Precision Adaptive Control Research Articles

A 0.58-mm2 2.76-Gb/s 79.8-pJ/b 256-QAM Message-Passing Detector for a 128 × 32 Massive MIMO Uplink System

Massive multiple-input-multiple-output (MIMO) detection uses a large number of antennas to increase spectral efficiency at a cost of large computation resources and power in a base station. In this article, we demonstrate a 0.58-mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 128×32 (it denotes 128 base station antennas and 32 single-antenna users) 256-QAM massive MIMO uplink detector based on message-passing detection (MPD). With the proposed symbol hardening processing, the complexity is reduced by more than 60% compared to the direct implementation of MPD. The detector implements a grouped layer-parallel architecture to accelerate convergence, enabling an average throughput of 2.76 Gb/s (running, on average, 4.92 iterations with early termination) at 221 mW. The chip incorporates adaptive precision control and clock gating to improve energy efficiency further by up to 43%.

Multi-fidelity algorithms for the horizontal alignment problem in road design

Multi-fidelity algorithms for solving the horizontal alignment problem in road design are considered. A multi-fidelity surrogate model is built and quantile regression is used to understand its accuracy at various fidelity levels. Two algorithms are compared: a generalized pattern search algorithm with adaptive precision control, and a trust-region algorithm for unconstrained problems with controlled error. To make a fair comparison, the parameters of each algorithm are tuned on five small roads using performance profiles. Then the algorithms are evaluated on 35 roads, ranging from small to very large roads. The results show that using multi-fidelity surrogates in optimization algorithms provide notable speed-up when compared to single-fidelity algorithms while preserving the quality of solutions (cost error ). On the longest roads, higher speed-up and better accuracy are observed.

High precision adaptive control for piezo-actuated stage

The piezo-actuated stage is composed of a piezo electric actuator (PEA) and a positioning mechanism (PM). Due to the existence of hysteretic non-linearity in the PEA and the friction in the PM, the high precision control of the piezo-actuated stage is a challenging task. This paper discusses the high precision adaptive control for the piezo-actuated stage, where the hysteresis is described by Prandtl-Ishlinskii model. Only the parameters which are directly needed in the controller design are estimated. The proposed control law ensures the global stability of the controlled stage, and the position error can be controlled to approach to zero asymptotically. Experimental results show the effectiveness of the proposed method.

Advanced control for the XY-table driven by piezo-actuators

AbstractThe XY table is composed of two piezo electric actuators (PEA) and a positioning mechanism (PM). Due to existence of hysteretic nonlinearity in the PEA and the friction in the PM, the high precision control for the XY table is a challenging task. This paper discusses the high precision adaptive control for the XY talbe, where the hysteresis is described by Prandtl-Ishlinskii model. The proposed control law ensures the global stability of the controlled stage, and the position error can be controlled to approach to zero asymptotically. Experimental results show the effectiveness of the proposed method.

Optimal multigrid preconditioned semi‐monotonic augmented Lagrangians applied to the Stokes problem

AbstractWe propose an optimal computational complexity algorithm for the solution of quadratic programming problems with equality constraints arising from partial differential equations. The algorithm combines a variant of the semi‐monotonic augmented Lagrangian (SMALE) method with adaptive precision control and a multigrid preconditioning for the Hessian of the cost function and for the inner product on the space of Lagrange variables. The update rule for penalty parameter acts as preconditioning of constraints. The optimality of the algorithm is theoretically proven and confirmed by numerical experiments for the two‐dimensional Stokes problem. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Minimizing quadratic functions with separable quadratic constraints

This article deals with minimizing quadratic functions with a special form of quadratic constraints that arise in 3D contact problems of linear elasticity with isotropic friction [Haslinger, J., Kučera, R. and Dostál, Z., 2004, An algorithm for the numerical realization of 3D contact problems with Coulomb friction. Journal of Computational and Applied Mathematics, 164/165, 387–408.]. The proposed algorithm combines the active set method with the conjugate gradient method. Its general scheme is similar to the algorithms of Polyak’s type that solve the quadratic programming problems with simple bounds. As the algorithm does not terminate in a finite number of steps, the convergence is proved. The implementation uses an adaptive precision control of the conjugate gradient loops. Numerical experiments demonstrate the computational efficiency of the method.

Semi-monotonic inexact augmented Lagrangians for quadratic programing with equality constraints

A variant of the augmented Lagrangian algorithm for strictly convex quadratic programing problems with equality constraints is considered. An update rule for the penalty parameter is introduced that is related to an increase of the augmented Lagrangian. The algorithm exploits an adaptive precision control of the inexact solution of auxiliary unconstrained problems. Global convergence in primal variables is proved and an explicit bound on the penalty parameter independent of the constraints is given. A qualitatively new feature of our algorithm is a simple bound on the feasibility error that is independent of the conditioning of the constraints. The theoretical results are illustrated on numerical solution of a model problem.

Inexact Semimonotonic Augmented Lagrangians with Optimal Feasibility Convergence for Convex Bound and Equality Constrained Quadratic Programming

A variant of the augmented Lagrangian-type algorithm for strictly convex quadratic programming problems with bounds and equality constraints is considered. The algorithm exploits the adaptive precision control in the solution of auxiliary bound constraint problems in the inner loop while the Lagrange multipliers for the equality constraints are updated in the outer loop. The update rule for the penalty parameter is introduced that depends on the increase of the augmented Lagrangian. Global convergence is proved and an explicit bound on the penalty parameter is given. A qualitatively new feature of our algorithm is a bound on the feasibility error that is independent of conditioning of the constraints. When applied to the class of problems with the spectrum of the Hessian matrix in a given interval, the algorithm returns the solution in O(1) matrix-vector multiplications. The results are valid even for linearly dependent constraints. Theoretical results are illustrated by numerical experiments including the solution of an elliptic variational inequality.

A Proportioning Based Algorithm with Rate of Convergence for Bound Constrained Quadratic Programming

The proportioning algorithm with projections turned out to be an efficient algorithm for iterative solution of large quadratic programming problems with simple bounds and box constraints. Important features of this active set based algorithm are the adaptive precision control in the solution of auxiliary linear problems and capability to add or remove many indices from the active set in one step. In this paper a modification of the algorithm is presented that enables to find its rate of convergence in terms of the spectral condition number of the Hessian matrix and avoid any backtracking. The modified algorithm is shown to preserve the finite termination property of the original algorithm for problems that are not dual degenerate.

Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints

In this paper we discuss a specialization of the augmented Lagrangian-type algorithm of Conn, Gould, and Toint to the solution of strictly convex quadratic programming problems with simple bounds and equality constraints. The new feature of the presented algorithm is the adaptive precision control of the solution of auxiliary problems in the inner loop of the basic algorithm which yields a rate of convergence that does not have any term that accounts for inexact solution of auxiliary problems. Moreover, boundedness of the penalty parameter is achieved for the precision control used. Numerical experiments illustrate the efficiency of the presented algorithm and encourage its usage.

Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Equality Constraints: Corrigendum and Addendum

In this paper we give corrections to our paper on an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints.

High Dynamic Precision Adaptive Control System for Solution of Fault Tolerance Problem

Adaptive control can provide desirable behaviour of a process even though the process parameters are unknown or may vary with time. Conventional adaptive control requires that the speed of adaptation must be more rapid than that of the parameter changes. In practice, however, problems do arise when this is not the case. For example, when fault occurs in a process, the parameters may change very dramatically. A new approach based on simultaneous identification and adaptation of unknown parameters is suggested for compensation of rapidly changing parameters of a multivariable process.

High Dynamic Precision Adaptive Control System for Solution of Fault Tolerance Problem of SISO Process

Adaptive control can provide desirable behaviour of a process even though the process parameters are unknown or may vary with time. Conventional adaptive control requires that the speed of adaptation must be more rapid than that of the parameter changes. However, in practice, problems do arise when this is not the case. For example, when fault occurs in a process, the parameters may change very dramatically. A new approach based on simultaneous identification and adaptation of unknown parameters is suggested for compensation of rapidly changing parameters. High dynamic precision adaptive control can be used for the solution of a fault tolerance problem in complex and multivariable processes and systems.

Augmented Lagrangians with Adaptive Precision Control forQuadratic Programming with Equality Constraints

In this paper we introduce an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints. The new feature of the proposed algorithm is the adaptive precision control of the solution of auxiliary problems in the inner loop of the basic algorithm. Global convergence and boundedness of the penalty parameter are proved and an error estimate is given that does not have any term that accounts for the inexact solution of the auxiliary problems. Numerical experiments illustrate efficiency of the algorithm presented

Analysis of semicoercive contact problems using symmetric BEM and augmented Lagrangians

We present a parallel algorithm for identification of the contact interface and evaluation of contact stresses of systems of elastic bodies in contact that may comprise bodies which admit some rigid body motion. The algorithm is based on the discrete reciprocal formulation obtained by the symmetric boundary element method. The solution of the resulting problem is reduced to the solution of a sequence of strictly convex quadratic programming problems with simple bounds by a variant of the augmented Lagrangian method. The algorithm in the inner loop uses projections and adaptive precision control for the solution of auxiliary problems so that it can efficiently identify the contact interface. Both theoretical results and numerical experiments indicate that there are problems which may be solved efficiently by the algorithm presented. Since the coupling procedure is iterative, the algorithm may process most information concerning each body locally so that it is suitable for parallel implementation.