Adaptive pole-assignment subject to saturation constraints

This paper considers a class of type-1 plants and an adaptive pole-assignment control which is constrained by a saturation non-linearity. The adaptive control system is BIBO stable if a constrained parameter estimation algorithm is employed. Also, the desired system performance can be achieved under certain conditions.     

Optimal drug dosage subject to constraints

Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 174–176, November–December, 1993.     

Target tracking and obstacle avoidance for multi-agent networks with input constraints

In this paper, the problems of target tracking and obstacle avoidance for multi-agent networks with input constraints are investigated. When there is a moving obstacle, the control objectives are to make the agents track a moving target and to avoid collisions among agents. First, without considering the input constraints, a novel distributed controller can be obtained based on the potential function. Second, at each sampling time, the control algorithm is optimized. Furthermore, to solve the problem that agents cannot effectively avoid the obstacles in dynamic environment where the obstacles are moving, a new velocity repulsive potential is designed. One advantage of the designed control algorithm is that each agent only requires local knowledge of its neighboring agents. Finally, simulation results are provided to verify the effectiveness of the proposed approach.     

带二次约束的容积卡尔曼目标跟踪算法

为了提高对带约束目标的跟踪精度,提出了一种带二次约束的容积卡尔曼目标跟踪算法。使用容积卡尔曼滤波得到当前时刻后验估计,通过将系统二次约束作为测量方程引入系统,对后验估计进行修正,最后采用仿真实验对算法性能进行测试。实验结果表明,相对于传统的约束卡尔曼滤波算法,在同等条件下,该算法提高了目标跟踪精度,并且稳定性更强。     

Control system design subject to SNR constraints

This paper deals with networked control systems comprising LTI plants controlled over scalar additive noise channels subject to signal-to-noise ratio (SNR) constraints. We present a general framework, based upon convex optimization concepts, that can accommodate several situations of interest. Our results make explicit the fact that exploiting feedback around the channel plays a key role in reducing the minimal SNR that is compatible with stability. The results also provide a characterization of the best achievable performance subject to an SNR constraint. We apply the results to specific networked control architectures, and provide a numerical example.     

Decentralized bandwidth control subject to two-layer constraints

This paper is concerned with the new bandwidth allocation model that considers the structural allocation constraints. Suppose that a system is composed of finite groups of users and the bandwidth assigned to each user and to each group of users has pre-specified upper and lower bounds. If each user is granted with the utility function satisfying the standard continuity and concavity conditions, the existence, uniqueness, fairness and optimality properties of the Nash equilibrium point in the allocation game are studied. To identify the equilibrium point, an algorithm proved to converge globally is proposed and illustrated with a numerical example.     

Two-dimensional path finding subject to geometric constraints

The trajectory planning on a plane is considered as the problem of finding a path in a graph of a special form. Algorithms that are able to solve this problem in the case of geometric constraints, more precisely, under the assumptions that the trajectory is composed of a sequence of straight segments such that the angle between the adjacent segments does not exceed a given threshold, are analyzed. This statement is important for the development of effective navigation methods for unmanned vehicles. A novel algorithm for solving this problem is proposed, and the results of theoretical and experimental studies are presented. The experimental results confirm that the proposed algorithm can be used in practice for planning the trajectory of low-flying unmanned multirotor aerial vehicles in an urban area. They also show that the proposed algorithm significantly exceeds other available algorithms in terms of the number of successfully accomplished tasks.     

Filter design subject to nonlinear side constraints

Preliminary results show sequential unconstrained minimization techniques (SUMT) to be a viable filter design method. A nonlinear optimal filter design problem subject to nonlinear side constraints is formulated and solved using SUMT.     

Output regulation of linear plants subject to constraints

Output regulation problems for continuous-time linear systems with state and/or input constraints are studied. The problems are formulated in global and semi-global setting by using state or full information feedback. The goal of this paper is to develop solvability conditions for the posed problems. Moreover, appropriate regulators are constructed under the solvability conditions. To state the solvability conditions clearly, a taxonomy of constraints is introduced which delineates the constraints into several categories. Such a taxonomy of constraints provides a classification of linear plants with constraints and identifies what types of output regulation problems are solvable. Results developed here include as a special case the results obtained in the literature for systems with only input constraints. The constraint taxonomy also identifies some intrinsically hard constraints (non-right invertible constraints) for which the solvability conditions of global/semi-global output regulation problems are not clear yet. As a special case of output regulation, we also consider tracking problems with constraints. It is shown that if there exists a state feedback controller with a stabilizing domain of attraction, then one can find a regulator with a tracking domain of attraction arbitrarily close to the stabilizing domain.     

SWEEP operator for least-squares subject to linear constraints

The purpose of the paper is to present some additional properties of the SWEEP operator in the area of least-squares estimates subject to linear constraints in case of illconditioning of the SS&CP (sum of squares and cross-product) matrix. Regardless of many alternative approaches, the SWEEP operator may also be used successfully, and what is most important — the output interpretation remains the same as in the standard case.     

Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints

In this paper, a discrete-time recurrent neural network with global exponential stability is proposed for solving linear constrained quadratic programming problems. Compared with the existing neural networks for quadratic programming, the proposed neural network in this paper has lower model complexity with only one-layer structure. Moreover, the global exponential stability of the neural network can be guaranteed under some mild conditions. Simulation results with some applications show the performance and characteristic of the proposed neural network.     

Optimization of a catalytic reactor subject to temperature constraints

The optimal design for maximum yield of SO₃ in the oxidation of SO₂ over a commercial vanadium pentoxide catalyst is considered. The control variables are the wall heat flux and the reactor radius, both as functions of axial distance. The volume and length of the reactor are both specified, as well as the maximum radial-average temperature. The problem is attacked by a partial averaging technique, whereby the full set of state partial differential equations are integrated forward, but a set of ordinary functional-differential adjoint equations are integrated on the backward pass in order to determine the new estimate of the optimal control. It is found that the optimal design consists of two approximately constant-radius adiabatic sections separated by a small intercooler, which is fairly close to existing commercial designs.     

Target recognition and tracking

Advances in image and signal processing permit implementation of sophisticated sensor fusion algorithms for tracking and target identification. The polymoprhic estimator (PME) accomplishes these tasks simultaneously. However, it has been observed that there is an identification bias toward more languorous targets. This bias can be overcome with higher-quality sensors. It is shown here that, in some cases, more precise modelling of the target motion is an even better solution.     

Optimum design of composite shells subject to natural frequency constraints

A technique for the optimum (minimum weight) design of a composite shell subject to constraints on its natural frequencies is presented. The optimization problem is posed as a general mathematical programming problem in which one or more of the inequality constraints involves the shell natural frequencies, which must be evaluated numerically during the optimization. For this reason, a method for numerically evaluating the natural frequencies of composite shells is also presented. The method is based upon the finite element method of structural analysis and Rayleigh's principle. Because the element used is applicable to anisotropic shells of arbitrary shape, the method is very general. By using Rayleigh's principle, the necessity of assembling overall mass and stiffness matrices for the shell is eliminated. The optimization is performed by nondimensionalizing the mathematical programming problem and using the penalty function method of Fiacco and McCormick to transform the problem to a sequence of unconstrained minimizations having solutions which converge to the solution of the original (constrained) problem. The unconstrained minimizations are performed using the variable metric method of Fletcher and Powell. Derivatives of the nondimensional frequency constraints are evaluated numerically using difference equations. The frequency calculation method is demonstrated by calculating the fundamental frequency for the transverse vibration mode of a multilayered cylindrical shell with fixed overall geometry and variable composite geometry. Results indicate that the frequency increases with increasing fiber orientation angle, fiber volume fraction, or lamina thickness. The optimization technique is demonstrated by minimizing the weight of the shell discussed above subject to a constraint on its fundamental transverse frequency. The design variables are the fiber orientation angle, the fiber volume fraction, and the lamina thickness. Results are presented and explained in terms of the physical aspects of the problem.     

Topological optimization of structures subject to Von Mises stress constraints

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation. Therefore, this sensitivity can be naturally used as a descent direction in a structural topology design problem. However, according to the literature concerning the topological derivative, only the classical approach based on flexibility minimization for a given amount of material, without control on the stress level supported by the structural device, has been considered. In this paper, therefore, we introduce a class of penalty functionals that mimic a pointwise constraint on the Von Mises stress field. The associated topological derivative is obtained for plane stress linear elasticity. Only the formal asymptotic expansion procedure is presented, but full justifications can be deduced from existing works. Then, a topology optimization algorithm based on these concepts is proposed, that allows for treating local stress criteria. Finally, this feature is shown through some numerical examples.     

Optimal discrete sizing of truss structures subject to buckling constraints

The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckling constraints. The algorithm begins with a continuous optimum followed by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predicted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for those variables fixed on discrete values in each intermediate mixed-discrete nonlinear problem. It is shown that a continuous design based on the regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A range of examples is used to illustrate that with conservative regression, discrete designs can be achieved which are significantly lighter than those in which the variables have been rounded up.