Showing papers on "Sliding mode control published in 1968"
TL;DR: A method is described for constructing a feedback control law which remains optimal for a class of systems with unknown parameters whose values may lie in given regions and which results in a (2n+1)th-order approximation of the optimally adaptive performance index.
Abstract: A method is described for constructing a feedback control law which remains optimal for a class of systems with unknown parameters whose values may lie in given regions. The control depends only on the input and output, and there is no explicit dependence on the unknown parameters. In contrast to the usual adaptive strategy, there is no identification or adjustment period. The optimal controls generated in a Taylor series form, but truncation of the series results in a feedback control which is close to optimal for a range of parameter values. An n th-order truncation of the control results in a (2n+1)th-order approximation of the optimally adaptive performance index.
52 citations
TL;DR: In this article, the optimal adaptive control of linear discrete systems with constant but imprecisely known gain is considered, and the identification and control aspects are separated to the extent that the identification of the system gain is formulated as an optimal estimation problem; while selection of the optimal control policy is accomplished by minimization of the expected value of a quadratic cost functional, conditioned up on the information available at the time of control application and subject to the constraints imposed by the identification techniques.
Abstract: The optimal, adaptive control of linear discrete systems with constant but imprecisely known gain is considered. It is assumed that a priori, Gaussian distribution functions are available for the unknown gain and for any random disturbances or observation error. The identification and control aspects are separated to the extent that the identification of the system gain is formulated as an optimal estimation problem; while selection of the optimal control policy is accomplished by minimization of the expected value of a quadratic cost functional, conditioned up on the information available at the time of control application and subject to the constraints imposed by the identification techniques. The interaction between identification and control is explicitly shown by the form of these constraints. The effects of this interaction are examined by considering a simple, first order system and the average performance of the optimal adaptive control law is compared to that of the optimal deterministic control.
24 citations
21 citations
TL;DR: In this paper, a systematic approach based on recent results in filtering theory is presented to treat the problem of optimally controlling a linear stochastic system with a set of unknown but fixed control gains.
Abstract: A systematic approach is presented based on recent results in filtering theory to treat the problem of optimally controlling a linear stochastic system with a set of unknown but fixed control gains. New suboptimal solutions are proposed for the control, and the non-Gaussian problem is treated. The interaction between filtering and control is clarified. Computer experiments illustrate some of the analytic results.
16 citations
01 Aug 1968
TL;DR: In this article, the authors present results on the synthesis of time-optimal control for a second-order nonlinear system, where the problem is to determine the feedback control as a function of the state variables.
Abstract: : The report presents results on the synthesis of time-optimal control for a second-order nonlinear system. The problem is to determine the feedback control as a function of the state variables. This is equivalent to finding the switching locus, since the time-optimal control is a relay control. The nonlinear system is represented by a soft spring characterized by the Duffing equation with negative nonlinear term.
3 citations
TL;DR: In this article, the problem of determining the set of initial conditions for which a given nonlinear control system is asymptotically stable and the trajectory remains within a given region of the state space is formulated mathematically.
Abstract: The mathematical problem of determining the set of initial conditions for which a given nonlinear control system is asymptotically stable in the sense of Liapunov has been the object of considerable research. The more practical problem of determining the set of initial conditions for which a given nonlinear control system is asymptotically stable and the trajectory remains within a given region of the state space is formulated mathematically. An approach to estimating the defined region of acceptable motions is indicated.
2 citations