Showing papers by "Petar V. Kokotovic published in 1978"
TL;DR: In this article, a class of nonlinear singularly perturbed systems, feedback stabilizing and near-optimal controls are designed using two separate lower-order subsystems, which greatly simplify the stability analysis and the nonlinear controller design.
Abstract: For a class of nonlinear singularly perturbed systems, feedback stabilizing and near-optimal controls are designed using two separate lower order subsystems. The two-time-scale properties greatly simplify the stability analysis and the nonlinear controller design. Two electric machine examples (a dc motor and a synchronous generator) illustrate the proposed design procedure.
89 citations
TL;DR: A mass-spring-damper example shows that a stiff spring can be regarded as a perturbation of a rigid rod and an interconnected power system example illustrates the occurrence of coherency and inter-machine oscillations.
78 citations
01 Jan 1978
TL;DR: In this paper, a linear-quadratic Nash game for systems with slow and fast modes is discussed and the well-posedness of different solutions corresponding to different state feedback information structures is considered.
Abstract: This paper discusses linear-quadratic Nash games for systems with slow and fast modes. Singular perturbation is employed to replace a Nash game played on the full model by a game played on a reduced order model. The well-posedness of different solutions corresponding to different state feedback information structures is considered. An important relation between the feedback information structure and the well-posedness of the game is found and used to conjecture special cases when the linear memoryless closed-loop solution is well-posed.
35 citations
TL;DR: In this paper, a series expansion method is developed for a class of nonlinear singularly perturbed optimal regulator problems, and the resulting feedback control is near-optimal and can stabilize essentially nonlinear systems when linearized models provide no stability information.
Abstract: A new series expansion method is developed for a class of nonlinear singularly perturbed optimal regulator problems. The resulting feedback control is near-optimal and can stabilize essentially nonlinear systems when linearized models provide no stability information. The stability domain is shown to include large initial conditions of the fast variables. The control law is implemented in two-time-scales, with the feedback from the fast state variables depending on slow state variables as parameters. The coefficients of the formal expansions of the optimal value function are obtained from equations involving only the slow variables.
35 citations
01 Jan 1978
TL;DR: In this paper, the problem of optimally controlling the nonlinear system with respect to the performance index was considered, where µ > 0 is the small singular perturbation parameter, and u is an r-dimensional control.
Abstract: The problem considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=?0 ?[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.
7 citations
01 Jan 1978
TL;DR: In this paper, simple asymptotic expressions that characterize the effects of the actuator-sensor parasitics are presented, where large feedback gains are used to investigate the interactions of the high frequency modes with high frequency parasitivities of the sensor and actuator dynamics.
Abstract: Interactions of the high frequency modes with high frequency parasitics of the sensor and actuator dynamics occur when large feedback gains are used. Such phenomena are investigated in this paper. Simple asymptotic expressions that characterize the effects of the actuator-sensor parasitics are presented.
2 citations
01 Jan 1978
TL;DR: 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.
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.
1 citations