Showing papers on "Sliding mode control published in 1975"
TL;DR: In this article, a control strategy based on the optimal constrained aim of trajectory derivatives and intended for the regulation of special nonlinear systems is presented, and an example of its application to a transient power-system model, and a qualitative comparison of the optimal-aim strategy and a classical optimal-control strategy for a linear harmonic-oscillator model is given.
Abstract: A control strategy based on the optimal constrained aim of trajectory derivatives and intended for the regulation of special nonlinear systems is presented. A theorem useful for generating and implementing optimal-aim controls, an example of its application to a transient power-system model, and a qualitative comparison of the optimal-aim strategy and a classical optimal-control strategy for a linear harmonic-oscillator model are given.
36 citations
TL;DR: In this article, a sufficient condition is derived that one system locally approximates the other, i.e., there exists a map between the state spaces which carries the trajectory of the first system for any control into the trajectory for the same control with an error that grows like a power of t.
27 citations
TL;DR: In this paper, a special optimal control problem with a solution expressible in linear feedback form is discussed, which is characterized by a dynamic system that is nonlinear with respect to both the state and the control and by a linear objective function.
Abstract: This paper discusses a special optimal control problem having a solution expressible in linear feedback form. The problem structure is characteristic of certain economic investment problems where the control influences the rate of deterioration of a capital good. An example of an economic problem of this type is the determination of the optimal maintenance policy for a housing unit when the effectiveness of maintenance is subject to decreasing returns to scale. Mathematically, the problem is characterized by a dynamic system that is nonlinear with respect to both the state and the control and by a linear objective function. Both the control and the state are restricted to be nonnegative and to lie below given upper bounds. The problem possesses a unique global optimal solution expressible in linear feedback form. The associated control law is derived from the solution of an auxiliary ordinary differential equation that can be solved backward in time. In addition to the linear control law, the problem possesses other important linearity properties. The closed-loop system is linear; that is, although the system itself is nonlinear, when the optimal control law is substituted for the control, the resulting system is linear with respect to the state. And, the optimal return function is affine; that is, the optimal value that can be attained from a given point is an affine function of the value of the state at that time.
21 citations
TL;DR: Various optimal control problems for discrete-time systems with time-lag controls are discussed and basic features of this type of system are noted.
Abstract: Various optimal control problems for discrete-time systems with time-lag controls are discussed. Some of the basic features of this type of system are noted. A simple example is given for illustrative purpose.
16 citations
TL;DR: In this article, a new approach to the sub-optimal control of non-linear time-delay systems is presented, which consists of three stages, in the first stage the original time delay system state equation is expanded about its nominal functions, the resulting linear time-varying system with delay is then reduced to a linear non-delay non-homogeneous system whose optimal control is the same.
Abstract: A new approach to the sub-optimal control of non-linear time-delay systems is presented in this paper. It consists of three stages. In the first stage the original time-delay system state equation is expanded about its nominal functions. The resulting linear time-varying system with delay is then reduced to a linear non-delay non-homogeneous system whose optimal control is the same. The third stage is the application of the maximum principle to the transformed system leading to the desired sub-optimal control. The method is applied to a non-linear system.
11 citations
TL;DR: In this article, two suboptimal control policies employing integral state feedback suitable for nonlinear systems and nonquadratic performance functionals have been proposed and necessary conditions are obtained using the variational approach to select optimally the time-invariant parameters for a general control structure of which the two sub-optimal policies proposed are particular cases.
Abstract: Two suboptimal control policies employing integral state feedback suitable for nonlinear systems and nonquadratic performance functionals have been proposed. Necessary conditions are obtained using the variational approach to select optimally the time-invariant parameters for a general control structure of which the two suboptimal policies proposed are particular cases. A numerical example is worked out and the results compared and discussed.
6 citations
TL;DR: In this article, the problem of control of a stochastic system with control dependent noise is investigated, and the control policy given by the algorithm reduces to the optimal control policy in two cases in which the optimal controlling policy is known.
3 citations
TL;DR: In this article, a simplified existence criterion for the linear quadratic optimal control law for systems with state dependent noise is proposed. But the existence criterion is not applicable to the case of state-dependent noise.
Abstract: This note proposes a simplified existence criterion for the linear quadratic optimal control law for systems with state dependent noise.
2 citations
01 Dec 1975
TL;DR: The problem of control of a linear stochastic system observed by both linear and hard limited measurements is considered and it is shown that the feedback nature of the control induces a natural probing which activates the filter.
Abstract: The problem of control of a linear stochastic system observed by both linear and hard limited measurements is considered. The control used is the LQG or deterministic linear feedback control where the state estimate is generated by a recursive nonlinear filter. It is shown that the feedback nature of the control induces a natural probing which activates the filter. The results of this feedback system with a nonlinear filter in the feedback loop is compated to a system with an extended Kalman filter in the feedback loop. The state estimation accuracy is also compared to the system without a control to demonstrate how the control activates the nonlinear filter.
1 citations
01 Jan 1975
TL;DR: In this paper, a linear system with two sets of controls, one primary and the other redundant, is considered and a two level optimization procedure is used to control the system and to maintain maximal availability of the primary control.
Abstract: A linear system with two sets of controls, one primary and the other redundant, is considered. A two level optimization procedure is used to control the system and to maintain maximal availability of the primary control.