45 research outputs found
Fixed-order FIR approximation of linear systems from quantized input and output data
Abstract The problem of identifying a fixed-order {FIR} approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization, is dealt with in this paper. A fixed-order {FIR} model providing the best approximation of the input–output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. The considered problem is firstly formulated in terms of robust optimization. Then, two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented. The effectiveness of the proposed approach is illustrated by means of a simulation example
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 convex relaxation approach to set-membership identification of LPV systems
Abstract Identification of linear parameter varying models is considered in this paper, under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. First, the problem of computing parameter uncertainty intervals is formulated in terms of nonconvex optimization. Then, on the basis of the analysis of the regressor structure, we present an ad hoc convex relaxation scheme for computing parameter bounds by means of semidefinite optimization
Bounding the parameters of block-structured nonlinear feedback systems
In this paper, a procedure for set-membership identification of block-structured nonlinear feedback systems is presented. Nonlinear block parameter bounds are first computed by exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner signal are computed. Finally, linear block parameter bounds are evaluated on the basis of output measurements and computed inner-signal bounds. The computation of both the nonlinear block parameters and the inner-signal bounds is formulated in terms of semialgebraic optimization and solved by means of suitable convex LMI relaxation techniques. The problem of linear block parameter evaluation is formulated in terms of a bounded errors-in-variables identification problem
Set-membership LPV model identification of vehicle lateral dynamics
Set-membership identification of a Linear Parameter Varying (LPV) model describing the vehicle lateral dynamics is addressed in the paper. The model structure, chosen as much as possible on the ground of physical insights into the vehicle lateral behavior, consists of two single-input single-output {LPV} models relating the steering angle to the yaw rate and to the sideslip angle. A set of experimental data obtained by performing a large number of maneuvers is used to identify the vehicle lateral dynamics model. Prior information on the error bounds on the output and the time-varying parameter measurements are taken into account. Comparison with other vehicle lateral dynamics models is discussed
Enhancing low-rank solutions in semidefinite relaxations of Boolean quadratic problems
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation,
semidefinite programming relaxations (SDR’s) are proposed in the literature to approximate the solution, which recasts the problem into convex optimization. Nevertheless, SDR’s
do not guarantee the extraction of the correct binary minimizer. In this paper, we present a novel approach to enhance the binary solution recovery. The key of the proposed method is the exploitation of known information on the eigenvalues of the desired solution. As the proposed approach yields a non-convex program, we develop and analyze an iterative descent strategy, whose practical effectiveness is shown via numerical results
Sparse linear regression with compressed and low-precision data via concave quadratic programming
We consider the problem of the recovery of a k-sparse vector from compressed
linear measurements when data are corrupted by a quantization noise. When the
number of measurements is not sufficiently large, different -sparse
solutions may be present in the feasible set, and the classical l1 approach may
be unsuccessful. For this motivation, we propose a non-convex quadratic
programming method, which exploits prior information on the magnitude of the
non-zero parameters. This results in a more efficient support recovery. We
provide sufficient conditions for successful recovery and numerical simulations
to illustrate the practical feasibility of the proposed method
Fast implementation of model predictive control with guaranteed performance
A fast implementation of a given predictive controller for nonlinear systems is introduced through a piecewise constant approximate function defined over an hyper-cube partition of the system state space. Such a state partition is obtained by maximizing the hyper-cube volumes in order to guarantee, besides stability, an a priori fixed trajectory error as well as input and state constraints satisfaction. The presented approximation procedure is achieved by solving a set of nonconvex polynomial optimization problems, whose approximate solutions are computed by means of semidefinite relaxation techniques for semialgebraic problems
A convex optimization approach to online set-membership EIV identification of LTV systems
This paper addresses the problem of recursive set-membership identification
for linear time varying (LTV) systems when both input and output measurements
are affected by bounded additive noise. First we formulate the problem of
online computation of the parameter uncertainty intervals (PUIs) in terms of
nonconvex polynomial optimization. Then, we propose a convex relaxation
approach based on McCormick envelopes to solve the formulated problem to the
global optimum by means of linear programming. The effectiveness of the
proposed identification scheme is demonstrated by means of two simulation
examples.Comment: Accepted for publication in the 2021 60th Annual Conference of the
Society of Instrument and Control Engineers of Japan (SICE
Set-membership identification of block-structured nonlinear feedback systems
In this paper a three-stage procedure for set-membership identification of block-structured nonlinear feedback systems is proposed. Nonlinear block parameters bounds are computed in the first stage exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner-signal are computed in the second stage. Finally, linear block parameters bounds are computed in the third stage on the basis of output measurements and computed inner signal bounds. Computation of both the nonlinear block parameters and the inner-signal bounds is formulated in terms of semialgebraic optimization and solved by means of suitable convex LMI relaxation techniques. Linear block parameters are bounded solving a number of linear programming problems