63 research outputs found
A Unified Filter for Simultaneous Input and State Estimation of Linear Discrete-time Stochastic Systems
In this paper, we present a unified optimal and exponentially stable filter
for linear discrete-time stochastic systems that simultaneously estimates the
states and unknown inputs in an unbiased minimum-variance sense, without making
any assumptions on the direct feedthrough matrix. We also derive input and
state observability/detectability conditions, and analyze their connection to
the convergence and stability of the estimator. We discuss two variations of
the filter and their optimality and stability properties, and show that filters
in the literature, including the Kalman filter, are special cases of the filter
derived in this paper. Finally, illustrative examples are given to demonstrate
the performance of the unified unbiased minimum-variance filter.Comment: Preprint for Automatic
On Minimum-time Paths of Bounded Curvature with Position-dependent Constraints
We consider the problem of a particle traveling from an initial configuration
to a final configuration (given by a point in the plane along with a prescribed
velocity vector) in minimum time with non-homogeneous velocity and with
constraints on the minimum turning radius of the particle over multiple regions
of the state space. Necessary conditions for optimality of these paths are
derived to characterize the nature of optimal paths, both when the particle is
inside a region and when it crosses boundaries between neighboring regions.
These conditions are used to characterize families of optimal and nonoptimal
paths. Among the optimality conditions, we derive a "refraction" law at the
boundary of the regions that generalizes the so-called Snell's law of
refraction in optics to the case of paths with bounded curvature. Tools
employed to deduce our results include recent principles of optimality for
hybrid systems. The results are validated numerically.Comment: Expanded version of paper in Automatic
Simultaneous State and Unknown Input Set-Valued Observers for Some Classes of Nonlinear Dynamical Systems
In this paper, we propose fixed-order set-valued (in the form of l2-norm
hyperballs) observers for some classes of nonlinear bounded-error dynamical
systems with unknown input signals that simultaneously find bounded hyperballs
of states and unknown inputs that include the true states and inputs. Necessary
and sufficient conditions in the form of Linear Matrix Inequalities (LMIs) for
the stability (in the sense of quadratic stability) of the proposed observers
are derived for ()- Quadratically Constrained
(()-QC) systems, which includes several classes of
nonlinear systems: (I) Lipschitz continuous, (II) ()-QC*
and (III) Linear Parameter-Varying (LPV) systems. This new quadratic constraint
property is at least as general as the incremental quadratic constraint
property for nonlinear systems and is proven in the paper to embody a broad
range of nonlinearities. In addition, we design the optimal
observer among those that satisfy the quadratic
stability conditions and show that the design results in Uniformly
Bounded-Input Bounded-State (UBIBS) estimate radii/error dynamics and uniformly
bounded sequences of the estimate radii. Furthermore, we provide closed-form
upper bound sequences for the estimate radii and sufficient condition for their
convergence to steady state. Finally, the effectiveness of the proposed
set-valued observers is demonstrated through illustrative examples, where we
compare the performance of our observers with some existing observers.Comment: Under review in Automatic
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