4,595 research outputs found
A unified framework for solving a general class of conditional and robust set-membership estimation problems
In this paper we present a unified framework for solving a general class of
problems arising in the context of set-membership estimation/identification
theory. More precisely, the paper aims at providing an original approach for
the computation of optimal conditional and robust projection estimates in a
nonlinear estimation setting where the operator relating the data and the
parameter to be estimated is assumed to be a generic multivariate polynomial
function and the uncertainties affecting the data are assumed to belong to
semialgebraic sets. By noticing that the computation of both the conditional
and the robust projection optimal estimators requires the solution to min-max
optimization problems that share the same structure, we propose a unified
two-stage approach based on semidefinite-relaxation techniques for solving such
estimation problems. The key idea of the proposed procedure is to recognize
that the optimal functional of the inner optimization problems can be
approximated to any desired precision by a multivariate polynomial function by
suitably exploiting recently proposed results in the field of parametric
optimization. Two simulation examples are reported to show the effectiveness of
the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic
Control (2014
A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding
Set-membership estimation is usually formulated in the context of set-valued
calculus and no probabilistic calculations are necessary. In this paper, we
show that set-membership estimation can be equivalently formulated in the
probabilistic setting by employing sets of probability measures. Inference in
set-membership estimation is thus carried out by computing expectations with
respect to the updated set of probability measures P as in the probabilistic
case. In particular, it is shown that inference can be performed by solving a
particular semi-infinite linear programming problem, which is a special case of
the truncated moment problem in which only the zero-th order moment is known
(i.e., the support). By writing the dual of the above semi-infinite linear
programming problem, it is shown that, if the nonlinearities in the measurement
and process equations are polynomial and if the bounding sets for initial
state, process and measurement noises are described by polynomial inequalities,
then an approximation of this semi-infinite linear programming problem can
efficiently be obtained by using the theory of sum-of-squares polynomial
optimization. We then derive a smart greedy procedure to compute a polytopic
outer-approximation of the true membership-set, by computing the minimum-volume
polytope that outer-bounds the set that includes all the means computed with
respect to P
Data-driven filtering for linear systems using Set Membership multistep predictors
This paper presents a novel data-driven, direct filtering approach for
unknown linear time-invariant systems affected by unknown-but-bounded
measurement noise. The proposed technique combines independent multistep
prediction models, identified resorting to the Set Membership framework, to
refine a set that is guaranteed to contain the true system output. The filtered
output is then computed as the central value in such a set. By doing so, the
method achieves an accurate output filtering and provides tight and minimal
error bounds with respect to the true system output. To attain these results,
the online solution of linear programs is required. A modified filtering
approach with lower online computational cost is also presented, obtained by
moving the solution of the optimization problems to an offline preliminary
phase, at the cost of larger accuracy bounds. The performance of the proposed
approaches are evaluated and compared with those of standard model-based
filtering techniques in a numerical example
A data-driven model inversion approach to cancer immunotherapy control
A novel data-driven control design approach for Multiple Input Multiple Output nonlinear systems is proposed in the paper, relying on the identification of a polynomial prediction model of the system to control and its on-line inversion. A simulated study is then presented, concerning the design of a control strategy for cancer immunotherapy. This study shows that the proposed approach may be quite effective in treating cancer patients, and may give results similar to (or perhaps better than) those provided by “standard” methods. The fundamental difference is that “standard” methods are typically based on the unrealistic assumption that an accurate physiological model of the cancer-immune mechanism is avail- able; in the approach proposed here, the controller is designed without such a strong assumption
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
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