Abstract: The present paper is concerned with the control of certain parabolic systems whose boundary conditions involve time delays. The optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control and to fixed-time, minimum-norm control problems.

Abstract: This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizes t , where t is defined as an integer such that the controller drives the output to zero in no more than t steps for any set of initial conditions of the system and the observer.

Abstract: It is often desirable to have controllers which respond fast to large errors and which respond slowly to the small errors that are often due to sensor noise. Some nonlinear controllers having these properties are developed here by modifying optimal linear state feedback controllers so that they have state-dependent gains. A general approach is developed for the nonlinear control of multivariable systems such that the transient responses exhibit the desired properties, and the closed loop systems are asymptotically stable.

Abstract: The paper develops a constant-linear-output feedback optimal-control system for an a.c. turbogenerator system, requiring only the measurement of readily available signals from the power system. The control law is derived from the output prediction formulation of linear-system dynamics, releasing the designer from the need for either state-estimation techniques, or the selection of the number of output measurements to be equal to the number of states. The method is applied to a single machine connected to an infinite busbar, and the performance of the controlled machine investigated in a wide range of operating conditions. These include step changes in demand, and a 3-phase fault at the generator terminals, the results being compared to those achievable with full state-feedback optimal control.

Abstract: The sequential minimization of quadratic cost functions is considered for stochastic linear systems. The class of admissible controls is constrained to be the set of linear functions of the output, sampled at discrete instants of time. Unlike other formulations, sequential minimization results in output-feedback controllers that can be computed on-line. The state of the optimum closed-loop system tends to zero in a finite time interval for almost all sample paths. These results are specialized to deterministic systems to show that any state X_{N} \epsilon R^{n} is reachable by discrete output feedback, provided the system under consideration is discrete-time completely observable and completely controllable.

Abstract: A new criterion for jump resonance of nonlinear control systems is presented. The jump resonance phenomenon is classified into various types according to the form of the frequency response curve, some of which are new and not found in the previous publications. A simple graphical method to predict each type of jump resonance is studied. Experimental results by analog simulation are shown.

Abstract: The effect of dynamic output feedback on a linear time-invariant system is studied and it is shown that a dynamic compensator introduces trensmission zeros in the closed-loop system which are located at the poles of the compensator. A similar result is also obtained for the transmission zeros between disturbances and outputs ("disturbance zeros") of the closed-loop system.

Abstract: : A synthesis theory for feedback systems with nonlinear uncertain plants to satisfy prescribed output tolerances is presented. The essence of the theory is to convert the nonlinear plant set to a linear time-invariant one for which a design procedure exists. Schauder's fixed point theorem is applied to prove the equivalence of these two plant sets.

Abstract: The design of noninteracting multivariable control systems by slate feedback has received considerable attention recently, and an extensive theory is now available. One area, however, that requires further clarification concerns the case where the state vector is not accessible to measurement, and feedback of output is inadequate for the purpose of decoupling. In this paper a new technique is described by means of which it is possible to decouple a system which is not olherwise decouplable by proportional feedback of the output vector. The technique is based on the addition of a dynamic controller in the forward path, and is analogous to cascade compensation in single-loop systems. It is shown that a necessary and sufficient condition for the success of this method of decoupling control is that the Original system should satisfy the condition for state feedback decoupling.

Abstract: The note describes the effect of output feedback on a linear system in the general case where there is direct transmission from input to output. A simple method is given for determining an output-feedback matrix which assigns the poles of the cloaed-loop system. The method is illustrated by a numerical example.

Abstract: In the disturbance decoupling problem (DDP) of the linear system (A, B, C), the A-invariant subspace and the (A, B)-invariant subspace are proved to play a key role. The purpose of this paper is to extend the study of the DDP to nonlinear control systems. It must be noted that the problems are stated on the tangent bundle over the state space. The state space and the tangent bundle over it can be identified in the analysis of linear systems, but they must be distinguished in the case of nonlinear systems. So it is needed to establish the corresponding concepts in the state space to extend the A-invariance and the (A, B)-invariance to nonlinear systems. From such a point of view, the invariant structure and the structure which can be modified invariant by nonlinear state feedback are introduced as the state space representations of the A-invariant subspace and the (A, B)-invariant subspace. The main result obtained here, is the algebraic necessary and sufficient condition for the DDP of the nonlinear control systems.

Abstract: An open-loop control circuit is described which, in conjunction with a cosine wave crossing technique, provides a linear transfer characteristics of a phase-controlled converter under both continuous and discontinuous conduction, regardless of ?L/R values of the load. The nonlinear transfer characteristic between the signal and the output voltage at discontinuous conduction has been counteracted by an inversely nonlinear control function for different ?L/R values. The control functions have been approximated by piecewise linear segments, synthesized by analog circuits, and identified by digital addresses. A complete control circuit has been designed and tested with a single-phase center-tap converter. The experimental results agree well with the theory. The principle can be extended to polyphase and multiquadrant converters.

Abstract: For linear multivariable systems a simple method is developed for the exact synthesis of desired closed-loop transfer-function matrices using constant feedback and cascade matrices. The feedback matrix operates on the system output.

Abstract: A simple and direct derivation of necessary conditions for optimality of output feedback gains for a linear time-invariant system is presented. The dependence of the cost on the initial state x(0) is eliminated by the well-known technique of averaging the initial state over the surface of the n -dimensional unit sphere.

Abstract: The practical work impossibility of some controllers designed by Bongiorno and Youla, and the inadmissibility in the design, ignoring some old-theory categories, are demonstrated.

Abstract: The time-optimal control of a class of nonlinear singularly perturbed systems possesses the two time-scale property that the optimal control is made of a control in a slow-time scale followed by a control in a fast time-scale. Based on this property a near time-optimal control is defined. Two examples illustrating the computation of the near-optimal control and a simple iterative technique are presented.

Abstract: Necessary and sufficient conditions for output feedback decoupilng of linear time-invariant multivariable systems into single input-multioutput subsystems are derived in frequency domain. The conditions imply a new constructive method for determining a constant gain output feedback matrix and some of its elements can be freely chosen to reassign the closed-loop poles.

Abstract: A new approach to the problem of stationary feedback controller design for linear time-invariant systems in the discrete time domain is presented. A single-input single-output deterministic system is considered first and it is shown that the gain vector that defines a state feedback controller is conveniently computed if the design criterion corresponds to the specified values of n members of the output sequence, n being the order of the given system. Extension of the proposed method to the case of single-input single-output stochastic systems is studied next. Finally, the case of multi-input multi-output systems is dealt with by converting the given system into an equivalent single-input system. The results are illustrated through numerical examples.

Abstract: Root-locus techniques are applied to non-linear control systems which exhibit multiple bifurcating steady-state solutions, depending on a system parameter k (e.g. k = feedback factor). Modified root-locus construction rules are derived. They provide an easy method for a stability analysis of the closed-loop system in a neighbourhood of the different solution branches.

Abstract: The arrangement is for vehicle control, esp. for remote radio control of model vehicles. It uses a non-linear element in the signal transfer chain to give a small gain for small control movements and a larger gain for larger movements without requiring a gain switching mechanism. The transfer function of the whole signal transfer chain is non-linearised by the use of one non-linear element which may be electrical or mechanical. The element may consist of a potentiometer with variable metal deposition thickness giving variable resistance change for control movement.

Abstract: The structure of linear, time-invariant, completely controllable and observable multivariable systems under the action of constant output feedback control laws is studied. A structure theorem is stated and proved. Following Dickinson (1976), the notion of covariant output feedback control laws is introduced. It is shown that these results can be used to investigate the problems concerning (i) our ability to alter some of the Popov (1972) invariants by employing constant output feedback control, and (ii) the asymptotic behaviour of the closed loop poles under the variation of the output feedback gain matrix.

Abstract: Critical systems are defined as systems whose stability behavior cannot be decided in first approximation.The linear part of the corresponding operator has at least one eigenvalue with vanishing real part and the rest with negative real parts.