Showing papers on "Sliding mode control published in 1970"
TL;DR: This paper records the development of a state variable model of the megawatt-frequency control problem of multiarea electric energy systems in a mathematical form necessary for application of theorems of modem optimal control theory.
Abstract: This paper records the development of a state variable model of the megawatt-frequency control problem of multiarea electric energy systems. The model is in a mathematical form necessary for application of theorems of modem optimal control theory.
668 citations
TL;DR: It is shown that these so-called bilinear systems have a variable dynamical structure that makes them quite controllable and may utilize appropriately controlled unstable modes of response to enhance controllability.
Abstract: A nonlinear class of models for biological and physical processes is surveyed. It is shown that these so-called bilinear systems have a variable dynamical structure that makes them quite controllable. While control systems are classically designed so there are no unstable modes, bilinear systems may utilize appropriately controlled unstable modes of response to enhance controllability.
447 citations
TL;DR: In this paper, a method 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 is presented.
Abstract: 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.
223 citations
TL;DR: In this paper, the authors considered the problem of designing the optimal feedback controller of order (n −m) required to control an nth-order linear system with output of order m(m
Abstract: The problem is considered of designing the optimal, fixed configuration, dynamical feedback controller of order (n—m) required to control an nth-order linear system with output of order m(m
29 citations
TL;DR: In this paper, an algorithm for determining a sub-optimal control of a linear time-invariant system with incomplete feedback is presented, where the set of admissible controls is constrained to be a constant linear feedback control of the system output.
Abstract: An algorithm is developed for determining a sub-optimal control of a linear time-invariant system with incomplete feedback. The set of admissible controls is constrained to be a constant linear feedback control of the system output. The merits of the control thus developed relative to that of known techniques are discussed, and two examples are solved to illustrate the method.
12 citations
01 Feb 1970
11 citations
TL;DR: In this paper, the theoretical basis of a sub-optimal control for plants consisting of a set of pure integrators is developed by invoking dimensional considerations. But the theoretical analysis is limited to the case where the optimal system has certain types of invariance under changes of scale.
Abstract: The optimal control signal for saturating or relay control systems is usually a complicated function of several state variables. A sub-optimal control method is to use instead a simpler signal which is a linear combination of functions each of which has only one state variable as argument. Persson has investigated this type of sub-optimal control for plants consisting of a set of pure integrators. In the present paper the theoretical basis of Persson's controller is developed by invoking dimensional considerations. It is shown that the optimal system has certain types of invariance under changes of scale. If a similar property for the sub-optimal system is adopted, the controller design problem can be reduced to the determination of a few parameters.
11 citations
TL;DR: In this paper, the problem of regulation in the presence of a fixed but unknown disturbance is considered, and a control law is designed as if the disturbance were known, and an estimate given by an observer is used in the control law.
Abstract: The problem of regulation in the presence of a fixed but unknown disturbance is considered. The control law is designed as if the disturbance were known, and an estimate given by an observer is used in the control law. A system results having as many integrators as outputs.
8 citations
TL;DR: In this paper, an approximate method of stochastic terminal control for nonlinear dynamical systems with state-independent noise is proposed, which is based on the state variable representation concept in control theory.
Abstract: The purpose of this paper is to establish an approximate method of stochastic terminal control for nonlinear dynamical systems with state-independent noise. Guided by the state variable representation concept in control theory, we describe approximately mathematical models for both the dynamical system and the observation mechanism by the nonlinear vector stochastic differential equations of Ito-type. First, for the purpose of overcoming difficulties caused by nonlinear characteristics, a method of stochastic linearization is introduced. By using the stochastic linearization technique presented here, an approximate method is described for solving state estimation problems of nonlinear dynamical systems in a Markovian framework. Secondly, by using the estimator dynamics obtained, an approximation to the optimal control is presented for a terminal cost functional. Finally, detailed discussions are given by an example, including quantitative aspects of sample paths behavior of state estimation and optimal control signal.
5 citations
TL;DR: In this article, an existence theorem for controi systems whose state variables for every t are in C, the set of continuous functions varying over a given set L is considered, and the dependence of the state variables upon a ~/ is induced by their dependence upon the initial state and the state equation governing the system.
Abstract: We consider an existence theorem for controi systems whose state variables for every t are in C, the set of continuous functions varying over a given set L The dependence of the state variables upon a ~/is induced by their dependence upon the initial state and the state equation governing the system. In contrast, the control u ---- u(t) is taken as a measur- able function of t alone. The usual space constraints and boundary conditions are also allowed to vary over a ~l, and the cost functional is now taken to be a continuous functional over a suitable class of continuous functions. We also discuss an application of these results to control systems with stochastic boundary conditions.
3 citations
TL;DR: In this paper, control laws for cascaded-vehicle systems are derived by the application of modal control theory, and it is shown that the control laws thus derived lead to much simpler control Systems than alternative systems which have been derived by both continuous-time and discrete-time optimal control theory.
Abstract: In this paper, control laws for cascaded-vehicle systems are derived by the application of modal control theory. It is shown that the control laws thus derived lead to much simpler control Systems than alternative systems which have been derived by the application of both continuous-time and discrete-time optimal control theory.
TL;DR: In this article, a general class of nonlinear control laws is shown to be optimal for a large class of systems with respect to a certain class of functionals, which generalizes previous studies on the optimization of asymmetrical space vehicles.
Abstract: It is shown that a fairly general class of nonlinear control laws is optimal (with respect to a certain class of functionals) for a large class of nonlinear systems. The work generalizes previous studies on the optimization of asymmetrical space vehicles.
01 Mar 1970
TL;DR: The synthesis of nonperiodic piecewise-constant feedback gains for a class of nonlinear systems with nonquadratic performance indices is presented and the linear suboptimal control law is compared to other recently published results.
Abstract: The synthesis of nonperiodic piecewise-constant feedback gains for a class of nonlinear systems with nonquadratic performance indices is presented in this paper. A mean-square error type performance index measuring the difference between the closed-loop and the open-loop control is minimized. A gradient algorithm is then used to synthesize the feedback gains and switching times for the suboptimal control law. The linear suboptimal control law so obtained is then compared to other recently published results.