Showing papers on "Sliding mode control published in 1971"

An explicit procedure for discretizing continuous, optimal control problems

Abstract: An explicit procedure for obtaining discrete approximations to general, nonlinear, fixed-time, continuous, optimal control problems with no intermediate trajectory constraints is presented. It is proved that, if the associated system of differential equations is linear in the control variable, then the optimal solutions of these approximationsconverge to extremals of the original continuous problem.

A neighboring optimal feedback control scheme for systems using discontinuous control

Abstract: The calculation and implementation of the neighboring optimal feedback control law for multiinput, nonlinear dynamical systems, using discontinuous control, is discussed. An initialization procedure is described which removes the requirement that the neighboring initial state be in the neighborhood of the nominal initial state. This procedure is a bootstrap technique for determining the most appropriate control-law gain for the neighboring initial state. The mechanization of the neighboring control law described is closed loop in that the concept of time-to-go is utilized in the determination of the control-law gains appropriate for each neighboring state. The gains are chosen such that the time-to-go until the next predicted switch time or predicted final time is the same for both the neighboring and nominal trajectories. The procedure described is utilized to solve the minimum-time satellite attitude-acquisition problem.

Analysis of Nonlinear Control Systems with Transport Lag

Abstract: Control systems with transport lag are commonly encountered, and the presence of nonlinearities in such systems makes stability analysis difficult. Parameter plane equations for such systems are formulated and used to map the imaginary axis of the s plane onto the parameter plane. Stability conditions are studied for a system with transport lag and one single-valued nonlinearity and also for a system with transport lag and a hysteretic-type non-linearity. In both cases the existence and characteristics of limit cycles are studied. Application of the method is made to an aircraft pitch control system.

On an inverse optimal control problem

Abstract: A straightforward method is given for determining a performance index which is minimized by a class of nonlinear autonomous systems. The results of this method are then compared with some earlier results of Thau.

The identification and control of unknown linear discrete systems

Abstract: This investigation is concerned with the optimal control of unknown, time-invariant. linear discrete systems. Of particular interest is the relationship among the identification problem, the specification of the control law assuming the system is known and the overall optimalizing control. For single-stage control with noiseless observations, conditions under which the use of separate identification and control procedures results in overall optimal control are established. The complexity inherent in the control problem is illustrated with a simple single-stage example wherein optimal control calls for filtering of the observed data by a time-varying, data-dependent operator, for which no simple recursive implementation exists.

Dual control of stochastic nonlinear systems

Abstract: In stochastic control of nonlinear systems, estimation and control are dependent-the control, in addition to its effect on the state of the system, affects the estimation performance A method for obtaining a dual control sequence is discussed that leads to a one-step optimization problem and a control strategy called the one-step dual control An example problem is used to indicate the performance improvement when using the one-step dual control instead of the separation control policy

Instability of Optimal Stochastic Control Systems under Parameter Variations

Abstract: The deterioration of a linear optimal stochastic control scheme, designed under the assumptions of the certainty-equivalence principle (the optimal filter and controller, determined independently, combine to give a totally optimal system), is investigated when the parameters of the actual system do not coincide with the design values. This linear suboptimal stochastic system is described by a covariance matrix composed of covariances of the estimates of the state variables, the errors in the estimates of the state variables, and the correlation between these errors and the estimates. In particular, this paper is concerned with the covariance matrix resulting from a single state dynamical system and a scalar linear measurement function of both the state variable and the control variable (e.g., accelerometer measurements). A modeling error in the control variable coefficient of the measurement function may induce instability in the stochastic system with either unstable or stable dynamics. Furthermore, the absolute magnitude of the error in the control variable coefficient directly influences system stability, not the relative error. Thus, relatively small errors compared to the design value of this coefficient may be quite important. 4 LTHOUGH there are many studies on divergence of op-£^- tirnal filters, little attention has been given to the effect of modeling inaccuracies on optimal linear stochastic control systems. Here we extend Fitzgerald's1 investigation of Kalman filter divergence to optimal linear stochastic control systems. These systems are designed under the certainty equivalence principle2 which states that if the expected value of a quadratic function of the state and the control variables is to be minimized subject to linear dynamics, the optimal system is composed of an optimal filter in cascade with an optimal controller. This separation is possible because the estimate in the state is uncorrelated with the error in this estimate. If the parameters in the assumed model of the dynamics or the measurement device deviate from the parameters of the actual system, the estimate and the error in the estimate become correlated. The behavior of the system because of the gains based on an inaccurate model is studied by considering the coupled matrix covariance equation composed of the Covariances of the error in the estimate, the estimate, and the estimate with its error. Some of the characteristics of this linear matrix equation are studied through a scalar linear dynamic equation. The errors in system parameters enter into the 2X2 covariance equation in a dimensionless form allowing the following general results to be obtained: 1) The stochastic control system may be unstable when the nonoptimal filter and deterministic control systems individually are stable. 2) Instability occurs only when the error in the parameter exceeds a finite threshold value. 3) If the measurement is a linear function of the control variable as well as the state (e.g., accelerometer measurements) and there are errors in the coefficient of the control, then instability of the total system may occur for both stable and unstable dynamical systems. 4) The filter or control gains are not functions of the coefficient of the control variable in the measurement function. Consequently, Presented as Paper 70-36 at the AIAA 8th Aerospace Sciences

A Dual Mode Excitation Control of Synchronous Machine for Suppressing its Hunting

Abstract: To suppress the hunting of synchronous machine caused by stepwise load change, a dual mode field excitation control was investigated for conventional (one-axis) machine and 2-axis machine. For one-axis machine, a dual mode is applied successively, the first one being a bang-bang suboptimal control mode decided by use of energy function instead of Pontryagin's switching function, this mode is applicable to dynamic equation described in nonlinear form. The second one is a linear feedback control mode composed of a linear combination of state variables, and it will be adopted to the range near the steady state operating point where the equation will be linearized. For 2-axis machine at the instant of load change the original excitation introduced by mixing these two controls is efficiently applied. From the results of the investigation it is recognized that the employment of 2-axis synchronous machine is a potential means for the improvement of system stability.

On cross coupling and stability in nonlinear control systems

Abstract: A stability criterion for cross-coupled symmetrical two-dimensional nonlinear systems is presented The effect of cross coupling on the stability of the system is discussed

A canonical form for a multivariable, multi-output linear control system†

Abstract: A transformation procedure is developed for a completely observable, multi variable, multi-output, linear control system. The transformed system is made up of several simple sub-systems which have the output vectors and control input vectors of the original system as their inputs. The form of each sub-system is especially suitable for the design of a Luenberger observer

Low sensitivity feedback control of non-linear discrete systems†

Abstract: The synthesis of a feedback controller of non-linear discrete systems is considered. The control systems designed arc optimal and low sensitive to parameter variations. The first step in the synthesis of the controller is to quasilinearize the non-linear difference equations which describe the nonlinear discrete systems. Dynamic programming is then applied to find the feedback control law with respect to a quadratic performance index which includes the state variable, control variable, trajectory sensitivity function and control sensitivity function as its arguments. The optimal gains in the feedback control law for the non-linear systems are then determined by iteration. An example is studied in detail to show the superiority of this technique over the optimal control system without including the sensitivity functions.

Function space derived algorithms for the optimal control of continuous time nonlinear stochastic systems

Abstract: The continuous time nonlinear stochastic control problem is considered, and several implementable optimal control algorithms are discussed.