Output regulation of discrete‐time linear plants subject to state and input constraints

Discrete‐time output regulation of linear systems with state and/or input constraints on magnitude is considered. Structural properties of linear plants are identified under which the so‐called constrained semi‐global and global output regulation problems are solvable. As in the case of continuous‐time systems, an important aspect of our development is a taxonomy of constraints showing a clear relationship between the constraint types and the output regulation results. Solvability conditions are developed for semi‐global and global output regulation problems. Appropriate regulators are constructed for problems that are solvable. Copyright © 2003 John Wiley & Sons, Ltd.     

Output regulation for linear discrete-time systems subject to input saturation

The purpose of this paper is to examine the problem of controlling a linear discrete-time system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that a semi-global framework, rather than a global framework, for this problem is a natural one. Within this framework, a set of solvability conditions are given and feedback laws which solve the problem are constructed. The theory developed in this paper parallels the one we developed earlier for the continuous-time system. © 1997 by John Wiley & Sons, Ltd.     

Output regulation for linear delta operator systems subject to actuator saturation

In this paper, output regulation for linear delta operator systems subject to actuator saturation is investigated by state feedback. The relation between the regulatable regions and the null controllable region is described in this paper. A set of all initial conditions of a plant and a exosystem is called asymptotically regulatable region for which output regulation is possible. An asymptotically regulatable region is characterized according to a null controllable region of an anti‐stable subsystem of the plant. Feedback laws are constructed to solve the problems on output regulation. A numerical example is given to illustrate the effectiveness and potential for the developed techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Output feedback stabilisation for uncertain nonlinear time-delay systems subject to input constraints

Robust stabilisation of a class of imperfectly known systems with time-varying time-delays via output feedback is investigated. The systems addressed are composed of a nonlinear nominal system influenced by nonlinear perturbations which may be time-, state-, delayed state- and/or input-dependent. The output of the system is modelled by a nonlinear function, which may depend on the delayed states, and inputs, together with a feed-through term. Using bounding information on the perturbations, in terms of specified growth conditions, classes of unconstrained and constrained output feedback controllers are designed in order to guarantee a prescribed stability property for the closed-loop systems, provided appropriate stability criteria hold. Two stability criteria are given: one in terms of a linear matrix inequality (LMI) and the other is algebraic in nature, obtained using a Ger?gorin Theorem.     

Suboptimal control of linear time-invariant systems subject to control structure constraints

A method is presented for designing controllers for linear time-invariant systems whose states are not all available or accessible for measurement and where the structure of the controller is constrained to be a linear time-invariant combination of the measurable states of the system. Two types of structure constraints are considered: 1) each control channel is constrained to be a linear, time-invariant combination of one set of measurable states; 2) each control channel is constrained to he a linear, time-invariant combination of different sets of measurable states. The control system, subject to these constraints is selected such that the resulting closed-loop system performs as "near" to some known optimal system as is possible, i.e., suboptimal. The nearness of the optimal system to the suboptimal system is defined in two ways and thus, two types of suboptimal controllers are found.     

Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

A subgradient selection method for minimizing convex functions subject to linear constraints

A readily implementable subgradient algorithm is given for minimizing a convex, but not necessarily differentiable, functionf subject to a finite number of linear constraints. It is shown that the algorithm converges to a solution, if any. The convergence is finite iff is piecewise linear.     

Output regulation for linear distributed parameter systems

This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in Francis (1997) and Isidori and Byrnes (1990). We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system     

A recurrent neural network for solving nonlinear convex programs subject to linear constraints

In this paper, we propose a recurrent neural network for solving nonlinear convex programming problems with linear constraints. The proposed neural network has a simpler structure and a lower complexity for implementation than the existing neural networks for solving such problems. It is shown here that the proposed neural network is stable in the sense of Lyapunov and globally convergent to an optimal solution within a finite time under the condition that the objective function is strictly convex. Compared with the existing convergence results, the present results do not require Lipschitz continuity condition on the objective function. Finally, examples are provided to show the applicability of the proposed neural network.     

m/nCCS: linear consecutively connected systems subject to combined gap constraints

Motivated by practical applications (e.g. flow transfer systems, electromagnetic accelerating systems and defense systems), in this paper, we consider combined gap constraints in modelling and analysing linear multistate consecutively connected systems (LMCCS). The system has linearly ordered nodes. To provide certain connectivity among these nodes required by the system functionality, some of them host statistically independent multistate connection elements (MCEs). Each MCE is used to provide a connection between its host and a random number of next nodes according to a known probability mass function. The system fails if it contains at least m nodes not connected with any previous node or at least n ≤ m consecutive nodes not connected with any previous node. In other words, the system functions as long as the number of single-node gaps is less than m and the size of any consecutive gap is smaller than n. Such systems with the combined gap constraints are referred to as m/nCCS. An algorithm based on universal generating functions is proposed for the reliability evaluation of m/nCCS and its computational complexity is analysed. Based on the suggested reliability evaluation algorithm, importance analysis is also performed for m/nCCS, which can assist in identifying the most influential elements or weakness of the system design. Illustrative examples are provided.     

Control of linear systems subject to time-domain constraints with polynomial pole placement and LMIs

This note focuses on the control of continuous-time linear systems subject to time-domain constraints (input amplitude limitation, output overshoot) on closed-loop signals. Using recent results on positive polynomials, it is shown that finding a Youla-Kuc/spl breve/era polynomial parameter of fixed degree (hence, a controller of fixed order) such that time-domain constraints are satisfied amounts to solving a convex linear matrix inequality (LMI) optimization problem as soon as distinct strictly negative closed-loop poles are assigned by pole placement. Proceeding this way, time-domain constraints are handled by an appropriate choice of the closed-loop zeros.     

Application of linear programming to the optimal plastic design of circular plates subject to technological constraints

This paper is concerned with plastic minimum-volume design of circular or annular plates under axially symmetric loading. Accordingly, all characteristics of the plate depend only on the radial coordinate r. The plate is divided into rings of constant yield moment. Other technological constraints may be added, for instance bounds on the yield moments of the rings. Linear programming is used to obtain an approximate solution of the problem, and the optimality criteria are derived from the duality relations. The method is illustrated by examples which show that it is quite accurate.     

An affine-scaling derivative-free trust-region method for solving nonlinear systems subject to linear inequality constraints

In this paper, an affine-scaling derivative-free trust-region method with interior backtracking line search technique is considered for solving nonlinear systems subject to linear inequality constraints. The proposed algorithm is designed to take advantage of the problem structured by building polynomial interpolation models for each function in the nonlinear system function F. The proposed approach is developed by forming a quadratic model with an appropriate quadratic function and scaling matrix: there is no need to handle the constraints explicitly. By using both trust-region strategy and interior backing line search technique, each iteration switches to backtracking step generated by the trust-region subproblem and satisfies strict interior point feasibility by line search backtracking technique. Under reasonable conditions, the global convergence and fast local convergence rate of the proposed algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.     

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.     

Output regulation of linear systems with bounded continuous feedback

This paper studies the classical problem of output regulation for linear systems subject to control constraint. The asymptotically regulatable region, the set of all initial conditions of the plant and the exosystem for which output regulation is possible, is characterized in terms of the controllable region of the antistable subsystem of the plant. Continuous output regulation laws, of both state feedback type and error feedback type, are constructed from a given stabilizing state feedback law. It is shown that a stabilizing feedback law that achieves a larger domain of attraction leads to a feedback law that achieves output regulation on a larger subset of the asymptotically regulatable region. A feedback law that achieves global stabilization on the asymptotically controllable region leads to a feedback law that achieves output regulation on the entire asymptotically regulatable region.     

Output regulation for linear systems via adaptive internal model

Given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear stable exosystem with unknown parameters and known order, the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered. The system is assumed to be known while the frequencies of the exosystem are unknown; all exosystem oscillatory modes are assumed to be excited by the initial condition. A global solution is proposed consisting of a dynamic output feedback controller which includes exponentially convergent estimates of the unknown frequencies.