On the controllability of linear systems with delay in control

By connecting information rates (entropy rate and mutual information rate) with classic poles and zeros analysis using Bode's integral formulas, the performance limits and the. conservation law of variety' in scale linear time invariant feedback control systems are discussed from the viewpoint of information theory. A new kind of design constraints is also derived.

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

The contribution is intended to present a method of computing robustly stabilizing PI controllers for linear time-invariant systems with unstructured multiplicative uncertainty. This graphical technique is based on the application of basic robust stability condition and plotting the robust stability border pairs of P-I parameters, which subsequently leads to the robust stability region. The illustrative example is presented to show the effectivity of this straightforward approach.

In the present paper finite-dimensional dynamical control systems described by linear higherorder ordinary differential state equations with multiple point delays in control are considered. Using algebraic methods, necessary and sufficient condition for relative controllability in a given time interval for linear dynamical system with multiple point delays in control is formulated and proved. This condition is generalization to relative controllability case some previous results concerning controllability of linear dynamical systems without multiple point delays in the control. Simple numerical example, which illustrates theoretical result is also given. Finally, some remarks and comments on the existing results for controllability of dynamical systems with delays in control are also presented.

This paper is concerned with the problem of designing linear time-invariant control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues in the interval shown in figure 1. This new algorithm can also be used for the placement of closed-loop eigenvalues in a specified interval in z-plane and can be employed for large-scale linear time-invariant control systems. Some illustrative examples are presented to show the advantages of this new technique.

In this two-part paper we study stabilization and optimal control of linear time-invariant systems with stochastic multiplicative uncertainties. We consider structured multiplicative perturbations, which, unlike in robust control theory, consist of static, zero-mean stochastic processes, and we assess the stability and performance of such systems using mean-square measures. While Part 2 of this paper tackles and solves optimal control problems under the mean-square criterion, Part 1 is devoted to the stabilizability problem. We develop fundamental conditions of mean-square stabilizability which ensure that an open-loop unstable system can be stabilized by output feedback in the mean-square sense. For single-input single-output systems, a general, explicit stabilizability condition is obtained. This condition, both necessary and sufficient, provides a fundamental limit imposed by the system's unstable poles, nonminimum phase zeros and time delay. For multi-input multi-output systems, we provide a complete, computationally efficient solution for minimum phase systems possibly containing time delays, in the form of a generalized eigenvalue problem readily solvable by means of linear matrix inequality optimization. Limiting cases and nonminimum phase plants are analyzed in depth for conceptual insights, revealing, among other things, how the directions of unstable poles and nonminimum phase zeros may affect mean-square stabilizability in MIMO systems. Other than their independent interest, stochastic multiplicative uncertainties have found utilities in modeling networked control systems pertaining to, e.g., packet drops, network delays, and fading. Our results herein lend solutions applicable to networked control problems addressing these issues.

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.

In this article, we study the controllability of finite-dimensional dynamical control systems modelled by semilinear impulsive ordinary differential equations with multiple constant time delays in the control function. Initially, we recall a necessary and sufficient condition for the controllability of the corresponding linear system without impulses, with multiple constant time delays in the control function in terms of a matrix rank condition. Then under some sufficient conditions, we show that the actual system is also controllable for certain classes of non-linearities and impulse functions. We employ Schauder fixed-point theorem and Banach contraction mapping principle to establish the results. Our obtained results are applicable for both autonomous and non-autonomous systems. An example is given to illustrate the theoretical results.

SummaryAt the present time, there is a great deal of interest in the adaptive control of systems with rapidly varying parameters. Such problems arise in different forms and in many disciplines including finance, sociology, biology, and engineering. In general, these problems are intractable mathematically and the time variations have to be classified in some form to obtain rigorous results. In this paper, we consider the adaptive identification and control of linear systems with periodically varying parameters (referred to as linear time‐varying periodic (LTP) systems). The class of systems with known periodic parameters has been investigated widely since the pioneering work of Floquet and lends itself to rigorous mathematical analysis. However, very little was known until the early years of the last decade concerning the adaptive control of such systems. The problem was introduced by Xu and explored in detail by Narendra and Zhiling in 2006 and 2009, respectively. In 2012, a new method was introduced in adaptive control by Han and Narendra and is referred to as second‐level adaptation. In this paper, the adaptive identification and control of LTP systems using second‐level adaptation is discussed.

This paper focuses on the synthesis problem of robust and reliable H/sup /spl infin// control for linear systems with norm-bounded time-varying parameter uncertainty in the state and delayed-state matrices, and also with actuator failures among a pre-specified subset of actuators. Actuator failures are considered as disturbance signals of arbitrary values to the system. A linear matrix inequality (LMI) method is given for the memoryless state feedback synthesis problem to quadratically stabilize the given systems with H/sup /spl infin//-norm bound constraints on attenuation of augmented disturbances, including failure signals in cases of actuator failures for any admissible uncertainty. The results depend on the size of the time-delay via the use of a Razumikhin-type theorem.

Robust controller design methodology for multivariable chemical processes: Structured perturbations

This study shows that a controllable system [xdot] = Ax + Bu, where x is an n-vector, can be driven from an arbitrary initial condition x(0) = x0 to an arbitrary final condition x(tf = xf by a polynomial control function of degree M = 2r + 1, where r = n − rank (B), through a polynomial trajectory of degree M. A simple algorithm for finding u by solving a set of linear equations, the solution of which yields the polynomial coefficients, is given.

Robust state feedback controllers for linear time-invariant systems with uncertain parameters are considered. Both matched and unmatched uncertainty structures are studied. A basic tool of analysis is a special auxiliary LQR problem without uncertainties. The solution to this problem guarantees unconditionally robust stabilization in the matched case. In the unmatched case, if some testable sufficient conditions are satisfied, the solution of the LQR problem is robustly stabilizing as well. Moreover, robust pole placement into an arbitrary left halfplane is constructively proved to be achievable in the matched case. In the unmatched case, our sufficient conditions for robust stabilization can be modified for the robust pole placement problem but they become void if the required set, into which the eigenvalues ought to be placed, is too far away from the imaginary axis.

Event-triggered Observers-based Output Feedback H∞ Control for Linear Time-invariant Systems with Quantization

This paper deals with output-feedback tracking control of linear time-invariant systems with unknown parameters. Controller parameters are updated in real time based on the estimation of unknown parameters using multiple observers.