Polynomial approach to quadratic tracking in discrete linear systems

In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems for plants with inaccessible states, which thus extends the results for discrete-time plants with accessible states previously obtained by Bradshaw and Porter (1975). The design method is illustrated by the presentation of the results of computer simulation studies.

Linear discrete controlled systems and linear discrete pursuit games are considered in the problem where the control vector of the pursuer is subject to a geometrical constraint and the control of the pursued object is subject an integral constraint. Necessary and sufficient conditions of solvability of the 0-controllability problem and that of coming together at the zero point are proved by way of constructive selection of the control vector.

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

In this paper a basis is developed for the systematic design of linear multivariable continuous-time tracking systems for plants with inaccessible states which thus extends the results for continuous-time plants with accessible states previously obtained by Porter and Bradshaw (1974). The design method is illustrated by the presentation of the results of computer simulation studies.

In this paper, we consider the analysis and synthesis problem for linear time-invariant distributed discrete time systems. These systems occur in many practical applications such as formation flight, control of systems described by partial differential equations, and control of automated vehicles moving in a platoon. Computationally attractive linear matrix inequality conditions are obtained for ensuring stability and induced /spl Lscr//sub 2/ performance. An example is given to motivate the class of systems we consider.

Bayesian optimal control for a non-autonomous stochastic discrete time system

Consider a discrete dynamical system given by a square matrix $M \in \mathbb{Q}^{d \times d}$ and a starting point $s \in \mathbb{Q}^d$. The orbit of such a system is the infinite trajectory $\langle s, Ms, M^2s, \ldots\rangle$. Given a collection $T_1, T_2, \ldots, T_m \subseteq \mathbb{R}^d$ of semialgebraic sets, we can associate with each $T_i$ an atomic proposition $P_i$ which evaluates to true at time $n$ if, and only if, $M^ns \in T_i$. This gives rise to the LTL Model-Checking Problem for discrete linear dynamical systems: given such a system $(M,s)$ and an LTL formula over such atomic propositions, determine whether the orbit satisfies the formula. The main contribution of the present paper is to show that the LTL Model-Checking Problem for discrete linear dynamical systems is decidable in dimension 3 or less.

S-54-2 - The integration of intrinsic properties and synaptic inputs in locus coeruleus

An optimal predictive control algorithm is introduced for the control of linear and nonlinear discrete-time multivariable systems. The controller is specified in a ‘restricted structure’ form involving a set of given linear transfer-functions and a set of gains that minimise a Generalised Predictive Control (GPC) cost-index. The set of functions can be chosen as proportional, integral and derivative terms, however, a wide range of controller structures is possible. This is referred to as Restricted-Structure GPC control. The multi-step predictive control cost-function is novel, since it includes weightings on the ‘low-order’ controller gains and the rate of change of gains. This considerably improves the numerical computations ensuring critical inverse computations cannot lead to a singular matrix. It also provides the option of adding soft or hard constraints on the controller gains which provides additional flexibility for control design. The ability to include a plant model that can include a general nonlinear operator is also new for restricted structure control solutions. The low-order controller provides a potential improvement in robustness, since it is often less sensitive to plant uncertainties. The simple controller structure also enables relatively unskilled staff to retune the system using familiar tuning terms, and provides a potentially simpler QP problem for the constrained case.

Mathematical model in the form of discrete linear system of equations with multiple input and multiple output (MIMO) describes different important for practice dynamic processes. Model predictive control (MPC) in recent years is a very intensively developing field of control theory and application. In given chapter, some of the possible realizations of MPC for discrete MIMO linear system are considered. Developed approach is based on the Cauchy formula for discrete linear system. Problem of control design is reduced to solving series of extremal problems including constrained optimization problems. It has succeeded to obtain final results in analytical form which is appropriate for solving different problems including control analysis and design.

It is shown that receding-horizon controllers with horizon length N ≥ v (v being the controllability index of the system) stabilize a given discrete-time linear multi-variable system. Necessary and sufficient conditions for a receding-horizon controller to be a deadbeat controller are also given. It is further shown that by modifying a receding-horizon controller m of the poles of the closed-loop system (where m is the dimension of the input space) can be assigned to zero with simultaneous stabilization. The deadbeat properties of such modified receding-horizon controllers are also investigated,

The sampled-data control based model matching problem of unmodeled high-frequency dynamics is examined using the singular perturbation method. A novel perfect model matching control in a linear discrete-time multivariable system is presented. Modifying the transfer function matrix of the sampled-data slow subsystem, the discrete model matching controller for the slow subsystem is developed. It is shown that the controller designed on the basis of the sampled-data slow subsystem is able to make the original system with high-frequency dynamics match a lower-order stable model for a sufficiently small perturbation parameter. >

The partial realization problem for 2D discrete linear shift-invariant systems is discussed. The authors attempt to establish a reasonable definition of minimality and propose a method for finding the degree and the system function of a minimal realization of a 2D linear system characterized by a given 2D impulse response array. The method used is based on the 2D Berlekamp-Massey algorithm which has a close connection with the 2D Hankel matrix derived from the 2D array. While it compares in efficiency with other methods for identification and approximation of 2D linear systems, it gives a novel approach to the problem in the sense that one does not need any knowledge or assumptions concerning the system degree. >

In this work an algorithm for the suboptimal state estimation of an nth order linear discrete time system, which receives quantized vector measurements, has been developed. The proposed filter is decentralized in the sense that the nth order system has been partitioned into n first order systems which simultaneously process the components of the quantized measurement vector at each stage.

An interactor plays a basic role in the design problems of multivariable control systems, such as the model matching control, decoupling control, adaptive control, and disturbance decoupling control. For example, it is well known that a linear multivariable system is decouplable by the static state feedback if and only if it has a diagonal interactor. But, in general, the interactor is a lower left triangular matrix, which makes the design problems of multivariable control systems complicated. From this point of view, the precompensator such that the total system has a diagonal interactor is important for multivariable control systems to simplify their design procedure. This paper concerns the systematic design method of the precompensator for a diagonal interactor using Markov parameters of the plant. It will also be proved that this compensator is always obtained by the proposed design algorithm. Furthermore, this argument will be a basic idea when this technique is applied to the nonlinear multivariable systems. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(1): 65–72, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20599