http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2002/data/content/02294/2294.pdf

State dependent differential riccati equation for nonlinear estimation and control

The state-dependent Riccati equation-based estimator is becoming a popular estimation tool for nonlinear systems since it does not use system linearization. In this paper, the state-dependent Riccati equation-based estimator is compared with the widely used extended Kalman filter for three simple examples that appear in the open literature. It is demonstrated that, by simulation, the state-dependent Riccati equation-based estimator at best has comparable results to the extended Kalman filter but is often worse than the extended Kalman filter. In some cases, the state-dependent Riccati equation-based estimator does not converge, even though the system considered satisfies all the mathematical constraints on controllability and observability. Sufficient detail is presented in the paper so that the interested reader cannot only duplicate the results but perhaps make suggestions on how to get the state-dependent Riccati equation-based estimator to perform better.

Comparisons Between the Extended Kalman Filter and the State-Dependent Riccati Estimator

A globally stable algorithm for jointly estimating the state and parameters in deterministic nonlinear dynamic systems is developed. This is accomplished by combining the concepts developed by Raghavan (1992) for the design of a full-order adaptive observer with the techniques used by Friedland (1997) for development of reduced-order estimators. The result is a method whose applicability exceeds that of many existing techniques in that it can accommodate multi-output systems. Several previously developed methods applicable to the same class of nonlinear system are restricted to single-output systems. In addition, the new method is shown to have some computational, advantages.

Nonlinear reduced-order state and parameter observer

We investigate the on-line parameter and state estimation of switched affine systems. We first adapt standard techniques available for affine (time-varying) systems to the considered class of systems, which leads to new linear matrix inequality-based conditions for the design of the estimator gains. We then explain how to derive decoupled estimators in the sense that the state and the parameter estimates are generated by cascaded switched differential equations, which is numerically more efficient and thus easier to implement in practice. A first solution is presented, which generates state estimates with jumps at the switching instants. To overcome this potential issue, two “bumpless” strategies are proposed. The first one relies on a persistency of excitation (PE) condition, while the second one applies to a given class of switching rules and avoids the PE condition. Both estimation strategies ensure the global exponential convergence to zero of the estimation errors. The results are illustrated on a model describing the behavior of a DC-DC power converter.

/pdf/parameter-and-state-estimation-of-switched-affine-systems-3ibzqg07b4.pdf

Parameter and state estimation of switched affine systems

ON-LINE STATE AND PARAMETER ESTIMATION IN NONLINEAR SYSTEMS by David A. Haessig On-line, simultaneous state and parameters estimation in deterministic, nonlinear dynamic systems of known structure is the problem considered. Available methods are few and fall short of user needs in that they are difficult to apply, their applicability is restricted to limited classes of systems, and for some, conditions guaranteeing their convergence don't exist. The new methods developed herein are placed into two categories: those that involve the use of Riccati equations, and those that do not. Two of the new methods do not use Riccati equations, and each is considered to be a different extension of Friedland's parameter observer for nonlinear systems with full state availability to the case of partial state availability. One is essentially a reduced-order variant of a state and parameter estimator developed by Raghavan. The other is developed by the direct extension of Friedland's parameter observer to the case of partial state availability. Both are shown to be globally asymptotically stable for nonlinear systems affine in the unknown parameters and involving nonlinearities that depend on known quantities, a class restriction also true of existing state and parameter estimation methods. The two new methods offer, however, the advantages of improved computational efficiency and the potential for superior transient performance, which is demonstrated in a simulation example. Of the new methods that do involve a Riccati equation, there are three. The first is the separate-bias form of the reduced-order Kalman filter. The scope of this filter is somewhat broader than the others developed herein in that it is an optimal filter for linear, stochastic systems involving noise-free observations. To apply this filter to the joint state and parameter estimation problem, one interprets the unknown parameters as constant biases. For the system class defined above, the method is globally asymptotically stable. The second Riccati equation based method is derived by the application of an existing method, the State Dependent Algebraic Riccati Equation (SDARE) filtering method, to the problem of state and parameter estimation. It is shown to work well in several nonlinear examples involving a few unknown parameters; however, as the number of parameters increases, the method's applicability is diminished due to an apparent loss of observability within the filter which hinders the generation of filter gains. The third is a new filtering method which uses a State Dependent Differential Riccati Equation (SDDRE) for the generation of filter gains, and through its use, avoids the "observability" shortcomings of the SDARE method. This filter is similar to the Extended Kalman Filter (EKF), and is compared to the EKF with regard to stability through a Lyapunov analysis, and with regard to performance in a 4 th order stepper motor simulation involving 5 unknown parameters. For the very broad class of systems that are bilinear in the state and unknown parameters, and potentially involving products of unmeasured states and unknown parameters, the EKF is shown to possess a semi-global region of asymptotic stability, given the assumption of observability and controllability along estimated trajectories. The stability of the new SDDRE filter is discussed. ON-LINE STATE AND PARAMETER ESTIMATION IN NONLINEAR SYSTEMS

/pdf/on-line-state-and-parameter-estimation-in-nonlinear-systems-3hqx4pgfc8.pdf

David A. Haessig

Papers

On-line state and parameter estimation in nonlinear systems