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

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

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

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

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 $k$-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

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

A convex relaxation approach to set-membership identication of LPV systems

Identification of linear parameter varying models is considered in the 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 to compute parameter bounds by means of semidefinite optimization