Consider a convergent sequence {xk} generated by the application of the logarithmic barrier function method to a smooth convex programming problem. In this paper we show how to construct an auxiliary sequence {[xbar]k...
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Consider a convergent sequence {xk} generated by the application of the logarithmic barrier function method to a smooth convex programming problem. In this paper we show how to construct an auxiliary sequence {[xbar]k} that converges superlinearly faster than the original sequence {xk}. We then use the auxiliary sequence to develop a superlinearly convergent long step, predictor-corrector version of the barrier function method. Limited computational experience with the method of centres, a special version of the barrier method, on quadratically constrained programs suggests that our method deserves further study
Numerical tools for constraints solving are a cornerstone to control verification problems. This is evident by the plethora of research that uses tools like linear and convex programming for the design of control syst...
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Numerical tools for constraints solving are a cornerstone to control verification problems. This is evident by the plethora of research that uses tools like linear and convex programming for the design of control systems. Nevertheless, the capability of linear and convex programming is limited and is not adequate to reason about general nonlinear polynomials constraints that arise naturally in the design of nonlinear systems. This limitation calls for new solvers that are capable of utilizing the power of linear and convex programming to reason about general multivariate polynomials. In this paper, we propose PolyAR, a highly parallelizable solver for polynomial inequality constraints. PolyAR provides several key contributions. First, it uses convex relaxations of the problem to accelerate the process of finding a solution to the set of the non-convex multivariate polynomials. Second, it utilizes an iterative convex abstraction refinement process which aims to prune the search space and identify regions for which the convex relaxation fails to solve the problem. Third, it allows for a highly parallelizable usage of off-the-shelf solvers to analyze the regions in which the convex relaxation failed to provide solutions. We compared the scalability of PolyAR against Z3 8.9 and Yices 2.6 on control designing problems. Finally, we demonstrate the performance of PolyAR on designing switching signals for continuous-time linear switching systems.
We consider optimal experiment design for parametric prediction error system identification of linear time-invariant multi-input multi-output systems in closed-loop. The optimization is performed jointly over the cont...
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We consider optimal experiment design for parametric prediction error system identification of linear time-invariant multi-input multi-output systems in closed-loop. The optimization is performed jointly over the controller and the external input. We use a partial correlation approach, i.e. parametrize the set of admissible controller - external input pairs by a finite set of matrix-valued trigonometric moments. Our main contribution is to derive a description of the set of admissible finite-dimensional moment vectors by a linear matrix inequality. Optimal input design problems with constraints and criteria which are linear in these moments can then be cast as semi-definite programs and solved by standard semi-definite programming packages. Our results can be applied to most of the usual model structures, but we assume that the true system is in the model set.
This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits ...
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This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits the structure of the dynamic system to eliminate the state equations. The linear inequalities on inputs and states are replaced by a finite set of linear inequalities on the mode coefficients and changing the problem of trajectory generation to finding a convex polytope on the mode coefficients. The procedure is demonstrated in an example and verified experimentally.
In this paper a dual approach is suggested for solving discrete optimal control problems with linear systems, with convex constraints on control and state-space variables, and with a convex performance index. The corr...
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In this paper a dual approach is suggested for solving discrete optimal control problems with linear systems, with convex constraints on control and state-space variables, and with a convex performance index. The corresponding dual problems are shown to be unconstrained and therefore easier to handle then the original ones. The existence of a solution, as well as optimality conditions and inverse transformation are discussed in detail.
An output feedback constrained MPC control scheme for uncertain LFR/Norm-Bounded discrete-time linear systems is discussed. The design procedure consists of an off-line step in which a state-feedback and an asymptotic...
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An output feedback constrained MPC control scheme for uncertain LFR/Norm-Bounded discrete-time linear systems is discussed. The design procedure consists of an off-line step in which a state-feedback and an asymptotic observer (dynamic primal controller) are designed via BMI optimization and used to robustly stabilize a suitably augmented system. The on-line moving horizon procedure adds N free control moves to the action of the primal controller and its computation consists of solving an online LMI optimization problem whose numerical complexity grows up only linearly with the control horizon N. The effectiveness is illustrated by a numerical example.
This paper discusses the convexifying approach to separable nonconvex large-scale steady-state systems with general constraints by means of partly introducing the penalty terms to the constraints. A new approach has b...
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This paper discusses the convexifying approach to separable nonconvex large-scale steady-state systems with general constraints by means of partly introducing the penalty terms to the constraints. A new approach has been suggested which not only convexifies the original nonconvex performance function, but also capable of making the augmented Lagrangian function separable. The hierarchical optimization algorithm used to solve the large-scale problem is given, and the convergence proof as well as the estimation of the rate of convergence are also discussed. Simulation of a two subsystems example is also given.
In this paper we consider a linear system depending in non-linear fashion on a vector of uncertain parameters. Assuming that the parameters range in a hyperrectangle, we provide a necessary and sufficient condition fo...
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In this paper we consider a linear system depending in non-linear fashion on a vector of uncertain parameters. Assuming that the parameters range in a hyperrectangle, we provide a necessary and sufficient condition for the quadratic stabilizability of the system in terms of convex optimization procedures. Dans ce texte nous traitons un systéme linéaire qui dépend dans une maniére pas linéaire d'un vecteur de paramétres incertains. Supposé que les paramétres se trouvent dans un hyperectangle, nous donnons une condition nécessaire et suffisante pour la stabilisabilité quadratique du systéme en termes des procédures d'optimisation convexe.
作者：
Taha ZoulaghHicham El AissAbdelaziz HmamedAhmed El HajjajiLESSI Laboratory
Department of Physics Faculty of Sciences Dhar El Mehraz University Sidi Mohamed Ben Abdellah B.P. 1796 Fes-Atlas Morocco Modeling
Information System (MIS) Laboratory University of Picardie Jules Verne UFR of Sciences 33 Rue St Leu 80000 Amiens France
In this study, the analysis and design problems of filtering for a class of discrete-time-varying delay systems are investigated. The authors' attention is focused on the filter design using scaled small gain (SSG...
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In this study, the analysis and design problems of filtering for a class of discrete-time-varying delay systems are investigated. The authors' attention is focused on the filter design using scaled small gain (SSG) approach guaranteeing the robust asymptotic stability of the filtering error system with a prescribed performance. A novel transformation model of the filtering error system is obtained via three-term approximation method and input–output approach based on SSG theorem. Then, the desired filter design is obtained through a convex optimisation problem resolution under a set of linear matrix inequality constraints. Finally, the use of many examples from the literature demonstrates the effectiveness of the proposed approach.
In this paper H 2 robust filtering is considered. Particular attention is devoted to what we call optimality gap certification of robust filters for both continuous and discrete time invariant systems subject to polyt...
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In this paper H 2 robust filtering is considered. Particular attention is devoted to what we call optimality gap certification of robust filters for both continuous and discrete time invariant systems subject to polytopic parameter uncertainty. After a brief discussion on some of the most expressive methods available for H 2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H 2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational, stable and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature are solved and it is shown that the proposed method outperforms all other designs.
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