Linear Control Constraints Research Articles

Методы численного моделирования множеств 0-управляемости линейной дискретной динамической системы с ограниченным управлением на основе алгоритмов полиэдральной аппроксимации

<p>The article deals with the problem of constructing a polyhedral approximation of the 0-controllable sets of a linear discrete-time system with linear control constraints. To carry out the approximation, it is proposed to use two heuristic algorithms aimed at reducing the number of vertices of an arbitrary polyhedron while maintaining the accuracy of the description in the sense of the Hausdorff distance. The reduction of the problem of calculating the distance between nested polyhedra to the problem of convex programming is demonstrated. The issues of optimality of obtained approximations are investigated. Examples are given.</p>

Study on the effects of towed array on the resistance and flow characteristics of unmanned underwater vehicle

Unmanned underwater vehicle (UUV) towing a number of trailing bodies carrying detectors as a UUV-towed array system is widely used in fields such as submarine topography exploration, submarine pipeline laying, and submarine energy survey due to its simple structure. This study employs the Computational Fluid Dynamics (CFD) method, using the general submarine models Joubert BB2 and Persia 110 as tug and towing models, to calculate the hydrodynamic performance of the towed system under full control constraints, linear control constraints, and plane control constraints respectively, under the condition of infinite depth and fixed speed. The surrounding flow field velocity under the above three conditions is also analyzed. The study gradually explores the drag and lift of the towed body, the pressure distribution on the surface of the hull, and the force on the catenary, as well as the influence of the towing array on the main UUV and the surrounding flow field. The findings demonstrate that the existence of the towed array system will increase the resistance of the main UUV, with drag movement showing periodic reciprocating motion. Furthermore, the control degree of the towed cable becomes lighter the farther away it is from the main UUV, resulting in a larger range of motion.

Using redundant control to optimize control torque

The object of research is the process of automatic control of the redundant structure of the vessel's executive devices for extreme rotation in the yaw channel. Traditionally, redundant structures have been used to improve the reliability of automated control systems and the maneuverability of vessels. At the same time, control redundancy can also be used to optimize control processes, thereby reducing fuel consumption, increasing control forces and moments, and reducing the time required to perform operations. This allows gaining advantages in movement over vessels not equipped with optimization modules. The paper considers the optimal management of the redundant structure of an offshore vessel, which ensures the rotational movement of the vessel around the center of rotation with the maximum angular velocity. As well as simultaneous maintenance of a given position or movement in the longitudinal and lateral channel, taking into account control restrictions. This problem is reduced to a nonlinear optimization problem with nonlinear and linear control constraints. The method, algorithmic and software of the module of extreme rotation of the vessel with a redundant structure of executive devices have been developed. The workability and efficiency of the developed method, algorithmic and software are verified by mathematical modeling in the closed circuit «Control Object – Control System». The results of the conducted experiment showed that the use of optimal control allows, in comparison with traditional methods of splitting controls, to increase the control moment and angular speed of rotation by 1.5–2 times. The obtained opportunities are explained by the use of a mathematical model of the redundant control structure and the optimization procedure for calculating optimal controls in the on-board computer of the automated system. The developed method can be used on vessels, provided it is integrated into the existing automated system of the on-board computer with an open architecture, to increase the capabilities of automatic traffic control.

Scalable Long-Term Safety Certificate for Large-Scale Systems

This letter focuses on safe control problems for high-dimensional systems with large uncertainties. A major challenge is the computation load to account for long outlook horizons in large-scale systems. This challenge is tackled using an integration of probabilistic forward invariance, the comparison theorem, and PDE techniques. Specifically, we propose a probabilistic certificate for long-term safety that only requires myopically ensuring linear control constraints and evaluating two-dimensional PDEs regardless of the system dimension. The certificate is constructed by obtaining a long-term safe probability bound as a solution of the PDE using the comparison theorem and applying a new notion of probabilistic forward invariance on the probability bound. The use of forward invariance directly on probabilistic reachability allows our method to carry the former’s computation efficiency and the latter’s control over long-term behaviors. Its capability to efficiently ensure long-term safety for high-dimensional systems can be useful in many large-scale distributed autonomous systems operating with limited onboard resources in latency-critical environments.

On continuous-time constrained stochastic linear–quadratic control

This paper studies a class of continuous-time scalar-state stochastic Linear–Quadratic (LQ) optimal control problems with the linear control constraints. Using the state separation theorem induced from its special structure, we derive the analytical solution for this class of problems. The revealed optimal control policy is a piece-wise affine function of system state. This control policy can be computed efficiently by solving two Riccati equations off-line. Under some mild conditions, the stationary optimal control policy can be also achieved for this class of problems over an infinite horizon. Examples are presented to shed light on the theoretical results established.

The Π-strategy in a differential game with linear control constraints

The concept of a linear constraint on the controls of the players in a differential game of pursuit, which, in a certain sense, generalizes both integral and geometrical constraints, is introduced. The optimal parallel pursuit strategy (Π-strategy) is constructed for the corresponding problem.

Static output feedback stabilization of interconnected systems

This paper is concerned with the celebrated static output feedback control problem (SOFP) subject to linear constraints on control input K, e.g. bounds on control magnitude, zeros in some elements of K, etc. These constraints typically arise in the control of resource-limited systems interconnected to each other, where the local control for each system makes use of its own and neighboring systems’ outputs only, and its magnitude is bounded. This control problem can be approached by a spectral-norm minimization technique (q-SNM), whose preliminary version was previously introduced with little mathematical justification but shown to be promising for the regular SOFP without control constraints. This paper mathematically justifies q-SNM by showing its explicit relationship with spectral radius, and extends q-SNM to accommodate various linear control constraints. This paper also discusses the practical application of q-SNM to vehicle formation control, which demonstrates the merit of q-SNM.

PCA-Based Process Diagnosis in the Presence of Control

In PCA-based fault diagnosis, additive faults have directional signatures in the residual space. Ideally, these are determined by the eigenvectors spanning this space. If the PCA model is obtained in the presence of linear control constraints, this relationship may be spoiled. However, by simply varying the control gains or setpoints, the open-loop fault isolation properties are retained.

An optimal control problem involving a class of linear time-lag systems

A class of convex optimal control problems involving linear hereditary systems with linear control constraints and nonlinear terminal constraints is considered. A result on the existence of an optimal control is proved and a necessary condition for optimality is given. An iterative algorithm is presented for solving the optimal control problem under consideration. The convergence property of the algorithm is also investigated. To test the algorithm, an example is solved.

Optimal control computation for nonlinear time-lag systems

In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints. Several examples have been solved to test the efficiency of the technique.

Regular synthesis for the linear-quadratic optimal control problem with linear control constraints

In [l] sufficient conditions for the existence of a regular optimal control synthesis for an abstract optimal control problem have been given. It has been indicated that the theorem is modelled after the linear-quadratic optimal control problem with linear control constraints. In this paper we prove a theorem which says that if a certain non-degeneracy (or, as we shall say, normality) condition is satisfied then the latter problem satisfies the hypotheses of the theorem of [l] and, therefore, it admits a regular synthesis of the optimal control. The proof includes a proof of a result of independent interest: under the normality assumption, every optimal control passes only finitely many times from one face of the control domain to another (or, as we shall say, has finitely many switching points). A general result of this kind has so far been known for the linear time-optimal control problem only [3,4]. Recently, it has been extended to a certain class of nonlinear problems [5]. Although the paper is closely related to [l], most of its auxiliary results can be well understood without referring to the concepts of [l]. Therefore, the auxiliary results have been separated from the verification of the hypotheses of the abstract synthesis theorem of [l]. The former are contained in Sections 3, 4; the latter in Section 5. Section 2 contains the formulation of the optimal control problem as well as a summary of some of its known properties.

Existence of regular synthesis for general control problems

The concept of regular synthesis has been introduced by Bolt’anski in his classical paper [I] (cf. also [2]) on the sufficiency of the Pontrjagin maximum principle for time-optimal control problems. It has been used as an assumption on a closed-loop control to generate open-loop optimal controls. Using the theory of subanalytic sets it has been proved in [3] that every normal linear system admits a regular time-optimal synthesis. Subsequently, in [S], Sussmann has been able to dispose of the normality condition and to extend the theorem to a certain class of nonlinear systems. All of the mentioned papers deal entirely with the time-optimal control problem for systems which are linear in the control, with polyhedral control domains. The present paper constitutes an extension towards optimal control problems with general performance criteria and general control domains. The abstract theorem proved in this paper is modelled after an important class of problems-linear-quadratic optimal control problems with linear control constraints. This problem will be dealt with in a forthcoming paper. An important requirement in Bolt’anski’s definition of regular synthesis which is followed in [3,4] as well as [8, 91 is that the optimal trajectories enter the switching surfaces (called cells) transversally. This requirement has to be dropped not only in the linear-quadratic optimal control problem but also in the linear time-optimal control problem with a control domain having a piecewise smooth curvilinear boundary, as the following example demonstrates: Consider the system