the linear transformation of the control B are unknown, is solved assuming only that (A, B) is controllable and (A, Q(1)(1/2)) is observable, where Q(1), determines the quadratic form for the state in the integrand of the cost functional, A weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable and observable. A diminishing excitation is used with the adaptive control to ensure that the family of estimates is strongly consistent. A lagged certainty equivalence control using this family of estimates is shown to be self-optimizing for an ergodic, quadratic cost functional

Optimal control of partially observable linear quadratic systems with asymmetric observation errors

This paper deals with the optimal quadratic control problem for non-Gaussian discrete-time stochastic systems. Our main result gives explicit solutions for the optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. For this purpose an asymmetric version of the Kalman filter based on asymmetric least squares estimation is used. We illustrate the applicability of our approach with numerical results

Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces

© 2007 EUCA.A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decision-making horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller