Constrained state estimation and control

Carlos A Lana, Purdue University

Abstract

This dissertation addresses two important problems in control theory: state estimation with constraints and model predictive control. The focus of the dissertation is on two common issues found in practical applications: modeling inaccuracies and implementation cost. The first part considers a state estimation problem for a discrete-time linear system driven by a Gaussian random process. The covariance of this random process and the covariance of the system initial condition are uncertain. In estimation, constraints can be used to represent information about the system, and therefore, have the potential of increasing the estimation accuracy. Unfortunately, the use of constraints usually leads to an increase of the online computation requirements. The approach proposed in this dissertation allows the incorporation of probability constraints in the estimator design. The resulting estimator offers improved accuracy, compared to existing estimators, with no increase of the online computation requirements. The second part considers a model predictive control (MPC) problem where the model of the system is only partially known. A method is presented to increase the robustness of this control architecture from the choice of the uncertain model parameters. The method consists of penalizing the energy of the state trajectory sensitivity, with respect to these parameters, in the MPC cost function. The resulting controller has the potential of increasing the robustness of the conventional MPC architecture. This gain in robustness is achieved with no increase of the online computation requirements as this controller retains the on-line computational simplicity of the conventional MPC problem. An optimization-based method is proposed to design this controller and two benchmark problems are used to illustrate its potential.

Degree

Ph.D.

Advisors

Rotea, Purdue University.

Subject Area

Aerospace engineering

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