TY - GEN

T1 - Robust smoothing for continuous time uncertain nonlinear systems

AU - Kallapur, Abhijit G.

AU - Petersen, Ian R.

PY - 2013

Y1 - 2013

N2 - This paper presents the derivation of a robust smoothing algorithm for a class of uncertain nonlinear systems. The uncertainties in the system are described in terms of an integral quadratic constraint which provides for a rich class of uncertainties. The smoothing problem is divided into two component filtering problems: A forward filtering problem and a reverse filtering problem. Each filtering problem is formulated in a set-valued state estimation framework and recast into an optimal control problem whose solution is described in terms of Hamilton-Jacobi-Bellman partial differential equations. An approximate solution is obtained for this optimal control problem by assuming a quadratic approximation for the value function. Linear approximations are used for various nonlinear functions in the system dynamics, as in the case of the linearized smoothing approach for nonlinear systems. The final recursion equations for the robust smoother consist of two sets of Riccati differential equations, filter state equations, and level shift scalar equations. One set corresponds to the forward filter while the other is associated with the reverse filter. Although the level shift scalar equations are required to complete the definition of the set-valued state estimator, they do not affect the recursion equations for the filters.

AB - This paper presents the derivation of a robust smoothing algorithm for a class of uncertain nonlinear systems. The uncertainties in the system are described in terms of an integral quadratic constraint which provides for a rich class of uncertainties. The smoothing problem is divided into two component filtering problems: A forward filtering problem and a reverse filtering problem. Each filtering problem is formulated in a set-valued state estimation framework and recast into an optimal control problem whose solution is described in terms of Hamilton-Jacobi-Bellman partial differential equations. An approximate solution is obtained for this optimal control problem by assuming a quadratic approximation for the value function. Linear approximations are used for various nonlinear functions in the system dynamics, as in the case of the linearized smoothing approach for nonlinear systems. The final recursion equations for the robust smoother consist of two sets of Riccati differential equations, filter state equations, and level shift scalar equations. One set corresponds to the forward filter while the other is associated with the reverse filter. Although the level shift scalar equations are required to complete the definition of the set-valued state estimator, they do not affect the recursion equations for the filters.

UR - http://www.scopus.com/inward/record.url?scp=84883546528&partnerID=8YFLogxK

U2 - 10.1109/acc.2013.6580120

DO - 10.1109/acc.2013.6580120

M3 - Conference contribution

SN - 9781479901777

T3 - Proceedings of the American Control Conference

SP - 1944

EP - 1949

BT - 2013 American Control Conference, ACC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2013 1st American Control Conference, ACC 2013

Y2 - 17 June 2013 through 19 June 2013

ER -